Spin-phonon chains with bond coupling

Abstract

We investigate the antiadiabatic limit of an antiferromagnetic S = 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.

Peierls transition in the presence of finite-frequency phonons in the one-dimensional extended Peierls-Hubbard model at half-filling

“…(12) of Ref. 32, is expected to be exact in the anti-adiabatic limit, ω 0 /J → ∞, which here corresponds to U → ∞. It is in good agreement with numerical (SSE) results 29 for the spin-Peierls transition even for frequencies as low as ω 0 /J = 0.25.…”

“…26,29,30,31,32 This is in contrast to the adiabatic limit, where dimerization occurs for infinitesimal coupling.…”

“…Extensive studies of spin-Peierls models in recent years 26,27,28,29,30,31,32 have largely been spurred by the discovery of a spin-Peierls transition at unusually high temperature (14 K) in CuGeO 3 .…”

“…Considering, however, that the analytical form is accurate for the spin-Peierls model with ω 0 /J = 0.25, 29,32 and that the nonlinear spin-phonon coupling should be negligible for small α, the disagreement for the small-U region in Fig. 5 must be due to the poor correspondence between the full electron model and the spin chain with the lowest-order J in Eq.…”

The loop algorithm

“…Frustrated models with a sign problem have been simulated by making use of the increased precision [42, 107,160] and by removing the sign problem in a semifrustrated case [32]. Spin chains with quantum phonons have been investigated both in first [185] and second quantization [139,186,187]. Transport properties have recently become accessible in spin chains [118,188].…”