Year: 2023
Type: article
Abstract: 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.
Source: SciPost Physics
Institutions: University of Vienna, Ghent University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: G8923609168
OpenAlex ID: W3217159017