arXiv subjects

Dmitry A. Abanin

Publications and source records attributed to Dmitry A. Abanin.

At least 37 records · Page 2Linked to original sources

arXiv2024

Scalable tomography of many-body quantum environments with low temporal entanglement

Describing dynamics of a quantum system coupled to a complex many-body environment is a ubiquitous problem in quantum science. General non-Markovian environments are characterized by their influence matrix~(IM) -- a multi-time tensor arising from repeated interactions between the system and environment. While complexity of the most generic IM grows exponentially with the evolution time, recent works argued that for many instances of physical many-body environments, the IM is significantly less complex. This is thanks to area-law scaling of temporal entanglement, which quantifies the correlations between the past and the future states of the system. However, efficient classical algorithms for computing IM are only available for non-interacting environments or certain interacting 1D environments. Here, we study a learning algorithm for reconstructing IMs of large many-body environments simulated on a quantum processor. This hybrid algorithm involves experimentally collecting quantum measurement results of auxiliary qubits which are repeatedly coupled to the many-body environment, followed by a classical machine-learning construction of a matrix-product (MPS) representation of the IM. Using the example of 1D spin-chain environments, with a classically generated training dataset, we demonstrate that the algorithm allows scalable reconstruction of IMs for long evolution times. The reconstructed IM can be used to efficiently model quantum transport through an impurity, including cases with multiple leads and time-dependent controls. These results indicate the feasibility of characterizing long-time dynamics of complex environments using a limited number of measurements, under the assumption of a moderate temporal entanglement.

quant-ph↗

arXiv2024

Finite-size subthermal regime in disordered SU(N)-symmetric Heisenberg chains

SU(N) symmetry is incompatible with the many-body localized (MBL) phase, even when strong disorder is present. However, recent studies have shown that finite-size SU(2) systems exhibit non-ergodic, subthermal behavior, characterized by the breakdown of the eigenstate thermalization hypothesis, and by the excited eigenstates entanglement entropy that is intermediate between area and volume law. In this work, we extend previous studies of the SU(2)-symmetric disordered Heisenberg model to larger systems, using the time-dependent density matrix renormalization group (tDMRG) method. We simulate quench dynamics from weakly entangled initial states up to long times, finding robust subthermal behavior at stronger disorder. Although we find an increased tendency towards thermalization at larger system sizes, the subthermal regime persists at intermediate time scales, nevertheless, and therefore should be accessible experimentally. At weaker disorder, we observe signatures of thermalization, however, entanglement entropy exhibits slow sublinear growth, in contrast to conventional thermalizing systems. Furthermore, we study dynamics of the SU(3)-symmetric disordered Heisenberg model. Similarly, strong disorder drives the system into subthermal regime, albeit thermalizing phase is broader compared to the SU(2) case. Our findings demonstrate the robustness of the subthermal regime in spin chains with non-Abelian continuous symmetry, and are consistent with eventual thermalization at large system sizes and long time scales, suggested by previous works.

quant-ph↗

arXiv2023

A bound on approximating non-Markovian dynamics by tensor networks in the time domain

Spin-boson (SB) model plays a central role in studies of dissipative quantum dynamics, both due its conceptual importance and relevance to a number of physical systems. Here we provide rigorous bounds of the computational complexity of the SB model for the physically relevant case of a zero temperature Ohmic bath. We start with the description of the bosonic bath via its Feynman-Vernon influence functional (IF), which is a tensor on the space of spin's trajectories. By expanding the kernel of the IF functional via a sum of decaying exponentials, we obtain an analytical approximation of the continuous bath by a finite number of damped bosonic modes. We bound the error induced by restricting bosonic Hilbert spaces to a finite-dimensional subspace with small boson numbers, which yields an analytical form of a matrix-product state (MPS) representation of the IF. We show that the MPS bond dimension $D$ scales polynomially in the error on physical observables $ε$, as well as in the evolution time $T$, $D\propto T^4/ε^2$. This bound indicates that the spin-boson model can be efficiently simulated using polynomial in time computational resources.

quant-ph↗

arXiv2023

Kagome chiral spin liquid in transition metal dichalcogenide moiré bilayers

At $n=3/4$ filling of the moiré flat band, transition metal dichalcogenide moiré bilayers will develop kagome charge order. We derive an effective spin model for the resulting localized spins and find that its further neighbor spin interactions can be much less suppressed than the corresponding electron hopping strength. Using density matrix renormalization group simulations, we study its phase diagram and, for realistic model parameters relevant for WSe$_2$/WS$_2$, we show that this material can realize the exotic chiral spin liquid phase and the highly debated kagome spin liquid. Our work thus demonstrates that the frustration and strong interactions present in TMD heterobilayers provide an exciting platform to study spin liquid physics.

