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Journal of the Physical Society of Japan

Phase Diagram ofS=1/2 Quasi-One-Dimensional Heisenberg Model with Dimerized Antiferromagnetic Exchange

Nobuyuki Katoh, Masatoshi Imada

Published Dec 15, 1994• 56 citations
Publisher

Abstract

The quantum phase transition between a spin gap state and an antiferromagnetic phase is investigated. We study S =1/2 antiferromagnetic Heisenberg chains coupled by antiferromagnetic interchain interaction. The intrachain exchanges have alternating strength. The phase boundary between the antiferromagnetically ordered phase and a spin gap phase is also obtained in a parameter space of the amplitude of the interchain coupling and the dimerization. The spin-wave approximation substantially overestimates the antiferromagnetic phase. The competition between the long range order and the spin gap is examined in detail. We estimate a variety of critical exponents at the transition, namely, exponents ν, θ and z defined as the exponent of the correlation length, the magnetization curve and the dynamical exponent, respectively. From the quantum Monte Carlo simulation, the exponents ν, θ and z are estimated to be unity. The exponents ν and θ are different from the estimated values in one dimension. It suggests that the universality changes due to the dimensionality change. In our estimates, the exponent ν does not agree with the prediction from three dimensional classical Heisenberg model. We also discuss the relevance of our result to spin-Peierls systems with lattice distortion.

DOI
10.1143/jpsj.63.4529

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The quantum phase transition between a spin gap state and an antiferromagnetic phase is investigated. We study S =1/2 antiferromagnetic Heisenberg chains coupled by antiferromagnetic interchain interaction. The intrachain exchanges have alternating strength. The phase boundary between the antiferromagnetically ordered phase and a spin gap phase is also obtained in a parameter space of the amplitude of the interchain coupling and the dimerization. The spin-wave approximation substantially overestimates the antiferromagnetic phase. The competition between the long range order and the spin gap is examined in detail. We estimate a variety of critical exponents at the transition, namely, exponents ν, θ and z defined as the exponent of the correlation length, the magnetization curve and the dynamical exponent, respectively. From the quantum Monte Carlo simulation, the exponents ν, θ and z are estimated to be unity. The exponents ν and θ are different from the estimated values in one dimension. It suggests that the universality changes due to the dimensionality change. In our estimates, the exponent ν does not agree with the prediction from three dimensional classical Heisenberg model. We also discuss the relevance of our result to spin-Peierls systems with lattice distortion.
The S=1/2S=1/2S=1/2 and S=1S=1S=1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S=1,S=1,S=1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.
The zero and finite temperature spin-Peierls transitions in a quasi-one-dimensional spin-12\frac{1}{2}21​ 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 N\'eel 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 N\'eel 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 Tc{T}_{c}Tc​ shows a second order phase transition. The variation of the equilibrium bond length distortion ${\ensuremath{\delta}}_{eq}$ with temperature showed a power law relation which decayed to zero as the temperature was increased to Tc{T}_{c}Tc​, indicating a continuous transition from the dimerized phase to a paramagnetic phase with uniform bond length and zero antiferromagnetic susceptibility.
We investigate a one-dimensional S=1S=1S=1 antiferromagnetic Heisenberg model coupled to a lattice distortion by a quantum Monte Carlo method. Investigating the ground-state energy of the static bond-alternating chain, we find that the instability to a dimerized chain depends on the value of the spin-phonon coupling, unlike the case of S=12.S=\frac{1}{2}.S=21​. The spin state is the dimer state or the uniform Haldane state depending on whether the lattice distorts or not, respectively. At an intermediate value of the spin-phonon coupling, we find the first-order transition between the two states. We also find the coexistence of the two states.
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Quasi-one-dimensional quantum antiferromagnets formed by a ddd-dimensional hypercubic lattice of weakly coupled spin- 12\frac{1}{2}21​ antiferromagnetic Heisenberg chains are studied by combining exact results in one-dimension and renormalization group analyses of the interchain correlations. It is shown that ddd-dimensional magnetic long-range order develops at zero temperature for infinitesimal antiferromagnetic or ferromagnetic interchain couplings. In the presence of weak bond alternations, the order-disorder transition occurs at a finite interchain coupling. Relevances to the lightly doped quantum antiferromagnets and multilayer quantum Hall systems are discussed.