Application of the density matrix renormalization group method to finite temperatures and two-dimensional systems

TL;DR

This paper reviews the application of the density matrix renormalization group (DMRG) method to finite temperature and two-dimensional quantum systems, highlighting algorithmic developments and practical results.

Contribution

It introduces a reliable finite-temperature DMRG algorithm and demonstrates its application to two-dimensional quantum systems like quantum Hall models.

Findings

Finite-temperature DMRG provides accurate thermodynamic properties.

The method successfully models two-dimensional quantum Hall systems.

Reliable eigenvector calculations enable dynamic correlation analysis.

Abstract

The density matrix renormalization group (DMRG) method and its applications to finite temperatures and two-dimensional systems are reviewed. The basic idea of the original DMRG method, which allows precise study of the ground state properties and low-energy excitations, is presented for models which include long-range interactions. The DMRG scheme is then applied to the diagonalization of the quantum transfer matrix for one-dimensional systems, and a reliable algorithm at finite temperatures is formulated. Dynamic correlation functions at finite temperatures are calculated from the eigenvectors of the quantum transfer matrix with analytical continuation to the real frequency axis. An application of the DMRG method to two-dimensional quantum systems in a magnetic field is demonstrated and reliable results for quantum Hall systems are presented.