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Effective spin models for spin-phonon chains by flow equations\n

Carsten Raas, Alexander Bühler, Götz Silvester Uhrig

Published Jun 15, 2001• 87 citations
Publisher

Abstract

\n \nWe investigate the anti-adiabatic limit of an anti-ferromagnetic S=1/2\nHeisenberg chain coupled to Einstein phonons. The flow equation method is used\nto decouple the spin and the phonon part of the Hamiltonian. \nIn the effective spin model long range spin-spin interactions are generated.\nWe determine the phase transition from a gapless state to a gapped (dimerized)\nphase, which occurs at a non-zero value of the spin-phonon coupling.\nIn the effective phonon sector a phonon hardening is observed.\n\n\n

DOI
10.1007/bf01325397

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\n \nWe investigate the anti-adiabatic limit of an anti-ferromagnetic S=1/2\nHeisenberg chain coupled to Einstein phonons. The flow equation method is used\nto decouple the spin and the phonon part of the Hamiltonian. \nIn the effective spin model long range spin-spin interactions are generated.\nWe determine the phase transition from a gapless state to a gapped (dimerized)\nphase, which occurs at a non-zero value of the spin-phonon coupling.\nIn the effective phonon sector a phonon hardening is observed.\n\n\n
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We investigate the antiadiabatic limit of an antiferromagnetic S=1/2S=1/2S=1/2 Heisenberg chain coupled to Einstein phonons via a bond coupling. The flow equation method is used to decouple the spin and the phonon part of the Hamiltonian. In the effective spin model longer range spin-spin interactions are generated. The effective spin chain is frustrated. The resulting temperature-dependent couplings are used to determine the magnetic susceptibility and to determine the phase transition from a gapless state to a dimerized gapped phase. The susceptibilities and the phase diagram obtained via the effective couplings are compared with independently calculated quantum Monte Carlo results.
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Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.
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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.