A density matrix renormalisation group algorithm for quantum lattice systems with a large number of states per site

TL;DR

This paper introduces a modified density matrix renormalisation group algorithm tailored for one-dimensional quantum lattice systems with many states per site, enabling accurate energy calculations and critical property analysis.

Contribution

The paper presents a new variant of the DMRG algorithm capable of handling large local Hilbert spaces in quantum lattice models.

Findings

Accurately computes low-lying energies of complex quantum models.

Successfully applies to models with quantum phonons.

Resolves energy gaps suitable for finite-size scaling analysis.

Abstract

A variant of White's density matrix renormalisation group scheme which is designed to compute low-lying energies of one-dimensional quantum lattice models with a large number of degrees of freedom per site is described. The method is tested on two exactly solvable models---the spin-1/2 antiferromagnetic Heisenberg chain and a dimerised XY spin chain. To illustrate the potential of the method, it is applied to a model of spins interacting with quantum phonons. It is shown that the method accurately resolves a number of energy gaps on periodic rings which are sufficiently large to afford an accurate investigation of critical properties via the use of finite-size scaling theory.