Tensor Network Theory for strongly correlated quantum systems
Physical systems that display strong correlations as a result of interactions between their constituents are present everywhere around us in our daily lives. For example traffic jams form on our roads every day in the morning due to strong interactions between cars that do not allow two of them to occupy the same piece of road. However, ants marching in a line never form such traffic jams despite facing very similar restrictions of not being allowed to sit on top of each other. These two examples demonstrate how subtle differences in the precise microscopic nature of interactions may lead to qualitatively different macroscopically observed properties and this poses major challenges for their theoretical study. In the quantum case strong interactions lead to some of the least well understood phenomena of condensed matter like highTc superconductivity, frustration, and topological phases such fractional quantum Hall physics which only appear in materials with a dominant two dimensional character.
An amazing feature of these systems is that one can readily write down simple looking models which are believed to capture the main physics on a macroscopic level. However, because of the strong interactions even these simple models turn out to be very hard to solve. Despite almost four decades of research in this area a detailed theoretical understanding of macroscopic properties in thermodynamic equilibrium emerging from strong interactions is still lacking for many of these seemingly simple models. In addition recent experimental progress now allows for the dynamical study of driven strongly correlated quantum systems far away from equilibrium and this poses new opportunities for applications in quantum enhanced devices as well as new challenges for theoretical physics research.
In this project we will develop high performance software which will enable tackling basic questions about models for strongly correlated systems in the quantum and also in the classical case. The underlying socalled tensor network algorithms have been developed over the past two decades but it is only now that a unified framework for these algorithms is known. This justifies the development of high performance computer software which will encompass existing and welltested algorithms but is also sufficiently versatile to form the basis for future developments in this field of research. Indeed, the software developed in this project will be available to researchers throughout the UK and form the backbone of numerical studies based on tensor network algorithms for the next decade and possibly beyond.
Developing this powerful new tool for enhancing simulation methods will enable such things as the optimisation of quantum enhanced effects in promising new generations of technology. Improved numerical algorithms will enable sensors as well as energy transfer and storage devices to utilise physically enhanced processes at the scale where dynamical quantum effects are crucial. In particular the software will be required to study strongly correlated models without being hindered by boundary effects or minussign problems inherent in some other methods. The insights gained from this research could lead to novel superconducting materials or the exploitation of dynamical nonequilibrium properties in applications of nanomaterials. Furthermore these may also be applicable to everyday classical strongly interacting systems like e.g. the formation of traffic jams or the dynamics of queues forming at box offices or in order books at the stock exchange.
Related Publications

J. Tindall, F. Schlawin, M. Sentef and D. Jaksch,
Analytical Solution for the Steady States of the Driven Hubbard model,
Phys. Rev. B 103, 035146 (2021).
Under the action of coherent periodic driving a generic quantum system will undergo Floquet heating and continuously absorb energy until it reaches a featureless thermal state. The phasespace constraints induced by certain symmetries can, however, prevent this and allow the system to dynamically form robust steady states with offdiagonal longrange order. In this work, we take the Hubbard model on an arbitrary lattice with arbitrary filling and, by simultaneously diagonalising the two possible SU(2) symmetries of the system, we analytically construct the correlated steady states for different symmetry classes of driving. This construction allows us to make verifiable, quantitative predictions about the longrange particlehole and spinexchange correlations that these states can possess. In the case when both SU(2) symmetries are preserved in the thermodynamic limit we show how the driving can be used to form a unique condensate which simultaneously hosts particlehole and spinwave order.
created: 10112020, last modified: 01022021

