Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models

TL;DR

The paper introduces a linearized tensor renormalization group (LTRG) algorithm for calculating thermodynamic properties of one-dimensional quantum lattice models, demonstrating high accuracy and versatility compared to existing methods.

Contribution

A novel LTRG algorithm that directly handles 2D transfer matrices, applicable to finite and infinite systems, and extends to boson and fermion models.

Findings

Accurately computes thermodynamic quantities of the quantum XY spin chain.

Achieves precision comparable or superior to TMRG.

Handles both finite and infinite quantum systems.

Abstract

A linearized tensor renormalization group (LTRG) algorithm is proposed to calculate the thermodynamic properties of one-dimensional quantum lattice models, that is incorporated with the infinite time-evolving block decimation technique, and allows for treating directly the two-dimensional transfer-matrix tensor network. To illustrate its feasibility, the thermodynamic quantities of the quantum XY spin chain are calculated accurately by the LTRG, and the precision is shown to be comparable with (even better than) the transfer matrix renormalization group (TMRG) method. Unlike the TMRG scheme that can only deal with the infinite chains, the present LTRG algorithm could treat both finite and infinite systems, and may be readily extended to boson and fermion quantum lattice models.