Ergodicity breaking in matrix-product-state effective Hamiltonians

TL;DR

This paper shows that the DMRG effective Hamiltonian can be used to analyze thermalization and ergodicity breaking in large quantum many-body systems, capturing transitions and scars beyond exact methods.

Contribution

It demonstrates that the DMRG effective Hamiltonian encodes detailed spectral information about thermalization and ergodicity breaking in large systems.

Findings

Spectrum of the effective Hamiltonian captures transition from thermal to localized regimes.

Effective Hamiltonian reveals spatially resolved ergodic bubbles.

Approach also detects weak ergodicity breaking due to quantum many-body scars.

Abstract

Thermalization and its breakdown in interacting quantum many-body systems are governed by mid-spectrum eigenstates, which are typically accessible only in small system sizes amenable to exact diagonalization. Here we demonstrate that the density-matrix renormalization group (DMRG) effective Hamiltonian, an object routinely used to variationally approximate ground states, encodes detailed information about the dynamics far from equilibrium. In the random-field XXZ spin chain, the spectrum of the effective Hamiltonian is shown to capture the transition from thermal to many-body localized regimes, including spatially resolved probes of ergodic bubbles. Furthermore, the same approach also captures weak ergodicity breaking associated with quantum many-body scars. Our results establish the DMRG effective Hamiltonian as a versatile spectral probe of quantum thermalization and its breakdown in large systems beyond exact diagonalization.