Finite Temperature DMRG Investigation of the Spin-Peierls Transition in CuGeO$_3$

TL;DR

This paper uses advanced numerical methods to study the thermodynamics of dimerized frustrated Heisenberg chains, providing insights into the spin-Peierls transition in CuGeO$_3$ at very low temperatures.

Contribution

It introduces a finite temperature DMRG approach to analyze the spin-Peierls transition, enabling calculations previously inaccessible to ab initio methods.

Findings

Quantitative analysis of the crossover from quadratic to nonanalytic free energy behavior.

Comparison of theoretical results with experimental data for CuGeO$_3$.

Identification of the instability towards lattice dimerization at finite temperature.

Abstract

We present a numerical study of thermodynamical properties of dimerized frustrated Heisenberg chains down to extremely low temperatures with applications to CuGeO$_3$. A variant of the finite temperature density matrix renormalization group (DMRG) allows the study of the dimerized phase previously unaccessible to ab initio calculations. We investigate static dimerized systems as well as the instability of the quantum chain towards lattice dimerization. The crossover from a quadratic response in the free energy to the distortion field at finite temperature to nonanalytic behavior at zero temperature is studied quantitatively. Various physical quantities are derived and compared with experimental data for CuGeO$_3$ such as magnetic dimerization, critical temperature, susceptibility and entropy.