Cluster expansion for ground states of local Hamiltonians

TL;DR

This paper develops a cluster expansion method for ground states of local Hamiltonians, linking cluster amplitudes to physical quantities, and applies it to out-of-equilibrium quantum dynamics.

Contribution

It introduces a novel cluster expansion framework for ground states of local Hamiltonians, connecting cluster amplitudes to thermodynamics and local observables, including non-perturbative aspects.

Findings

Cluster amplitudes relate to thermodynamic quantities.

The method verifies consistency with perturbation theory.

Applications include proofs of equilibration and work statistics.

Abstract

A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quench.