Initial State Independent Equilibration at the Breakdown of the Eigenstate Thermalization Hypothesis

Abstract

This work aims at understanding the interplay between the Eigenstate Thermalization Hypothesis (ETH), initial state independent equilibration and quantum chaos in systems that do not have a direct classical counterpart. It is based on numerical investigations of asymmetric Heisenberg spin ladders with varied interaction strengths between the legs, i.e., along the rungs. The relaxation of the energy difference between the legs is investigated. Two different parameters, both intended to quantify the degree of accordance with the ETH, are computed. Both indicate violation of the ETH at large interaction strengths but at different thresholds. Indeed the energy difference is found not to relax independently of its initial value above some critical interaction strength which coincides with one of the thresholds. At the same point the level statistics shift from Poisson-type to Wigner-type. Hence the system may be considered to become integrable again in the strong interaction limit.

arXiv comment8 pages , 6 figures

References in corpus (27)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Quantum many-body systems out of equilibrium
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Canonical Typicality
• Quantum mechanical evolution towards thermal equilibrium
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Alternatives to Eigenstate Thermalization
• Finite-size scaling of eigenstate thermalization
• Effective thermal dynamics following a quantum quench in a spin chain
• Massive Parallel Quantum Computer Simulator
• Eigenstate thermalization within isolated spin-chain systems
• Dynamical typicality of quantum expectation values
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• Spin-current autocorrelations from single pure-state propagation
• Chaos and statistical relaxation in quantum systems of interacting particles
• Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
• Regression relation for pure quantum states and its implications for efficient computing
• Generalization of von Neumann's Approach to Thermalization
• Relevance of the eigenstate thermalization hypothesis for thermal relaxation
• Eigenstate Thermalization in Systems with Spontaneously Broken Symmetry
• Occurrence of exponential relaxation in closed quantum systems
• A necessary condition for the thermalization of a quantum system coupled to a quantum bath
• The approach to typicality in many-body quantum systems
• Dependence of a quantum mechanical system on its own initial state and the initial state of the environment it interacts with
• Parameter Dependent Commuting Matrices, Plücker relations and Related Quantum Glass Models

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