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Low-temperature Gibbs states with tensor networks

Denise Cocchiarella and Mari Carmen Bañuls

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Phys. Rev. Research 7, 033184 – Published 22 August, 2025

DOI: https://doi.org/10.1103/x2gx-wsp1

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.

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Phys. Rev. Research 7, 033184– Published 22 August, 2025
  • Received 24 January 2025
  • Accepted 29 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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