Correlated Quantum Systems Research Articles

Tensor product random matrix theory

The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach—essentially a fusion of the GΣ functional of the SYK model and the field theory of disordered systems—engineered to microscopically describe the full range of such crossover dynamics: from initial product states to a maximum entropy ergodic state. To showcase this approach in the simplest nontrivial setting, we consider a tensor product of coupled random matrices, and compare to exact diagonalization. Published by the American Physical Society 2024

Bell nonlocality and entanglement in e+e−→YY¯ at BESIII

The Bell nonlocality and entanglement are two kinds of quantum correlations in quantum systems. Due to the recent upgrade in the Beijing Spectrometer III (BESIII) experiment, it is possible to explore the nonlocality and entanglement in hyperon-antihyperon systems produced in electron-positron annihilation with high precision data. We provide a systematic method for studying quantum correlations in spin-1/2 hyperon-antihyperon systems through the measures for the nonlocality and entanglement. We find that with nonvanishing polarizations of the hyperon and its antihyperon, the kinematic region of nonlocality in the hyperon-antihyperon system is more restricted than the τ+τ− system in which polarizations of τ leptons are vanishing. We also present an experimental proposal to probe the nonlocality and entanglement in hyperon-antihyperon systems at BSEIII. Published by the American Physical Society 2024

Autoencoder-based analytic continuation method for strongly correlated quantum systems

Autoencoder-based analytic continuation method for strongly correlated quantum systems

Strong Spin-Motion Coupling in the Ultrafast Dynamics of Rydberg Atoms.

Rydberg atoms in optical lattices and tweezers is now a well-established platform for simulating quantum spin systems. However, the role of the atoms' spatial wave function has not been examined in detail experimentally. Here, we show a strong spin-motion coupling emerging from the large variation of the interaction potential over the wave function spread. We observe its clear signature on the ultrafast many-body nanosecond-dynamics of atoms excited to a Rydberg S state, using picosecond pulses, from an unity-filling atomic Mott-insulator. We also propose an approach to tune arbitrarily the strength of the spin-motion coupling relative to the motional energy scale set by trapping potentials. Our work provides a new direction for exploring the dynamics of strongly correlated quantum systems by adding the motional degree of freedom to the Rydberg simulation toolbox.

Dynamics of spin-momentum entanglement from superradiant phase transitions

Exploring operational regimes of many-body cavity QED with multilevel atoms remains an exciting research frontier for their enhanced storage capabilities of intralevel quantum correlations. In this work, we consider an experimentally feasible many-body cavity QED model describing a four-level system, where each of those levels is formed from a combination of different spin and momentum states of ultracold atoms in a cavity. The resulting model comprises a pair of Dicke Hamiltonians constructed from pseudospin operators, effectively capturing two intertwined superradiant phase transitions. The phase diagram reveals regions featuring weak and strong entangled states of spin and momentum atomic degrees of freedom. These states exhibit different dynamical responses, ranging from slow to fast relaxation, with the added option of persistent entanglement temporal oscillations. We discuss the role of cavity losses in steering the system's dynamics into such entangled states and propose a readout scheme that leverages different light polarizations within the cavity. Our work paves the way to connect the rich variety of non-equilibrium phase transitions that occur in many-body cavity QED to the buildup of quantum correlations in systems with multilevel atom descriptions. Published by the American Physical Society 2024

Extracting off-diagonal order from diagonal basis measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024

Dynamics of strongly correlated quantum systems from an extended Singwi‐Tosi‐Land‐Sjölander closure for the BBGKY hierarchy

AbstractThe BBGKY hierarchy in the Wigner representation is used with an extended Singwi‐Tosi‐Land‐Sjölander (STLS) ansatz for the two‐particle distribution function [H. Kählert, G. J. Kalman, and M. Bonitz, Phys. Rev. E 90, 011101 (2014)] to study the density response function and the dispersion relation of collective modes in a strongly coupled quantum system. It is shown that the local field correction (LFC) and the dispersion relation reduce to the results of the Quasi‐Localized Charge Approximation (QLCA) in the classical limit. In the quantum case, the LFC acquires a frequency‐dependence, similar to the quantum version of the STLS theory. The dispersion relation is governed by a generalization of the QLCA dynamical matrix. The results are expected to be relevant for the analysis of collective modes in quantum liquids with strong correlations.

Fundamental Limits on Anomalous Energy Flows in Correlated Quantum Systems.

