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arXiv:cond-mat/0505253 · Physical Review B

Spin conductance in one-dimensional spin-phonon systems

Kim Louis, X. Zotos

Published Dec 9, 2005• 6 citations
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Abstract

We present results for the spin conductance of the one-dimensional spin-$1∕2$ Heisenberg and $XY$ models coupled to phonons. We apply an approach based on the stochastic series expansion (quantum Monte Carlo) method to evaluate the conductance for a variety of phonon dispersions and values of spin-phonon coupling. From our numerical simulations and analytical arguments, we derive several scaling laws for the conductance.

DOI
10.1103/physrevb.72.214415

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The phonon dynamics in a one dimensional Heisenberg spin chain coupled to finite-frequency bond phonons is studied. We present the first detailed phonon spectra for these systems using Quantum Monte Carlo. The quantum phase transition is dominated by a central peak, yet the renormalisation of the main phonon branch depends strongly on the bare phonon frequency omega_0. The main branch remains largely unaffected at omega_0 \gsim J, but it softens completely when omega_0 is low enough. This is an unusual scenario for a structural phase transition and was observable only on sufficiently large systems. Approaching the dimerized phase from finite temperature, the lattice dynamics mirrors the behavior of a three dimensional system. For the efficient measurement of Greens functions, we introduce a mapping from the stochastic series expansion to continuous imaginary time.
The one-dimensional spin-1/2 Heisenberg model with nearest-neighbour interaction coupled to Einstein phonons is of interest for the understanding of materials which show the spin-Peierls phase transition. I examined this model by performing a finite-temperature quantum Monte Carlo simulation by using the very efficient loop algorithm. I studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-spin correlation function of this model for various spin-phonon couplings and phonon frequencies. In particular I gave evidence for a global effective spin-spin coupling and for the transition from a gapless to the massive phase by studying the finite-size behavior of the magnetic susceptibility.