M. Buzzi, D. Nicoletti, M. Fechner, N. TancogneDejean, M. Sentef, A Georges, M. Dressel, A. Henderson, T. Siegrist, J.A. Schlueter, K. Miyagawa, K. Kanoda, M.S. Nam, A. Ardavan, J.R. Coulthard, J. Tindall, F. Schlawin, D. Jaksch and A. Cavalleri,
Photomolecular HighTemperature Superconductivity,
Phys. Rev. X 10, 031028 (2020).
Superconductivity in organic conductors is often tuned by the application of chemical or external pressure. With this type of tuning, orbital overlaps and electronic bandwidths are manipulated, whilst the properties of the molecular building blocks remain virtually unperturbed.Here, we show that the excitation of local molecular vibrations in the chargetransfer salt K−(BEDT−TTF)2 Cu[N(CN)2]Br induces a colossal increase in carrier mobility and the opening of a superconductinglike optical gap. Both features track the density of quasiparticles of the equilibrium metal, and can be achieved up to a characteristic coherence temperature T* ~ 50K, far higher than the equilibrium transition temperature TC=12.5K. Notably, the large optical gap achieved by photoexcitation is not observed in the equilibrium superconductor, pointing to a light induced state that is different from that obtained by cooling. Firstprinciple calculations and model Hamiltonian dynamics predict a transient state with longrange pairing correlations, providing a possible physical scenario for photomolecular superconductivity.
created: 27012020, last modified: 10082020

P. Secular, N. Gourianov, M. Lubasch, S. Dolgov, S.R. Clark and D. Jaksch,
Parallel timedependent variational principle algorithm for matrix product states,
Phys. Rev. B 101, 235123 (2020).
Combining the timedependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving onedimensional (1D) quantum lattice systems with longrange interactions. We benchmark the accuracy and performance of the algorithm by simulating quenches in the longrange Ising and XY models. We show that our code scales well up to 32 processes, with parallel efficiencies as high as 86 percent. Finally, we calculate the dynamical correlation function of a 201site Heisenberg XXX spin chain with quadratically decaying interactions, which is challenging to compute sequentially. These results pave the way for the application of tensor networks to increasingly complex manybody systems.
created: 27012020, last modified: 06062020

J. Tindall, C. Sanchez Munoz, B. Buca and D. Jaksch,
Quantum Synchronisation Enabled by Dynamical Symmetries and Dissipation,
New J. Phys. 22, 013026 (2020).
In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying symmetrybased conditions which, when satisfied, guarantee completely synchronous, entangled limit cycles between the individual constituents of a generic open quantum system  no restrictions are placed on its microscopic details. We describe these systems as posssessing a strong dynamical symmetry and we prove that, to first order, they are completely robust to symmetrybreaking perturbations. Using these ideas we identify two central examples where synchronisation arises via this qualitatively new mechanism: a chain of quadratically dephased spin1s and the manybody chargedephased Hubbard model. In both cases, due to their dynamical symmetries, perfect phaselocking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit longlived signatures of both phase and frequencylocking.
created: 31072019, last modified: 07022020

M. Lubasch, J. Joo, P. Moinier, M. Kiffner and D. Jaksch,
Variational Quantum Algorithms for Nonlinear Problems,
Phys. Rev. A 101, 010301(R) (2020).
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schrödinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proofofprinciple results obtained on an IBM Q device.
created: 25072019, last modified: 14012020

C. Sanchez Munoz, B. Buca, J. Tindall, A. GonzalezTudela, D. Jaksch and D. Porras,
Symmetries and conservation laws in quantum trajectories: Dissipative freezing,
Phys. Rev. A 100, 042113 (2019).
In drivendissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical stochastic trajectory, this is a purely quantum effect with no classical analog. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behavior completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results on a coherently driven spin ensemble with a squeezed superradiant decay, a simple model that presents a wealth of nonergodic dynamics.
created: 14032019, last modified: 05122019

J. Tindall, B. Buca, J.R. Coulthard and D. Jaksch,
HeatingInduced LongRange etaPairing in the Hubbard Model,
Phys. Rev. Lett. 123, 030603 (2019).
We show how heating the spin degrees of freedom of the Hubbard model to infinite temperature can be used to melt the order within this sector and reach steady states, in any dimension, which have completely uniform longrange correlations between eta pairs. We induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state. This steady state is identical in both cases and displays distanceinvariant offdiagonal eta correlations. These correlations were first recognised in the superconducting eigenstates described in a seminal paper by C. N. Yang [Physical Review Letters, 63, 2144 (1989)], which are a subset of our steady states. Finally, we show that our results are a consequence of the symmetry properties of the model and independent of the microscopic details of the heating mechanism.
created: 14022019, last modified: 18072019

