Néel to spin-Peierls transition in a quasi-one-dimensional 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 Néel state to a spin-gapped Peierls state is studied in the parameter space spanned by spatial anisotropy, interchain coupling strength, and spin-lattice coupling strength. It is found that for any finite interchain coupling, the transition to a dimerized Peierls ground state only occurs when the spin-lattice coupling exceeds a finite, nonzero critical value. This is in contrast to the pure 1D model (zero interchain coupling), where adiabatic/classical phonons lead to a dimerized ground state for any nonzero spin-phonon interaction. The phase diagram in the parameter space shows that for a strong interchain coupling, the relation between the interchain coupling and the critical value of the spin-phonon interaction is linear whereas for weak interchain coupling, this behavior is found to have a natural logarithmlike relation. No region was found to have a long range magnetic order and dimerization occurring simultaneously. Instead, the Néel 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 δ 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.

Theory of triangular lattice quasi-one-dimensional charge-transfer solids

“…As mentioned above, simple spin-Peierls transition or VBS formation, as have been suggested within the effective 1 2 -filled model 55 , cannot be the origin of the observed SG in κ-B(CN) 4 [64][65][66] . The recent demonstration that the driving forces behind the apparent SL-like behavior in β ′ -EtMe 3 Sb[Pd(dmit) 2 ] 2 are charge and lattice fluctuations 24 , which are precluded in the 1 2 -filled band but are expected within the 1 4 -filled band characterization of the system 5 , gives a hint to the mechanism of the SG in κ-B(CN) 4 .…”

“…The large ratio of inter-chain to intra-chain hopping, ∼ 0.6 in κ-B(CN) 4 , implies absence of 1D nesting necessary for the spin-Peierls transition characteristic of quasi-1D systems (note here that spin-density wave, and not the spin-Peierls state characterizes the spatial broken symmetry in (TMTSF) 2 X where the same ratio at 0.2 is significantly smaller). It is also known from previous theoretical work that the Hubbard repulsion severely reduces bond dimerization in the 2D half-filled band even where nesting would have permitted this in the uncorrelated limit 64,65 . The VBS is also precluded theoretically within the triangular lattice 1 2 -filled band Hubbard model 66 .…”

Phase diagram of spin-1 chains with Dzyaloshinskii-Moriya interaction

“…Haldane's work 1,2 on quantum spin-1 chains has led to one of the first examples of a symmetry-protected topological phase. Indeed, the conjectured existence of a finite gap between the ground state and the excited states in antiferromagnetic spin-S Heisenberg chains with integer S has sparked a substantial research activity in integer-spin chains, mostly by means of numerical studies based on Monte Carlo simulations [3][4][5][6][7][8][9] or the Density Matrix Renormalization Group (DMRG). [10][11][12][13][14] It has also motivated experimentalists to search for host materials for spin-1 chains, and those were eventually realized in AgVP 2 S 6 [15][16][17][18] , SrNi 2 V 2 O 8 , [19][20][21] or CsNiCl 3 .…”