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Thermodynamics of Heisenberg Chains Coupled to Phonons

Rainer Walter Kühne

Published Mar 11, 2019• 0 citations
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Abstract

This PhD thesis examines the thermodynamical properties of spin-1/2 Heisenberg chains which are coupled to Einstein phonons. One result of this study is that these spin-phonon systems undergo a phase transition similar to a spin-Peierls transition (cf. Physical Review B 60 (1999) 12125-12133 and Physical Review B 65 (2002) 144438). Another result is that in the undimerized phase the critical exponent nu depends on both the phonon frequency and the spin-phonon coupling constant. This means that these spin-phonon systems change the universality class continuously with the spin-phonon coupling (cf. arXiv: cond-mat/9912150v1).

DOI
10.31219/osf.io/aj8wc

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This PhD thesis examines the thermodynamical properties of spin-1/2 Heisenberg chains which are coupled to Einstein phonons. One result of this study is that these spin-phonon systems undergo a phase transition similar to a spin-Peierls transition (cf. Physical Review B 60 (1999) 12125-12133 and Physical Review B 65 (2002) 144438). Another result is that in the undimerized phase the critical exponent nu depends on both the phonon frequency and the spin-phonon coupling constant. This means that these spin-phonon systems change the universality class continuously with the spin-phonon coupling (cf. arXiv: cond-mat/9912150v1).
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.
We performed a finite-temperature quantum Monte Carlo simulation of the one-dimensional spin-1/2 Heisenberg model with nearest-neighbor interaction coupled to Einstein phonons. Our method allows to treat easily up to 100 phonons per site and the results presented are practically free from truncation errors. We studied in detail the magnetic susceptibility, the specific heat, the phonon occupation, the dimerization, and the spin-correlation function for various spin-phonon couplings and phonon frequencies. In particular we give evidence for the transition from a gapless to a massive phase by studying the finite-size behavior of the susceptibility. We also show that the dimerization is proportional to g2/Ω for T<2J.
We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}256N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling $\ensuremath{\alpha}$ exceeds a critical value ${\ensuremath{\alpha}}_{c}$. Using sum rules, we show that the phonon spectral function has divergent (for $N\ensuremath{\rightarrow}\ensuremath{\infty}$) weight extending to zero frequency for $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$. The phonon correlations decay with distance rrr as 1/r1/r1/r. This behavior is characteristic for all $0<\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$ and the $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}$ phonon does not soften (to zero frequency) at $\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\alpha}}_{c}$.
Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green’s function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3. 1
We develop an analytical approach based on a unitary transformation to investigate S=1/2 antiferromagnetic Heisenberg chains coupled to phonons, and find a new quantum phase transition at zero temperature. Although the usual phase transition occurs depending on the strengths of the spin-spin and spin-phonon interactions, the phase transition in the present work is induced by a change in the geometrical structure of the spin-phonon interaction. The magnetic properties of the phase transition can be understood in relation to a phase transition that has already been found in the frustrated J1-J2 model.