J. Tangpanitanon, S.R. Clark, V.M. Bastidas, R. Fazio, D. Jaksch and D.G. Angelakis,
Hidden Order in Quantum Manybody Dynamics of DrivenDissipative Nonlinear Photonic Lattices,
Phys. Rev. A 99, 043808 (2019).
We study the dynamics of nonlinear photonic lattices driven by twophoton parametric processes. By means of matrixproduct state based calculations, we show that a quantum manybody state with longrange hidden order can be generated from the vacuum. This order resembles that characterizing the Haldane insulator. A possible explanation highlighting the role of the symmetry of the drive, and the effect of photon loss are discussed. An implementation based on superconducting circuits is proposed and analysed.
created: 29062018, last modified: 23052019

J. MurPetit, A. Relano, R.A. Molina and D. Jaksch,
Revealing missing charges with generalised quantum fluctuation relations,
Nature Communications 9, 2006 (2018).
The nonequilibrium dynamics of quantum manybody systems is one of the most fascinating problems in physics. Open fundamental and practical questions range from how they relax to equilibrium, to how to extract useful work from them. Here, we derive a set of exact results that relate outofequilibrium fluctuations in the energy and other observables of a quantum system to its equilibrium properties for a very general family of initial conditions. These quantum fluctuation relations generalise the Jarzynski and Crooks relations to quantum systems with conserved quantities, and can be applied to protocols driving the system between integrable and chaotic regimes, or coupling it to different reservoirs. We illustrate our results with simulations of an integrable model subject to quenches realisable with current technology. Our findings will help guiding research on the interplay of quantum and thermal fluctuations in quantum simulation, and their exploitation in the design of new quantum devices.
created: 06112017, last modified: 21092019

M. Lubasch, P. Moinier and D. Jaksch,
Multigrid Renormalization,
J. Comp. Phys. 372, 587 (2018).
We combine the multigrid method with stateoftheart concepts from the variational formulation of the numerical renormalization group. The resulting renormalization method is a natural generalization of the multigrid method for solving partial differential equations. When the solution on a grid of N points is sought, our method has a computational cost scaling as O(log(N)), as opposed to O(N) for the best standard MG method. Therefore it can exponentially speed up standard computations. To illustrate our method, we develop a novel algorithm for the ground state computation of the nonlinear Schroedinger equation. Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem. We compare several different methods for the nonlinear tensor update and find that the Newton method is the most efficient as well as precise. The combination of our method with the nonlinear ground state algorithm produces accurate results for the nonlinear Schroedinger equation on N=10^18 grid points in three spatial dimensions.
created: 08032018, last modified: 30062018

M. Kiffner, D. Jaksch and D. Ceresoli,
A polynomial Ansatz for Normconserving Pseudopotentials,
J. Phys.: Condens. Matter 30, 275501 (2018).
We show that efficient normconserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills the same smoothness conditions imposed by the TroullierMartins method [Phys. Rev. B 43, 1993 (1991)] where pseudopotentials are represented by a polynomial of degree twentytwo. We compare our method to the TroullierMartins approach in electronic structure calculations for diamond and iron in the bcc structure and find that the two methods perform equally well in calculations of the total energy. However, first and second derivatives of the total energy with respect to atomic coordinates converge significantly faster with the plane wave cutoff if the standard TroullierMartins potentials are replaced by the pseudopotentials introduced here.
created: 22032018, last modified: 14062018

M. Lubasch, A.A. Valido, J.J. Renema, W.S. Kolthammer, D. Jaksch, M. S. Kim, I.A. Walmsley and R. GarciaPatron,
Tensor network states in timebin quantum optics,
Phys. Rev. A 97, 062304 (2018).
The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode manybody quantum correlations and go beyond the usual phasespace formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of timebin interference in a single fiber loop. We then generalize our results to more complex timebin quantum setups and identify different classes of architectures for highcomplexity and lowoverhead boson sampling experiments.
created: 30012018, last modified: 11062018

