Simulating thermal density operators with cluster expansions and tensor networks

Autor(en)

Bram Vanhecke, David Devoogdt, Frank Verstraete, Laurens Vanderstraeten

Abstrakt

We provide an efficient approximation for the exponential of a local operator in quantum spin systems using tensor-network representations of a cluster expansion. We benchmark this cluster tensor network operator (cluster TNO) for one-dimensional systems, and show that the approximation works well for large real- or imaginary-time steps. We use this formalism for representing the thermal density operator of a two-dimensional quantum spin system at a certain temperature as a single cluster TNO, which we can then contract by standard contraction methods for two-dimensional tensor networks. We apply this approach to the thermal phase transition of the transverse-field Ising model on the square lattice, and we find through a scaling analysis that the cluster-TNO approximation gives rise to a continuous phase transition in the correct universality class; by increasing the order of the cluster expansion we find good values of the critical point up to surprisingly low temperatures.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Ghent University

Journal

SciPost Physics

Band

14

Anzahl der Seiten

18

ISSN

2542-4653

DOI

https://doi.org/10.48550/arXiv.2112.01507

Publikationsdatum

04-2023

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie, 103025 Quantenmechanik

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/c6010d9d-1af3-4be6-a034-6332198875f0