VBS/CFT Correspondence and Thermal Tensor Network

TL;DR

This paper proposes a simple phenomenological theory connecting 2D valence bond solid states to 1D thermal states using tensor networks, highlighting differences from multiscale entanglement renormalization.

Contribution

It introduces a new phenomenological framework for VBS/CFT correspondence based on finite-temperature tensor networks, clarifying its relation to existing entanglement renormalization methods.

Findings

Mapped 2D VBS states to 1D thermal density matrices

Developed a phenomenological tensor network model for the correspondence

Clarified differences between the proposed approach and MERA

Abstract

It has been recently observed that the reduced density matrix of a two-dimensional (2D) valence bond solid state can be mapped onto the thermal density matrix of a 1D Heisenberg quantum spin chain. Motivated by the observation, I propose a very simple phenomenological theory for this type of correspondence based on a finite-temperature tensor network formalism recently developed. I adress close relationship and sharp difference between the present correspondence and multiscale entanglement renormalization ansatz in terms of network geometry.