Cluster expansion for ground states of local Hamiltonians

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.

49 pages, 23 figures

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Cited by in corpus (7)

• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• Equilibration in one-dimensional quantum hydrodynamic systems
• Entanglement spreading and quasiparticle picture beyond the pair structure
• Quenches from gaussian bosons to Tonks-Girardeau gas: stationary states and effects of a confining potential
• Variational wavefunctions for Sachdev-Ye-Kitaev models
• Mechanisms for the emergence of Gaussian correlations
• Energy spectrum of interacting gas: cluster expansion method