Cluster expansion for ground states of local Hamiltonians

Alvise Bastianello; Spyros Sotiriadis

doi:10.1016/j.nuclphysb.2016.06.021

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arXiv · 1601.02532

Cluster expansion for ground states of local Hamiltonians

Alvise Bastianello·Spyros Sotiriadis

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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.

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cond-mat.stat-mech cond-mat.quant-gas hep-th math-ph math.MP

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Alvise Bastianello, Spyros Sotiriadis. 2016-05-13. Cluster expansion for ground states of local Hamiltonians. https://doi.org/10.1016/j.nuclphysb.2016.06.021

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