cond-mat.str-el↗

arXiv2023

Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action

In the $0+1$ dimensional imaginary-time path integral formulation of quantum impurity problems, the retarded action encodes the hybridization of the impurity with the bath. In this Article, we explore the computational power of representing the retarded action as matrix product state (RAMPS). We focus on the challenging Kondo regime of the single-impurity Anderson model, where non-perturbative strong-correlation effects arise at very low energy scales. We demonstrate that the RAMPS approach reliably reaches the Kondo regime for a range of interaction strengths $U$, with a numerical error scaling as a weak power law with inverse temperature. We investigate the convergence behavior of the method with respect to bond dimension and time discretization by analyzing the error of local observables in the full interacting problem and find polynomial scaling in both parameters. Our results show that the RAMPS approach offers promise as an alternative tool for studying quantum impurity problems in regimes that challenge established methods, such as multi-orbital systems. Overall, our study contributes to the development of efficient and accurate non-wavefunction-based tensor-network methods for quantum impurity problems.

cond-mat.str-el↗

arXiv2023

Many-body localization proximity effect in two-species bosonic Hubbard model

The many-body localization (MBL) proximity effect is an intriguing phenomenon where a thermal bath localizes due to the interaction with a disordered system. The interplay of thermal and non-ergodic behavior in these systems gives rise to a rich phase diagram, whose exploration is an active field of research. In this work, we study a bosonic Hubbard model featuring two particle species representing the bath and the disordered system. Using state of the art numerical techniques, we investigate the dynamics of the model in different regimes, based on which we obtain a tentative phase diagram as a function of coupling strength and bath size. When the bath is composed of a single particle, we observe clear signatures of a transition from an MBL proximity effect to a delocalized phase. Increasing the bath size, however, its thermalizing effect becomes stronger and eventually the whole system delocalizes in the range of moderate interaction strengths studied. In this regime, we characterize particle transport, revealing diffusive behavior of the originally localized bosons.

cond-mat.dis-nn↗

arXiv2022

Quantum and classical Floquet prethermalization

Time-periodic (Floquet) driving is a powerful way to control the dynamics of complex systems, which can be used to induce a plethora of new physical phenomena. However, when applied to many-body systems, Floquet driving can also cause heating, and lead to a featureless infinite-temperature state, hindering most useful applications. It is therefore important to find mechanisms to suppress such effects. Floquet prethermalization refers to the phenomenon where many-body systems subject to a high-frequency periodic drive avoid heating for very long times, instead tending to transient states that can host interesting physics. Its key signature is a strong parametric suppression of the heating rate as a function of the driving frequency. Here, we review our present understanding of this phenomenon in both quantum and classical systems, and across various models and methods. In particular, we present rigorous theorems underpinning Floquet prethermalization in quantum spin and fermionic lattice systems, extensions to systems with degrees of freedom that have unbounded local dimension. Further, we briefly describe applications to novel nonequilibrium phases of matter, and recent experiments probing prethermalization with quantum simulators. We close by describing the frontiers of Floquet prethermalization beyond strictly time-periodic drives, including time-quasiperiodic driving and long-lived quasi-conserved quantities enabled by large separation of energy scales.

cond-mat.stat-mech↗

arXiv2022

An efficient method for quantum impurity problems out of equilibrium

We introduce an efficient method to simulate dynamics of an interacting quantum impurity coupled to non-interacting fermionic reservoirs. Viewing the impurity as an open quantum system, we describe the reservoirs by their Feynman-Vernon influence functionals (IF). The IF are represented as matrix-product states in the temporal domain, which enables an efficient computation of dynamics for arbitrary interactions. We apply our method to study quantum quenches and transport in an Anderson impurity model, including highly non-equilibrium setups, and find favorable performance compared to state-of-the-art methods. The computational resources required for an accurate computation of dynamics scale polynomially with evolution time, indicating that a broad class of out-of-equilibrium quantum impurity problems are efficiently solvable. This approach will provide new insights into dynamical properties of mesoscopic devices and correlated materials.

cond-mat.str-el↗

arXiv2022

Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality

Describing non-equilibrium properties of quantum many-body systems is challenging due to high entanglement in the wavefunction. We describe evolution of local observables via the influence matrix (IM), which encodes the effects of a many-body system as an environment for local subsystems. Recent works found that in many dynamical regimes the IM of an infinite system has low temporal entanglement and can be efficiently represented as a matrix-product state (MPS). Yet, direct iterative constructions of the IM encounter highly entangled intermediate states - a temporal entanglement barrier (TEB). We argue that TEB is ubiquitous, and elucidate its physical origin via a semiclassical quasiparticle picture that exactly captures the behavior of integrable spin chains. Further, we show that a TEB also arises in chaotic spin chains, which lack well-defined quasiparticles. Based on these insights, we formulate an alternative light-cone growth algorithm, which provably avoids TEB, thus providing an efficient construction of the thermodynamic-limit IM as a MPS. This work uncovers the origin of the efficiency of the IM approach for thermalization and transport.