F. Cosco, M. Borrelli, J. J. MendozaArenas, F. Plastina, D. Jaksch and S. Maniscalco,
BoseHubbard lattice as a controllable environment for open quantum systems,
Phys. Rev. A 97, 040101(R) (2018).
We investigate the open dynamics of an atomic impurity embedded in a onedimensional BoseHubbard lattice. We derive the reduced evolution equation for the impurity and show that the BoseHubbard lattice behaves as a tunable engineered environment allowing one to simulate both Markovian and nonMarkovian dynamics in a controlled and experimentally realizable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of a superfluid and Mott insulator, respectively. Furthermore, our findings show how the excitations supported in the two phases can be characterized as information carriers.
created: 29062017, last modified: 10042018

S. AlAssam, S.R. Clark and D. Jaksch,
The tensor network theory library,
J. Stat. Mech. 2017, 093102 (2017).
In this technical paper we introduce the tensor network theory (TNT) library  an opensource software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of groundstate and dynamical calculations of onedimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.
created: 10102016, last modified: 13072018

J.R. Coulthard, S.R. Clark, S. AlAssam, A. Cavalleri and D. Jaksch,
Enhancement of superexchange pairing in the periodicallydriven Hubbard model,
Phys. Rev. B 96, 085104 (2017).
Recent experiments performed on cuprates and alkalidoped fullerides have demonstrated that key signatures of superconductivity can be induced above the equilibrium critical temperature by optical modulation. These observations in disparate physical systems may indicate a general underlying mechanism. Multiple theories have been proposed, but these either consider specific features, such as competing instabilities, or focus on conventional BCStype superconductivity. Here we show that periodic driving can enhance electron pairing in strongly correlated systems. Focusing on the strongly repulsive limit of the doped Hubbard model, we investigate ingap, spatially inhomogeneous, onsite modulations. We demonstrate that such modulations substantially reduce electronic hopping, while simultaneously sustaining superexchange interactions and pair hopping via drivinginduced virtual charge excitations. We calculate realtime dynamics for the onedimensional case, starting from zero and finitetemperature initial states, and we show that enhanced singletpair correlations emerge quickly and robustly in the outofequilibrium manybody state. Our results reveal a fundamental pairing mechanism that might underpin optically induced superconductivity in some strongly correlated quantum materials.
created: 18082016, last modified: 01082017

M. Kiffner, E. OBrien and D. Jaksch,
Topological spin models in Rydberg lattices,
Appl. Phys. B 123, 46 (2017).
We show that resonant dipoledipole interactions between Rydberg atoms in a triangular lattice can give rise to artificial magnetic fields for spin excitations. We consider the coherent dipoledipole coupling between
np and ns Rydberg states and derive an effective spin1/2 Hamiltonian for the np excitations. By breaking timereversal symmetry via external fields we engineer complex hopping amplitudes for transitions between two rectangular sublattices. The phase of these hopping amplitudes depends on the direction of the hop. This gives rise to a staggered, artificial magnetic field which induces nontrivial topological effects. We calculate the singleparticle band structure and investigate its Chern numbers as a function of the lattice parameters and the detuning between the two sublattices. We identify extended parameter regimes where the Chern number of the lowest band is C=1 or C=2
created: 17092016, last modified: 10052017

C. Noh, S.R. Clark, D. Jaksch and D.G. Angelakis,
Outofequilibrium physics in driven dissipative coupled resonator arrays,
Chapter in Quantum Simulations with Photons and Polaritons: Merging Quantum Optics with Condensed Matter Physics; edited by DG Angelakis, Quantum Science and Technology Series, Springer (2017).
Coupled resonator arrays have been shown to exhibit interesting manybody
physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms counterparts is in the dissipative nature of their photonic excitations. The natural equilibrium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise nontrivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes
beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisation, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the JaynesCummingsHubbard and BoseHubbard Hamiltonians. A brief review of
the analytical and sophisticated numerical methods required to tackle these systems is included.
created: 03032017

