Density Matrix Renormalization Group Applied to the Ground State of the XY-Spin-Peierls System

TL;DR

This paper applies the DMRG method to study the ground state of an XY-spin chain coupled to phonons, revealing a critical spin-phonon coupling and a classical-quantum crossover, marking the first such phonon application of DMRG.

Contribution

First application of DMRG to phonons, mapping the ground state of XY-spin-Peierls system and identifying critical coupling and crossover phenomena.

Findings

Existence of a critical spin-phonon coupling for spin gap onset

Observation of a classical-quantum crossover when the gap is comparable to phonon frequency

Strong renormalization of mean-field parameters by non-adiabatic effects in the classical regime

Abstract

We use the density matrix renormalization group (DMRG) to map out the ground state of a XY-spin chain coupled to dispersionless phonons of frequency $% \omega $. We confirm the existence of a critical spin-phonon coupling $% \alpha _c\propto \omega ^{0.7}$ for the onset of the spin gap bearing the signature of a Kosterlitz-Thouless transition. We also observe a classical-quantum crossover when the spin-Peierls gap $\Delta $ is of order $% \omega $. In the classical regime, $\Delta >\omega $, the mean-field parameters are strongly renormalized by non-adiabatic corrections. This is the first application of the DMRG to phonons.