The density matrix renormalisation group and critical phenomena

TL;DR

This paper adapts the density matrix renormalisation group (DMRG) method to study critical phenomena, providing a new approach to analyze phase transitions and improve upon traditional real space renormalisation techniques.

Contribution

It introduces a DMRG-based scheme for generating transformations in coupling constant space, enhancing the analysis of critical phenomena and phase transitions.

Findings

Qualitative improvement in thermal exponent estimation

Application to anisotropic spin-1/2 Heisenberg chain

Identification of renormalised blocks and operators via density matrix eigenvalues

Abstract

We adapt White's density matrix renormalisation group (DMRG) to the direct study of critical phenomena. We use the DMRG to generate transformations in the space of coupling constants. We postulate that a study of density matrix eigenvalues leads to a natural identification of renormalised blocks, operators and Hamiltonians. We apply the scheme to the phase transition in the anisotropic spin-1/2 Heisenberg chain. In the simplest case where the two most probable states in odd sized blocks are used to construct approximate renormalisation group transformations, we find qualitative improvement upon the standard real space renormalisation group method for the thermal exponent $\nu$.