J. Tangpanitanon, V.M. Bastidas, S. AlAssam, P. Roushan, D. Jaksch and D.G. Angelakis,
Topological pumping of photons in nonlinear resonator arrays,
Phys. Rev. Lett. 117, 213603 (2016).
We show how to implement topological or Thouless pumping of interacting photons in onedimensional nonlinear resonator arrays by simply modulating the frequency of the resonators periodically in space and time. The interplay between the interactions and the adiabatic modulations enables robust transport of Fock states with few photons per site. We analyze the transport mechanism via an effective analytic model and study its topological properties and its protection to noise. We conclude by a detailed study of an implementation with existing circuitQED architectures.
created: 15072016, last modified: 19112016

J.M. Kreula, S.R. Clark and D. Jaksch,
Nonlinear quantumclassical scheme to simulate nonequilibrium strongly correlated fermionic manybody dynamics,
Scientific Reports 6, 32940 (2016).
We propose a nonlinear, hybrid quantumclassical scheme for simulating nonequilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements nonequilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to selfconsistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case.
created: 29102015, last modified: 15092016

T.H. Johnson, Y. Yuan, W. Bao, S.R. Clark, C.J. Foot and D. Jaksch,
Hubbard Model for Atomic Impurities Bound by the Vortex Lattice of a Rotating BoseEinstein Condensate,
Phys. Rev. Lett. 116, 240402 (2016).
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupationdependent parameters to capture the effects of strong impurityimpurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the BoseEinstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes.
created: 04012016, last modified: 19062016

P.L. Giscard, Z. Choo, S.J. Thwaite and D. Jaksch,
Exact Inference on Gaussian Graphical Models of Arbitrary Topology using PathSums,
Journal of Machine Learning Research 17, 1 (2016).
We present the pathsum formulation for exact statistical inference of marginals on Gaussian graphical models of arbitrary topology. The pathsum formulation gives the covariance between each pair of variables as a branched continued fraction of finite depth and breadth. Our method originates from the closed form resummation of infinite families of terms of the walksum representation of the covariance matrix. We prove that the path sum formulation always exists for models whose covariance matrix is positive definite: i.e. it is valid for both walksummable and nonwalksummable graphical models of arbitrary topology. We show that for graphical models on trees the pathsum formulation is equivalent to Gaussian belief propagation. We also recover, as a corollary, an existing result that uses determinants to calculate the covariance matrix. We show that the pathsum formulation formulation is valid for arbitrary partitions of the inverse covariance matrix. We give detailed examples demonstrating our results.
created: 13062016

T.H. Johnson, F. Cosco, M.T. Mitchinson, D. Jaksch and S.R. Clark,
Thermometry of ultracold atoms via nonequilibrium work distributions,
Phys. Rev. A 93, 053619 (2016).
Estimating the temperature of a cold quantum system is difficult. Usually one measures a wellunderstood thermal state and uses that prior knowledge to infer its temperature. In contrast, we introduce a method of thermometry that assumes minimal knowledge of the state of a system and is potentially nondestructive. Our method uses a universal temperature dependence of the quench dynamics of an initially thermal system coupled to a qubit probe that follows from the TasakiCrooks theorem for nonequilibrium work distributions. We provide examples for a coldatom system, in which our thermometry protocol may retain accuracy and precision at subnanoKelvin temperatures.
created: 29102015, last modified: 25052016

J. J. MendozaArenas, S.R. Clark, S. Felicetti, G. Romero, E. Solano, D.G. Angelakis and D. Jaksch,
Beyond meanfield bistability in drivendissipative lattices: bunchingantibunching transition and quantum simulation,
Phys. Rev. A 93, 023821 (2016).
In the present work we investigate the existence of multiple nonequilibrium steady states in a coherently driven XY lattice of dissipative twolevel systems. A commonly used meanfield ansatz, in which spatial correlations are neglected, predicts a bistable behavior with a sharp shift between low and highdensity states. In contrast onedimensional matrix product methods reveal these effects to be artifacts of the meanfield approach, with both disappearing once correlations are taken fully into account. Instead, a bunchingantibunching transition emerges. This indicates that alternative approaches should be considered for higher spatial dimensions, where classical simulations are currently infeasible. Thus we propose a circuit QED quantum simulator implementable with current technology to enable an experimental investigation of the model considered.
created: 29102015, last modified: 26022016