In classical thermodynamics energy always flows from the hotter system to the colder one. However, if these systems are initially correlated, the energy flow can reverse, making the cold system colder and the hot system hotter. This intriguing phenomenon is called "anomalous energy flow" and shows the importance of initial correlations in determining physical properties of thermodynamic systems. Here we investigate the fundamental limits of this effect. Specifically, we find the optimal amount of energy that can be transferred between quantum systems under closed and reversible dynamics, which then allows us to characterize the anomalous energy flow. We then explore a more general scenario where the energy flow is mediated by an ancillary quantum system that acts as a catalyst. We show that this approach allows for exploiting previously inaccessible types of correlations, ultimately resulting in an energy transfer that surpasses our fundamental bound. To demonstrate these findings, we use a well-studied quantum optics setup involving two atoms coupled to an optical cavity.

Giant Rectification in Strongly Interacting Driven Tilted Systems

Correlated quantum systems feature a wide range of nontrivial effects emerging from interactions between their constituent particles. In nonequilibrium scenarios, these manifest in phenomena such as many-body insulating states and anomalous scaling laws of currents of conserved quantities, crucial for applications in quantum circuit technologies. In this work, we propose a giant-rectification scheme based on the asymmetric interplay between strong particle interactions and a tilted potential, each of which induces an insulating state on its own. While for reverse bias both cooperate and induce a strengthened insulator with an exponentially suppressed current, for forward bias they compete, generating conduction resonances; this leads to a rectification coefficient of many orders of magnitude. We uncover the mechanism underlying these resonances as enhanced coherences between energy eigenstates occurring at avoided crossings in the bulk energy spectrum of the system. Furthermore, we demonstrate the complexity of the many-body nonequilibrium conducting state through the emergence of enhanced density-matrix impurity and operator-space entanglement entropy close to the resonances. Our proposal paves the way for implementing a perfect diode in currently available electronic and quantum simulation platforms. Published by the American Physical Society 2024

Quantum Kolmogorov complexity and quantum correlations in deterministic-control quantum Turing machines

This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and define dcq-computable states as those that can be approximated by a dcq-TM. Moreover, we introduce (conditional) Kolmogorov complexity of quantum states and use it to study three particular aspects of the algorithmic information contained in a quantum state: a comparison of the information in a quantum state with that of its classical representation as an array of real numbers, an exploration of the limits of quantum state copying in the context of algorithmic complexity, and study of the complexity of correlations in quantum systems, resulting in a correlation-aware definition for algorithmic mutual information that satisfies symmetry of information property.

Selective weak measurement reveals super-ergotropy

The concept of ergotropy was previously introduced as the maximum extractable work from a quantum state. Its enhancement, which is induced by quantum correlation via projective measurement, was formulated as the daemonic ergotropy. In this work, we investigate the ergotropy in the presence of quantum correlation via weak measurement because of its elegant effects on the measured system. By considering a bipartite correlated quantum system consisting of main and ancillary systems, we demonstrate that the extractable work by the non-selective weak measurement on the ancilla is always equal to the situation captured by the strong measurement. However, the selective weak measurement interestingly reveals more work than the daemonic ergotropy and the ergotropy of the total system is greater than or equal to the daemonic ergotropy. Moreover, it is shown that for Bell diagonal states, at the cost of losing quantum correlation, the total extractable and thus non-local extractable works can be increased by using measurement. Also, we find that there is no direct relationship between quantum correlation and non-local extractable work for these cases.

Roton-like dispersion via polarisation change for elastic wave energy control in graded delay-lines

While roton dispersion relations had been restricted to correlated quantum systems at low temperature, recent works show the possibility of obtaining this unusual dispersion in acoustic and elastic metamaterials. Such phenomenon has been demonstrated in periodic structures by means of beyond-nearest-neighbour interactions, following the formulation firstly developed by Brillouin in the ′50s. In this paper, we demonstrate both numerically and experimentally that beyond-nearest-neighbour connections are not a necessary condition to obtain this unusual dispersion relation in elasticity. Leveraging the intrinsic complexity of elastic systems supporting different types of waves, we demonstrate that mode locking can be applied to obtain roton dispersion, without the need of elastic or magnetic interactions between non nearest neighbours. Moreover, the combination of roton dispersion and rainbow physics enables spatial separation of the energy fluxes with positive and negative group velocity.

The resource theory of nonclassicality of channel assemblages

When two parties, Alice and Bob, share correlated quantum systems and Alice performs local measurements, Alice's updated description of Bob's state can provide evidence of nonclassical correlations. This simple scenario, famously introduced by Einstein, Podolsky and Rosen (EPR), can be modified by allowing Bob to also have a classical or quantum system as an input. In this case, Alice updates her knowledge of the channel (rather than of a state) in Bob's lab. In this paper, we provide a unified framework for studying the nonclassicality of various such generalizations of the EPR scenario. We do so using a resource theory wherein the free operations are local operations and shared randomness (LOSR). We derive a semidefinite program for studying the pre-order of EPR resources and discover possible conversions between the latter. Moreover, we study conversions between post-quantum resources both analytically and numerically.

