Session W02: Thermodynamics of Many-body Quantum Systems

Classical simulation of thermal equilibrium and quantum dynamics

Quantum systems of many interacting particles appear in numerous branches of physics, from condensed matter to statistical or high energy physics. Their study, however, is often very complicated due to the high dimensions of the Hilbert spaces involved.

The field of quantum information brings a new perspective to the study of those systems. Through it, we can rigorously analyze whether specific physical problems are fundamentally complex, and will require a quantum computer, or whether they can be solved efficiently with (classical) numerical means.

In this talk, we show how many interesting properties about many-body systems both in equilibrium and out of it can be computed in polynomial time, with provable efficiency guarantees. In particular, we focus on the classical simulation of Gibbs or thermal states, and on the simulation of arbitrary dynamics for short times. We do this through the frameworks of tensor network methods, as well as cluster expansions, which highlight how fundamental physical features, such as locality, constrain the complexity of quantum systems.

    

Towards a more fundamental understanding of eigenstate thermalization

We explore several venues how eigenstate thermalization may be understood on a more fundamental level. In particular, we report on extensive numerical work in spin systems with random interactions, where a small subsystem is subject to thermalization. We discuss possible directions towards an understanding of our numerical results.   

Universal Eigenvalue Distribution for Locally Interacting Quantum Systems

Wigner has shown that the eigenvalue distribution of a Gaussian orthogonal or unitary ensemble of random matrices approaches a semicircle in the thermodynamic limit.[1] Here, we show that the joint eigenvalue distribution of locally interacting quantum systems, that is, ensembles of finite dimensional subsystems with local interactions between them, approaches a Gaussian distribution as the number of subsystems is taken to infinity. In the talk, we present our analytical results supported by numerical data and discuss possible implications of a Gaussian density of states for physical problems.   

Finite temperature scaling of multipartite entanglement in the critical 1-D spin ½ antiferromagnetic Heisenberg chain

Scaling laws of the bipartite entanglement entropy at 1+1-D conformally invariant quantum critical points motivated several developments in identifying signatures of critical behaviour in many body systems and their underlying field theories. Less is known about the critical behaviour of multipartite entanglement, which describes higher order infactorability of the many body density matrix. However, multipartite entanglement can be quantified through the Quantum Fisher information (QFI), an entanglement witness that can also be related to dynamical response functions. We show that the QFI can be expressed as the static structure factor, plus a correction that vanishes as T ? 0. Therefore, in systems with a divergent static structure factor, we can deduce finite temperature scaling of multipartite entanglement without integrating contributions to the QFI from arbitrarily high energy dynamical response. This result is useful when the critical theory has at most marginally relevant operators, where the real-space RG scaling theory of the QFI degenerates. The critical antiferromagnetic Heisenberg model is such a theory, and we show that the QFI in the Heisenberg chain diverges as log(ß)^3/2, the known scaling of the longitudinal static structure factor in this system. We use MPS simulations and calculations of the QFI from conformal field theory to demonstrate this scaling hypothesis. Our results imply that the Heisenberg chain hosts highly entangled states at experimentally accessible temperatures.   

Micromasers as quantum batteries

We show that a micromaser is an excellent model of quantum battery. A highly excited, pure, and effectively steady state of the cavity mode, charged by coherent qubits, can be achieved, also in the ultrastrong coupling regime of field-matter interaction. Stability of these appealing features against loss of coherence of the qubits and the effect of counter-rotating terms in the interaction Hamiltonian are also discussed.   

Topological information device operating at the Landauer limit

We propose and theoretically investigate a novel Maxwell's demon implementation based on the spin-momentum locking property of topological matter. We use nuclear spins as a memory resource which provides the advantage of scalability. We show that this topological information device can ideally operate at the Landauer limit; the heat dissipation required to erase one bit of information stored in the demon's memory approaches $k_B Tln2$. Furthermore, we demonstrate that all available energy, $k_B Tln2$ per one bit of information, can be extracted in the form of electrical work. Finally, we find that the current-voltage characteristics of the topological information device satisfy the conditions of an ideal memristor.   

