Low-temperature Gibbs states with tensor networks

TL;DR

This paper presents a tensor network method for approximating low-temperature thermal states of quantum many-body systems, starting from the ground state, which is especially effective near criticality and for computing thermodynamic and entanglement properties.

Contribution

The authors introduce a ground-state-based tensor network ansatz for finite-temperature states, offering an alternative to traditional imaginary time evolution methods.

Findings

Effective in one- and two-dimensional systems

Accurately captures finite-temperature scaling of entanglement

Demonstrates efficiency near critical points

Abstract

We introduce a tensor network method for approximating thermal equilibrium states of quantum many-body systems at low temperatures. Whereas the usual approach starts from infinite temperature and evolves the state in imaginary time (toward lower temperature), our ansatz is constructed from the zero-temperature limit, the ground state, which can be found with a standard tensor network approach. Motivated by properties of the ground state for conformal field theories, our ansatz is especially well suited near criticality. Moreover, it allows an efficient computation of thermodynamic quantities and entanglement properties. We demonstrate the performance of our approach with a tree tensor network ansatz, although it can be extended to other tensor networks, and present results illustrating its effectiveness in capturing the finite-temperature properties in one- and two-dimensional scenarios. In particular, in the critical one-dimensional case we show how the ansatz reproduces the finite temperature scaling of entanglement in a conformal field theory.