Neel to spin-Peierls transition in a quasi-1D Heisenberg model coupled to bond phonons

Abstract

The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is investigated using the Stochastic Series Expansion (SSE) Quantum Monte Carlo (QMC) method. The quantum phase transition from a gapless Neel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, inter-chain coupling strength and spin-lattice coupling strength. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, non-zero critical value. This is in contrast to the pure 1D model (zero inter-chain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any non-zero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong inter-chain coupling, the relation between the inter-chain coupling and the critical value of the spin-phonon interaction is linear whereas for weak inter-chain coupling, this behavior is found to have a natural logarithm-like relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the Neel state order vanishes simultaneously with the setting in of the spin-Peierls state. For the thermal phase transition, a continuous heat capacity with a peak at the critical temperature, $T_c$, shows a second order phase transition. The variation of the equilibrium bond length distortion, ${\delta }_{eq}$, with temperature showed a power law relation which decayed to zero as the temperature was increased to $T_c$, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.

7 pages, 5 figures, updated and extended version of arXiv:cond-mat/0307746

References in corpus (7)

• Quantum Monte Carlo with Directed Loops
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• Neel Temperature of Quasi-Low-Dimensional Heisenberg Antiferromagnets
• Peierls Distortion in Two-Dimensional Tight-Binding Model
• Ground-state properties of two-dimensional dimerized Heisenberg models
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Cited by in corpus (2)

• Theory of triangular lattice quasi-one-dimensional charge-transfer solids
• Phase diagram of spin-$1$ chains with Dzyaloshinskii-Moriya interaction