quant-ph↗

arXiv2022

Optimal steering of matrix product states and quantum many-body scars

Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states~(MPS). We compare counter-diabatic and leakage minimization approaches to the so-called local steering problem, that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS state in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counter-diabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally we apply our leakage minimization approach to construct quantum scars in the periodically driven non-integrable Ising model.

quant-ph↗

arXiv2022

Temporal entanglement, quasiparticles and the role of interactions

In quantum many-body dynamics admitting a description in terms of non-interacting quasiparticles, the Feynman-Vernon influence matrix (IM), encoding the effect of the system on the evolution of its local subsystems, can be analyzed exactly. For discrete dynamics, the temporal entanglement (TE) of the corresponding IM satisfies an area law, suggesting the possibility of an efficient representation of the IM in terms of matrix-product states. A natural question is whether and how integrable interactions, which preserve stable quasiparticles, affect the behavior of the TE. While a simple semiclassical picture suggests a sublinear growth in time, one can wonder whether interactions may lead to violations of the area law. We address this problem by analyzing quantum quenches in a family of discrete integrable dynamics corresponding to the real-time Trotterization of the interacting XXZ Heisenberg model. By means of an analytical solution at the dual-unitary point and numerical calculations for generic values of the system parameters, we provide evidence that, away from the non-interacting limit, the TE displays a logarithmic growth in time, thus violating the area law. Our findings highlight the non-trivial role of interactions, and raise interesting questions on the possibility to efficiently simulate the local dynamics of interacting integrable systems.

cond-mat.stat-mech↗

arXiv2022

Simulation Complexity of Many-Body Localized Systems

We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm for strong simulation of 1D MBL systems (i.e., calculating the expectation value of arbitrary products of local observables) evolved for any time polynomial in the system size. On the other side, we prove that even weak simulation, i.e. sampling, becomes formally hard after an exponentially long evolution time, assuming widely believed conjectures in complexity theory. Finally, using the consequences of our classical simulation results, we also show that the quantum circuit complexity for MBL systems is sublinear in evolution time. This result is a counterpart to a recent proof that the complexity of random quantum circuits grows linearly in time.

quant-ph↗

arXiv2022

Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain

Describing a quantum impurity coupled to one or more non-interacting fermionic reservoirs is a paradigmatic problem in quantum many-body physics. While historically the focus has been on the equilibrium properties of the impurity-reservoir system, recent experiments with mesoscopic and cold-atomic systems enabled studies of highly non-equilibrium impurity models, which require novel theoretical techniques. We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF). The efficiency of such a MPS representation rests on the moderate value of the temporal entanglement (TE) entropy of the IF, viewed as a fictitious "wave function" in the time domain. We obtain explicit expressions of this wave function for a family of one-dimensional reservoirs, and analyze the scaling of TE with the evolution time for different reservoir's initial states. While for initial states with short-range correlations we find temporal area-law scaling, Fermi-sea-type initial states yield logarithmic scaling with time, closely related to the real-space entanglement scaling in critical 1d systems. Furthermore, we describe an efficient algorithm for converting the explicit form of the reservoirs' IF to MPS form. Once the IF is encoded by a MPS, arbitrary temporal correlation functions of the interacting impurity can be efficiently computed, irrespective of its internal structure. The approach introduced here can be applied to a number of experimental setups, including highly non-equilibrium transport via quantum dots and real-time formation of impurity-reservoir correlations.

cond-mat.str-el↗

arXiv2021

Characterizing many-body localization via exact disorder-averaged quantum noise

Many-body localized (MBL) phases of disordered quantum many-particle systems have a number of unique properties, including failure to act as a thermal bath and protection of quantum coherence. Studying MBL is complicated by the effects of rare ergodic regions, necessitating large system sizes and averaging over many disorder configurations. Here, building on the Feynman-Vernon theory of quantum baths, we characterize the quantum noise that a disordered spin system exerts on its parts via an influence matrix (IM). In this approach, disorder averaging is implemented exactly, and the thermodynamic-limit IM obeys a self-consistency equation. Viewed as a wavefunction in the space of trajectories of an individual spin, the IM exhibits slow scaling of temporal entanglement in the MBL phase. This enables efficient matrix product states computations to obtain temporal correlations, providing a benchmark for quantum simulations of non-equilibrium matter. The IM quantum noise formulation provides an alternative starting point for novel rigorous studies of MBL.