P.L. Giscard, K. Lui, S.J. Thwaite and D. Jaksch,
An Exact Formulation of the TimeOrdered Exponential using PathSums,
Journal of Mathematical Physics 56, 053503 (2015).
We present the pathsum formulation for the timeordered exponential of a timedependent matrix. The pathsum formulation gives the timeordered exponential as a branched continued fraction of finite depth and breadth. The terms of the pathsum have an elementary interpretation as selfavoiding walks and selfavoiding polygons on a graph. Our result is based on a representation of the timeordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a superexponential decay bound for the magnitude of the entries of the timeordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.
created: 24042015, last modified: 11052015

J. J. MendozaArenas, S.R. Clark and D. Jaksch,
Coexistence of energy diffusion and local thermalization in nonequilibrium XXZ spin chains with integrability breaking,
Phys. Rev. E 91, 042129 (2015).
In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium onedimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient largescale matrix product simulations of the equation of motion of the system, we calculate its steady state in the longtime limit. We start by discussing the energy transport supported by the system, finding it to be ballistic in the integrable limit and diffusive when the staggered field is finite. Subsequently we examine the reduced density operators of neighboring sites and find that for large systems they are well approximated by local thermal states of the underlying Hamiltonian in the nonintegrable regime, even for weak staggered fields. In the integrable limit, on the other hand, this behavior is lost, and the identification of local temperatures is no longer possible. Our results agree with the intuitive connection between energy diffusion and thermalization.
created: 18112014, last modified: 24042015

S.J. Denny, S.R. Clark, Y. Laplace, A. Cavalleri and D. Jaksch,
Proposed Parametric Cooling of Bilayer Cuprate Superconductors by Terahertz Excitation,
Phys. Rev. Lett. 114, 137001 (2015).
We propose and analyse a scheme for parametrically cooling bilayer cuprates based on the selective driving of a caxis vibrational mode. The scheme exploits the vibration as a transducer making the Josephson plasma frequencies timedependent. We show how modulation at the difference frequency between the intra and interbilayer plasmon substantially suppresses interbilayer phase fluctuations, responsible for switching caxis transport from a superconducting to resistive state. Our calculations indicate that this may provide a viable mechanism for stabilizing nonequilibrium superconductivity even above Tc, provided a finite pair density survives between the bilayers out of equilibrium.
Editors` suggestion and Physics Synopsis: Making Superconductors Sturdier
created: 18112014, last modified: 31032015

T.H. Johnson, T. Elliot, S.R. Clark and D. Jaksch,
Capturing Exponential Variance Using Polynomial Resources: Applying Tensor Networks to Nonequilibrium Stochastic Processes,
Phys. Rev. Lett. 114, 090602 (2015).
Estimating the expected value of an observable appearing in a nonequilibrium stochastic process usually involves sampling. If the observable`s variance is high, many samples are required. In contrast, we show that performing the same task without sampling, using tensor network compression, efficiently captures high variances in systems of various geometries and dimensions. We provide examples for which matching the accuracy of our efficient method would require a sample size scaling exponentially with system size. In particular, the high variance observable exp(beta W, with W the work done quenching from equilibrium at inverse temperature beta, is exactly and efficiently captured by tensor networks.
created: 17112014, last modified: 09032015

D. Hangleiter, M.T. Mitchinson, T.H. Johnson, M. Bruderer, M.B. Plenio and D. Jaksch,
Nondestructive selective probing of phononic excitations in a cold Bose gas using impurities,
Phys. Rev. A 91, 013611 (2015).
We introduce a detector that selectively probes the phononic excitations of a cold Bose gas. The detector is composed of a single impurity atom confined by a doublewell potential, where the two lowest eigenstates of the impurity form an effective probe qubit that is coupled to the phonons via densitydensity interactions with the bosons. The system is analogous to a twolevel atom coupled to photons of the radiation field. We demonstrate that tracking the evolution of the qubit populations allows probing both thermal and coherent excitations in targeted phonon modes. The targeted modes are selected in both energy and momentum by adjusting the impurity`s potential. We show how to use the detector to observe coherent density waves and to measure temperatures of the Bose gas down to the nanokelvin regime. We analyze how our scheme could be realized experimentally, including the possibility of using an array of multiple impurities to achieve greater precision from a single experimental run.
created: 18112014, last modified: 13012015

