Simulating thermal density operators with cluster expansions and tensor networks

• URL: http://arxiv.org/abs/2112.01507v1
• Date: Thu, 2 Dec 2021 18:56:44 GMT
• Title: Simulating thermal density operators with cluster expansions and tensor networks
• Authors: Bram Vanhecke, David Devoogdt, Frank Verstraete and Laurens Vanderstraeten
• Abstract summary: We benchmark this cluster tensor network operator (cluster TNO) for one-dimensional systems. 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. We find through a scaling analysis that the cluster-TNO approximation gives rise to a continuous phase transition in the correct universality class.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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