Control of Correlation Using Confinement in Case of Quantum System

AbstractThis article investigates the behavior of a Moshinsky atom in a 1D harmonic trap. Focus is given on the theoretical foundations of confinement and its impact on the correlation between particles in the Moshinsky atom. The investigation begins by illustrating the (de)localization of the probability density function using Shannon entropy. The basics of correlation and interpretation of correlation using tools such as mutual information and statistical correlation coefficients and how these can be quantified are discussed. Then the concept of confinement is explored. The impact of interaction strength and confinement on Shannon entropy, statistical correlation coefficients, and mutual information is investigated. How interaction strength and confinement can be used to induce correlations between previously uncorrelated particles, as well as how they can be used to suppress correlations between previously correlated particles is discussed. Their implications for quantum information processing and quantum simulation are discussed. In conclusion, confinement is a powerful tool for controlling correlations in quantum systems, and its impact on correlation can be understood through theoretical models. The importance of experimental studies in this field, which provide insights into the behavior of quantum systems under confinement and pave the way for future applications in quantum technology is also emphasized.

Time-Linear Quantum Transport Simulations with Correlated Nonequilibrium Green’s Functions

We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes in the dynamics, thereby paving the way to the real-time characterization of correlated ultrafast phenomena in quantum transport. The open system dynamics is described in terms of an ``embedding correlator'' from which the time-dependent current can be calculated using the Meir-Wingreen formula. We show how to efficiently implement our approach through a simple grafting into recently proposed time-linear Green's function methods for closed systems. Electron-electron and electron-phonon interactions can be treated on equal footing while preserving all fundamental conservation laws.

A Global Optimization Approach for Multimarginal Optimal Transport Problems with Coulomb Cost

In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding the strongly correlated quantum systems. With a Monge-like ansatz, the orginal high-dimensional problems are transferred into mathematical programmings with generalized complementarity constraints, and thus the curse of dimensionality is surmounted. However, the latter ones are themselves hard to deal with from both theoretical and practical perspective. Moreover in the presence of nonconvexity, brute-force searching for global solutions becomes prohibitive as the problem size grows large. To this end, we propose a global optimization approach for solving the nonconvex optimization problems, by exploiting an efficient proximal block coordinate descent local solver and an initialization subroutine based on hierarchical grid refinements. We provide numerical simulations on some typical physical systems to show the efficiency of our approach. The results match well with both theoretical predictions and physical intuitions, and give the first visualization of optimal transport maps for some two dimensional systems.

Emergent Z_{2} Gauge Theories and Topological Excitations in Rydberg Atom Arrays.

Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.

Observation of multiple rotons and multidirectional roton-like dispersion relations in acoustic metamaterials

Roton dispersion relations were firstly predicted by Landau and have been extensively explored in correlated quantum systems at low temperatures. Recently, the roton-like dispersion relations were theoretically extended to classical acoustics, which, however, have remained elusive in reality. Here, we report the experimental observation of roton-like dispersions in acoustic metamaterials with beyond-nearest-neighbour interactions at ambient temperatures. The resulting metamaterial supports multiple coexisting modes with different wavevectors and group velocities at the same frequency and broadband backward waves, analogous to the ‘return flow’ termed by Feynman in the context of rotons. By increasing the order of long-range interaction, we observe multiple rotons on a single dispersion band, which have never appeared in Landau’s prediction or any other condensed-matter or classical-wave studies. Moreover, we have also theoretically proposed and experimentally observed multidirectional roton-like dispersion relations in a two-dimensional nonlocal acoustic metamaterial. The realization of roton-like dispersions in metamaterials could pave the way to explore novel physics and applications on quantum-inspired phenomena in classical systems.

One-particle entanglement for one-dimensional spinless fermions after an interaction quantum quench

Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large scale exact diagonalization and time dependent density matrix renormalization group calculations, we numerically compute the one body reduced density matrix for the J-V model, as well as its post-quench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.

A perspective on machine learning and data science for strongly correlated electron problems

Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times, challenges in recognizing novel phases, and the Fermion sign problem. Methods in machine learning (ML), artificial intelligence, and data science promise to help address these limitations and open up a new frontier in strongly correlated quantum system simulations. In this paper, we review some of the progress in this area. We begin by examining these approaches in the context of classical models, where their underpinnings and application can be easily illustrated and benchmarked. We then discuss cases where ML methods have enabled scientific discovery. Finally, we will examine their applications in accelerating model solutions in state-of-the-art quantum many-body methods like quantum Monte Carlo and discuss potential future research directions.