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 quantum quench.
|Titolo:||Cluster expansion for ground states of local Hamiltonians|
|Autori:||Bastianello, A.; Sotiriadis, S.|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||10.1016/j.nuclphysb.2016.06.021|
|Fulltext via DOI:||https://doi.org/10.1016/j.nuclphysb.2016.06.021|
|Appare nelle tipologie:||1.1 Journal article|