Transfer Matrix DMRG for Thermodynamics of One-Dimensional Quantum Systems

TL;DR

This paper introduces a transfer matrix DMRG method tailored for one-dimensional quantum systems, effectively calculating thermodynamic properties with high accuracy, demonstrated on the anisotropic spin-1/2 Heisenberg model.

Contribution

The paper develops a novel transfer matrix DMRG approach that incorporates symmetry and asymmetric reduced density matrices for improved thermodynamic calculations.

Findings

Results agree very accurately with exact solutions.

Relative errors for spin susceptibility are below 10^{-3} at low temperatures.

Method achieves high precision with 80 states kept.

Abstract

The transfer matrix DMRG method for one dimensional quantum lattice systems has been developed by considering the symmetry property of the transfer matrix and introducing the asymmetric reduced density matrix. We have evaluated a number of thermodynamic quantities of the anisotropic spin-1/2 Heisenberg model using this method and found that the results agree very accurately with the exact ones. The relative errors for the spin susceptibility are less than $10^{-3}$ down to $T=0.01J$ with 80 states kept.