Bilayer Linearized Tensor Renormalization Group Approach for Thermal Tensor Networks

TL;DR

This paper introduces an improved bilayer linearized tensor renormalization group (LTRG++) method for thermal tensor networks, enhancing accuracy in calculating thermodynamic properties of quantum lattice models and exploring phase phenomena.

Contribution

The paper develops the LTRG++ algorithm, a bilayer extension of LTRG, providing higher accuracy and applicability to both finite and infinite systems, and connects it to the transfer-matrix renormalization group.

Findings

LTRG++ achieves higher accuracy than single-layer LTRG.

Application to extended Hubbard model reveals phase separation and quantum criticality.

LTRG++ is equivalent to transfer-matrix RG in infinite systems.

Abstract

In this paper, we perform a comprehensive study of the renormalization group (RG) method on thermal tensor networks (TTN). By Trotter-Suzuki decomposition, one obtains the 1+1D TTN representing the partition function of 1D quantum lattice models, and then employs efficient RG contractions to obtain the thermodynamic properties with high precision. The linearized tensor renormalization group (LTRG) method, which can be used to contract TTN in an efficient and accurate way, is briefly reviewed. In addition, the single-layer LTRG can be generalized to a bilayer form, dubbed as LTRG++, in both finite- and infinite-size systems, with accuracies significantly improved. We provide the details of LTRG++ in finite-size system, comparing its accuracy with single-layer algorithm, and elaborate the infinite-size LTRG++ in the context of fermion chain model. We show that the LTRG++ algorithm in infinite-size system is in essence equivalent to transfer-matrix renormalization group method, while expressed in a tensor network language. LTRG++ is then applied to study an extended Hubbard model, where the phase separation phenomenon, groundstate phase diagram, as well as quantum criticality-enhanced magnetocaloric effects under external fields, are investigated.