Weak and strong typicality in quantum systems

TL;DR

This paper investigates how mixed states derived from many-body lattice Hamiltonian eigenstates exhibit weak and strong typicality, showing that various entropies converge to thermodynamic entropy under different tracing scenarios.

Contribution

It demonstrates the emergence of weak and strong typicality in many-body quantum systems and compares the behavior of different entropy measures and observables.

Findings

Diagonal entropy matches thermodynamic entropy when few sites are traced out.

Von Neumann entropy aligns with thermodynamic entropy when many sites are traced out.

Results for physical observables are similar across reduced, diagonal, and canonical ensembles.

Abstract

We study the properties of mixed states obtained from eigenstates of many-body lattice Hamiltonians after tracing out part of the lattice. Two scenarios emerge for generic systems: (i) the diagonal entropy becomes equivalent to the thermodynamic entropy when a few sites are traced out (weak typicality); and (ii) the von Neumann (entanglement) entropy becomes equivalent to the thermodynamic entropy when a large fraction of the lattice is traced out (strong typicality). Remarkably, the results for few-body observables obtained with the reduced, diagonal, and canonical density matrices are very similar to each other, no matter which fraction of the lattice is traced out. Hence, for all physical quantities studied here, the results in the diagonal ensemble match the thermal predictions.