Coarse grained belief propagation for simulation of interacting quantum systems at all temperatures

TL;DR

This paper advances quantum belief propagation by introducing a thermal potential framework and a coarse grained algorithm, enabling accurate simulation of quantum systems across all temperature ranges.

Contribution

It presents a new thermal potential approach and the CGBP algorithm, improving the accuracy and efficiency of quantum system simulations at all temperatures.

Findings

Effective thermal potential characterizes quantum correlations.

CGBP achieves high-accuracy thermodynamic calculations.

Results agree with known solutions and phase diagrams.

Abstract

We continue our numerical study of quantum belief propagation initiated in [Phys. Rev. A, 77 (2008), p. 052318]. We demonstrate how the method can be expressed in terms of an effective thermal potential that materializes when the system presents quantum correlations, but is insensitive to classical correlations. The thermal potential provides an efficient means to assess the precision of belief propagation on graphs with no loops. We illustrate these concepts using the one-dimensional quantum Ising model and compare our results with exact solutions. We also use the method to study the transverse field quantum Ising spin glass for which we obtain a phase diagram that is largely in agreement with the one obtained in [arXiv:0706.4391] using a different approach. Finally, we introduce the coarse grained belief propagation (CGBP) algorithm to improve belief propagation at low temperatures. This method combines the reliability of belief propagation at high temperatures with the ability of entanglement renormalization to efficiently describe low energy subspaces of quantum systems with local interactions. With CGBP, thermodynamic properties of quantum systems can be calculated with a high degree of accuracy at all temperatures.