Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network

TL;DR

This paper introduces a novel tensor network tailoring method to efficiently and accurately simulate the thermodynamics of quantum many-body systems at low temperatures by manipulating zero-temperature partition functions.

Contribution

The authors propose a new tensor network tailoring approach that improves efficiency and accuracy in simulating finite-temperature properties of quantum systems, surpassing previous methods.

Findings

Achieves high accuracy with fine-tuning surpassing previous methods

Time cost nearly independent of target temperature, including extremely low temperatures

Method extendable to higher-dimensional bosonic and fermionic systems

Abstract

Numerical annealing and renormalization group have conceived various successful approaches to study the thermodynamics of strongly-correlated systems where perturbation or expansion theories fail to work. As the process of lowering the temperatures is usually involved in different manners, these approaches in general become much less efficient or accurate at the low temperatures. In this work, we propose to access the finite-temperature properties from the tensor network (TN) representing the zero-temperature partition function. We propose to "scissor" a finite part from such an infinite-size TN, and "stitch" it to possess the periodic boundary condition along the imaginary-time direction. We dub this approach as TN tailoring. Exceptional accuracy is achieved with a fine-tune process, surpassing the previous methods including the linearized tensor renormalization group [Phys. Rev. Lett. 106, 127202 (2011)], continuous matrix product operator [Phys. Rev. Lett. 125, 170604 (2020)], and etc. High efficiency is demonstrated, where the time cost is nearly independent of the target temperature including the extremely-low temperatures. The proposed idea can be extended to higher-dimensional systems of bosons and fermions.