T.H. Johnson, S.R. Clark and D. Jaksch,
What is a quantum simulator?,
EPJ Quantum Technology 1, 10 (2014).
Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. Here we expand on this definition by answering several fundamental questions about the nature and use of quantum simulators. Our answers address two important areas. First, the difference between an operation termed simulation and another termed computation. This distinction is related to the purpose of an operation, as well as our confidence in and expectation of its accuracy. Second, the threshold between quantum and classical simulations. Throughout, we provide a perspective on the achievements and directions of the field of quantum simulation.
created: 14052014, last modified: 06092014

J. J. MendozaArenas, M.T. Mitchinson, S.R. Clark, J. Prior, D. Jaksch and M.B. Plenio,
Transport enhancement from incoherent coupling between onedimensional quantum conductors,
New J. Phys. 16, 053016 (2014).
We study the nonequilibrium transport properties of a highly anisotropic two dimensional lattice of spin&#8722;1/2 particles governed by a Heisenberg XXZ Hamiltonian. The anisotropy of the lattice allows us to approximate the system at finite temperature as an array of incoherently coupled onedimensional chains. We show that in the regime of strong intrachain interactions, the weak interchain coupling considerably boosts spin transport in the driven system. Interestingly, we show that this enhancement increases with the length of the chains, which is related to superdiffusive spin transport. We describe the mechanism behind this effect, compare it to a similar phenomenon in single chains induced by dephasing, and explain why the former is much stronger.
created: 08052014, last modified: 09052014

J. J. MendozaArenas, S. AlAssam, S.R. Clark and D. Jaksch,
Heat transport in the XXZ spin chain: from ballistic to diffusive regimes and dephasing enhancement,
J. Stat. Mech. P07007 (2013).
In this work we study the heat transport in an XXZ spin1/2 Heisenberg chain with homogeneous magnetic field, incoherently driven out of equilibrium by reservoirs at the boundaries. We focus on the effect of bulk dephasing (energydissipative) processes in different parameter regimes of the system. The nonequilibrium steady state of the chain is obtained by simulating its evolution under the corresponding Lindblad master equation, using the time evolving block decimation method. In the absence of dephasing, the heat transport is ballistic for weak interactions, while being diffusive in the stronglyinteracting regime, as evidenced by the heatcurrent scaling with the system size. When bulk dephasing takes place in the system, diffusive transport is induced in the weaklyinteracting regime, with the heat current monotonically decreasing with the dephasing rate. In contrast, in the stronglyinteracting regime, the heat current can be significantly enhanced by dephasing for systems of small size.
created: 27032013, last modified: 16072013

J. J. MendozaArenas, T. Grujic, D. Jaksch and S.R. Clark,
Dephasing enhanced transport in nonequilibrium stronglycorrelated quantum systems,
Phys. Rev. B 87, 235130 (2013).
A key insight from recent studies is that noise, such as dephasing, can improve the efficiency of quantum transport by suppressing coherent singleparticle interference effects. However, it is not yet clear whether dephasing can enhance transport in an interacting manybody system. Here we address this question by analysing the transport properties of a boundary driven spinless fermion chain with nearestneighbour interactions subject to bulk dephasing. The manybody nonequilibrium stationary state is determined using large scale matrix product simulations of the corresponding quantum master equation. We find dephasing enhanced transport only in the strongly interacting regime, where it is shown to induce incoherent transitions bridging the gap between bound darkstates and bands of mobile eigenstates. The generic nature of the effect is illustrated and shown not to depend on the integrability of the model considered. As a result dephasing enhanced transport is expected to persist in more realistic driven systems of stronglycorrelated particles.
created: 22032013, last modified: 24062013