Microscopic diagonal entropy and many-body dynamics

Yu-Hsueh Chen, Tarun Grover

Zhengan Wang, Zheng‐Hang Sun, Yu Zeng +4 more

Zheng‐Hang Sun, Jian Cui, Heng Fan

The authors present a method of charactering many-body localization transition via the quench dynamics of diagonal entropy, as an experimentally feasible quantity. The critical point of many-body localization transition can be efficiently detected. The adopted scaling ansatz respects the Harris-Luck bound, and the scaling exponent can provide information for the universality class of many-body localization transition.

Philipp Strasberg, Joseph Schindler

We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on Boltzmann, Gibbs or canonical entropy). This is done for the archetypal nonequilibrium setup of two systems exchanging energy, modeled here with random matrix theory, based on numerical integration of the Schrödinger equation. We consider three types of pure initial states (local energy eigenstates, decorrelated and entangled microcanonical states) and three classes of systems: (A) two normal systems, (B) a normal and a negative temperature system and (C) a normal and a negative heat capacity system. We find: (1) All types of initial states give rise to the same macroscopic dynamics. (2) Entanglement and diagonal entropy sensitively depend on the microstate, in contrast to all other entropies. (3) For class B and C, Gibbs-volume entropies can violate the second law and the associated temperature becomes meaningless. (4) For class C, Boltzmann-surface entropies can violate the second law and the associated temperature becomes meaningless. (5) Canonical entropy has a tendency to remain almost constant. (6) For a Haar random initial state, entanglement or diagonal entropy behave similar or identical to coarse-grained-observational entropy.

Pierre Gaspard

Yichen Huang

We study the entropy of small subsystems in thermalizing quantum many-body systems governed by local Hamiltonians. Assuming the eigenstate thermalization hypothesis, we derive an analytical formula for the von Neumann entropy of equilibrated subsystems. This formula reveals how subsystem entropy depends on the microscopic parameters of the Hamiltonian and the macroscopic properties of the initial state. Furthermore, our results provide a theoretical explanation for recent numerical findings by Maceira and Läuchli, obtained via exact diagonalization.