Matrix product purifications for canonical ensembles and quantum number distributions

Journal Article (Journal Article)

Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-1/2 chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as 1/L.

Full Text

Duke Authors

Cited Authors

  • Barthel, T

Published Date

  • September 26, 2016

Published In

Volume / Issue

  • 94 / 11

Electronic International Standard Serial Number (EISSN)

  • 2469-9969

International Standard Serial Number (ISSN)

  • 2469-9950

Digital Object Identifier (DOI)

  • 10.1103/PhysRevB.94.115157

Citation Source

  • Scopus