TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.4.085
TI  - Simulating thermal density operators with cluster expansions and tensor networks
PY  - 2023/04/26
UR  - https://www.scipost.org/SciPostPhys.14.4.085
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 4
SP  - 085
A1  - Vanhecke, Bram
AU  - Devoogdt, David
AU  - Verstraete, Frank
AU  - Vanderstraeten, Laurens
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.14.4.085,
	title={{Simulating thermal density operators with cluster expansions and tensor networks}},
	author={Bram Vanhecke and David Devoogdt and Frank Verstraete and Laurens Vanderstraeten},
	journal={SciPost Phys.},
	volume={14},
	pages={085},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.4.085},
	url={https://scipost.org/10.21468/SciPostPhys.14.4.085},
}