In this work we study a scenario where dynamics is restricted to a single excitation manifold, for particular physical observables with support in the manifold, which we label a `correlated quench'. We ask how such dynamics may in general differ from predictions of the eigenstate thermalization hypothesis (ETH). We show that if thermalization occurs, it will not fulfil other key predictions of the ETH; instead following differing generic behaviours. We show this by analysing long-time fluctuations, two-point correlation functions, and the out-of-time-ordered correlator; analytically detailing deviation from ETH predictions. We derive instead an ETH-like relation, with non-random off-diagonals, for matrix elements of observables, with correlations that alter long-time behaviour and constrain dynamics. Further, we analytically compute the time-dependence of the decay to equilibrium, showing that it is proportional to the survival probability of the initial state. We finally note that the conditions studied are common in many physical scenarios, such as under the rotating-wave approximation. We show numerically that predictions are robust to perturbations that break this approximation.
We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theori…
Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems
University of Science and Technology of China（中国科学技术大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies（复旦张肇韦量子中心，上海高等研究院）；CAS Key Laboratory of Microscale Magnetic Resonance（中国科学院微观磁学共振重点实验室）
We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section -- it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take local…
We study the non-equiliribium dynamics of atom-molecule Bose gases in a double-well potential. In this system, the internal atom-molecule tunneling has significant influence on the dynamics. We investigate the periodicity of dynamics by studying the level statistics of the quantum system. We find that chaotic energy eigenstates arise from the competition between the interwell and the atom-molecule internal tunnelings. Furthermore, we show that the physical quantities relax to the microcanonical averages in the full-quantum dynamics when the system is chaotic. This thermalization is caused by t…
The Eigenstate Thermalization Hypothesis (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for chaotic systems. Another signal of chaos is a positive Lyapunov exponent, defined on the basis of Loschmidt echo or out-of-time-order correlators. For this exponent to be positive, correlations between matrix elements unrelated by symmetry, usually neglected, have to exist. The same is true for the peak of the dynamic heterogeneity length, relevant for systems with slow dynamics. These correlations, as well as those between el…
Complexity of dynamics is at the core of quantum many-body chaos and exhibits a hierarchical feature: higher-order complexity implies more chaotic dynamics. Conventional ergodicity in thermalization processes is a manifestation of the lowest order complexity, which is represented by the eigenstate thermalization hypothesis (ETH) stating that individual energy eigenstates are thermal. Here, we propose a higher-order generalization of the ETH, named the $ k $-ETH ($ k=1,2,\dots $), to quantify higher-order complexity of quantum many-body dynamics at the level of individual energy eigenstates, wh…
We derive the Eigenstate Thermalization Hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by J. M. Deutsch [Phys. Rev. A 43, 2046 (1991)]. We approximate the coupling between a subsystem and a many-body environment by means of a random Gaussian matrix. We show that a common assumption in the analysis of quantum chaotic systems, namely the treatment of eigenstates as independent random vectors, leads to inconsistent results. However, a consistent approach to the ETH can be developed by introducing an interaction between random wave-functions that arises as a re…
Quantum Chaos and Spread of States in Krylov Subspace: A Topical Review
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Pohang University of Science and Technology（浦项科技大学）；Instituto de Física Teórica UAM/CSIC（马德里自治大学/西班牙国家科学研究委员会理论物理研究所）
The Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. However, its connection to the timescale of thermalization for open system dynamics has remained elusive. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Specifically, we demonstrate fast thermalization for a system coupled weakly to a bath of quasi-free Fermions that we refresh periodically. To describe the joint evolution, we derive a finite-time version of Davies' generator with explicit error bounds …
Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz within the eigenstate thermalization hypothesis (ETH). We study a quantum chaotic spin-fermion model in a one-dimensional lattice, which consists of a spin-1/2 XX chain coupled to a single itinerant fermion. In our study, we focus on translationally invariant observables including the charge and energy current, thereby also connecting the ETH with transport properties. Considering observables with a Hilbert-Schmidt norm of one, we first perform a comprehensive analysis of ETH in the mode…