cond-mat.dis-nn↗

arXiv2021

Propagation of Many-body Localization in an Anderson Insulator

Many-body localization (MBL) is an example of a dynamical phase of matter that avoids thermalization. While the MBL phase is robust to weak local perturbations, the fate of an MBL system coupled to a thermalizing quantum system that represents a "heat bath" is an open question that is actively investigated theoretically and experimentally. In this work we consider the stability of an Anderson insulator with a finite density of particles interacting with a single mobile impurity -- a small quantum bath. We give perturbative arguments that support the stability of localization in the strong interaction regime. Large scale tensor network simulations of dynamics are employed to corroborate the presence of the localized phase and give quantitative predictions in the thermodynamic limit. We develop a phenomenological description of the dynamics in the strong interaction regime, and demonstrate that the impurity effectively turns the Anderson insulator into an MBL phase, giving rise to non-trivial entanglement dynamics well captured by our phenomenology.

cond-mat.dis-nn↗

arXiv2021

Localization of a mobile impurity interacting with an Anderson insulator

Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently, the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and experimental attention. In this work, we study a mobile impurity, representing a small quantum bath, that interacts locally with an Anderson insulator with a finite density of localized particles. Using static Hartree approximation to obtain an effective disorder strength, we formulate an analytic criterion for the perturbative stability of the localization. Next, we use an approximate dynamical Hartree method and the quasi-exact time-evolved block decimation (TEBD) algorithm to study the dynamics of the system. We find that the dynamical Hartree approach which completely ignores entanglement between the impurity and localized particles predicts the delocalization of the system. In contrast, the full numerical simulation of the unitary dynamics with TEBD suggests the stability of localization on numerically accessible timescales. Finally, using an extension of the density matrix renormalization group algorithm to excited states (DMRG-X), we approximate the highly excited eigenstates of the system. We find that the impurity remains localized in the eigenstates and entanglement is enhanced in a finite region around the position of the impurity, confirming the dynamical predictions. Dynamics and the DMRG-X results provide compelling evidence for the stability of localization.

cond-mat.dis-nn↗

arXiv2021

Bilayer WSe$_2$ as a natural platform for interlayer exciton condensates in the strong coupling limit

Exciton condensates (EC) are macroscopic coherent states arising from condensation of electron-hole pairs. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study EC. The tunnel barrier suppresses recombination yielding long-lived excitons. However, this separation also reduces interlayer Coulomb interactions, limiting the exciton binding strength. Here, we report the observation of EC in naturally occurring 2H-stacked bilayer WSe$_2$. In this system, the intrinsic spin-valley structure suppresses interlayer tunneling even when the separation is reduced to the atomic limit, providing access to a previously unattainable regime of strong interlayer coupling. Using capacitance spectroscopy, we investigate magneto-EC, formed when partially filled Landau levels (LL) couple between the layers. We find that the strong-coupling EC show dramatically different behaviour compared with previous reports, including an unanticipated variation of the EC robustness with the orbital number, and find evidence for a transition between two types of low-energy charged excitations. Our results provide a demonstration of tuning EC properties by varying the constituent single-particle wavefunctions.

cond-mat.mes-hall↗

arXiv2021

Scaling of temporal entanglement in proximity to integrability

Describing dynamics of quantum many-body systems is a formidable challenge due to rapid generation of quantum entanglement between remote degrees of freedom. A promising approach to tackle this challenge, which has been proposed recently, is to characterize the quantum dynamics of a many-body system and its properties as a bath via the Feynman-Vernon influence matrix (IM), which is an operator in the space of time trajectories of local degrees of freedom. Physical understanding of the general scaling of the IM's temporal entanglement and its relation to basic dynamical properties is highly incomplete to present day. In this Article, we analytically compute the exact IM for a family of integrable Floquet models - the transverse-field kicked Ising chain - finding a Bardeen-Cooper-Schrieffer-like "wavefunction" on the Schwinger-Keldysh contour with algebraically decaying correlations. We demonstrate that the IM exhibits area-law temporal entanglement scaling for all parameter values. Furthermore, the entanglement pattern of the IM reveals the system's phase diagram, exhibiting jumps across transitions between distinct Floquet phases. Near criticality, a non-trivial scaling behavior of temporal entanglement is found. The area-law temporal entanglement allows us to efficiently describe the effects of sizeable integrability-breaking perturbations for long evolution times by using matrix product state methods. This work shows that tensor network methods are efficient in describing the effect of non-interacting baths on open quantum systems, and provides a new approach to studying quantum many-body systems with weakly broken integrability.

quant-ph↗