Efficient Sampling Scheme with Trotter Gates for Evaluating Thermal Expectation Values on Quantum Computers

Thermal expectation values of quantum many-body systems can be evaluated from expectation values obtained by sampled pure states. The efficiency of this sampling approach strongly depends on how one samples pure states. When a pure state is sampled Haar randomly, sample dependence decreases with the system size, and expectation values from a single sampled pure state represent thermal expectation values in sufficiently large systems. However, the preparation of Haar random states is difficult even on quantum computers because of exponentially many random numbers. In this study, we propose an alternative to a Haar random state: Pure states generated by applying Trotter gates to random product states. The number of applications is restricted to be proportional to the system size for the feasibility of the sampling on quantum computers. From the numerical investigation on sampling efficiency, we observe that the efficiency increases with system size like Haar random states when Trotter gates are made from a nonintegrable Hamiltonian. We also find some cases where the sampling efficiency of the proposed scheme is almost equal to that of the Haar random sampling.   

Concurrence Percolation in Quantum Networks

In this talk, I will explain how entanglement distribution on quantum networks (QN) is traditionally understood by mapping to classical percolation theory, which gives rise to a nontrivial threshold---in terms of the entanglement per link---for possibly transmitting entanglement between two arbitrarily distant nodes in QN. However, such a traditional comprehension is not complete. Indeed, a lower entanglement transmission threshold than what classical percolation predicts exists, as demonstrated on special network topology, that reveals a large-scale "quantum advantage." Naturally, we ask: Is such a "quantum advantage" general regardless of topology? I will address this question by introducing a new statistical theory, concurrence percolation theory (ConPT), that is remotely analogous to classical percolation but fundamentally different, built by generalizing bond percolation in terms of "sponge-crossing" paths instead of clusters. ConPT predicts a lower threshold than classical percolation for any network topology, showing that the existence of a large-scale "quantum advantage" is indeed general on any QN. [For more details see: Meng, X., Gao, J. & Havlin, S. Concurrence Percolation in Quantum Networks (https://arxiv.org/abs/2103.13985).]   

Entropy of the quantum work distribution

We study properties of the work distribution of a many-body system driven through a quantum phase transition for both sudden quenches and finite time ramps. We show how the information entropy of these distributions provides a strong signature of the phase transitions, characteristics which are not clearly evident in cumulants such as the mean and variance. We provide general bound on this entropy in terms of both the thermodynamic entropy and the relative entropy of coherence and demonstrate the applicability of our results for models containing both quantum and localisation phase transitions. Further interesting characteristics are shown to be examinable through the non-Gaussianity of the distribution, which we characterize through two quantitative metrics: the skewness and the negentropy. For the quantum Ising model we she that a finite duration of the ramp enhances the non-Gaussianity of the distribution for a finite size system.   

Multipartite Entanglement Spectroscopy with Single Particle Green's Functions

We demonstrate how to use the single particle electronic response functions to determine an itinerant electronic system's multipartite entanglement. We do so by computing the quantum Fisher information of a witness operator associated with the single particle Green's function. To allow the QFI to be an effective probe of the multipartite entanglement, we compute it for a doubled system, where there are two copies of the original model and the QFI witness operator hops electrons between the copies which otherwise do not interact. We apply this methodology to finite sized fermionic systems to demonstrate its ability to detect entanglement. We show that the amount of entanglement detected is sensitive to the wave vector of the hopping. This opens the possibility of using scanning tunneling microscopy and angle resolved photoemission probes to detect entanglement in many-body systems.   

Multipartite Entanglement Spectroscopy in a Quasi-one-dimensional Hubbard Model: A Single Particle Green’s Function Approach

We evaluate the multipartite entanglement in a quasi-one-dimensional Hubbard model by computing the quantum Fisher information (QFI) of a witness operator associated with the single-particle Green’s function. This method includes building two copies of the quasi-one-dimensional Hubbard model and a witness operator that hops between the two copies. Next, we numerically compute the QFI for a large system using the density matrix renormalization group (DMRG) technique and find that the amount of entanglement detected is sensitive to the wavevector of the hopping in the witness operator. This approach allows for experimentally detecting entanglement in many-body systems via scanning tunneling microscopy and angle-resolved photoemission probes.