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Journal of Physics Condensed Matter

Estimation of the critical magnetic field of the phase transition for an S=1 quantum spin chain

Hirohito Kiwata

Published Oct 9, 1995• 5 citations
Publisher

Abstract

It has been shown that there exists an additional magnetic phase transition of the magnetization curve for the S=1 SU(3) antiferromagnetic spin chain at zero temperature. As a the magnetic field decreases from the saturation field, there is a phase change at a critical field h c , where the magnetization curve versus the magnetic field has a cusp. The critical field is a boundary between two states, one of which contains the particles with the spin +1 and 0 and the other with the spin +1, 0 and -1. In this paper we estimate the critical field h c of the phase transition by examining the stability of these states.

DOI
10.1088/0953-8984/7/41/008

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It has been shown that there exists an additional magnetic phase transition of the magnetization curve for the S=1 SU(3) antiferromagnetic spin chain at zero temperature. As a the magnetic field decreases from the saturation field, there is a phase change at a critical field h c , where the magnetization curve versus the magnetic field has a cusp. The critical field is a boundary between two states, one of which contains the particles with the spin +1 and 0 and the other with the spin +1, 0 and -1. In this paper we estimate the critical field h c of the phase transition by examining the stability of these states.
We study the integrable SU( M ) and SU q ( M ) quantum spin chains in the high-magnetic-field region at zero temperature. For M =4 we found second-order phase transitions at two different fields, H 1 and H 2 . At both transition points, the magnetization curve versus magnetic field has cusps with discontinuities in the magnetic susceptibility. We clarify the mechanism of the phase transitions, from which we conclude that the SU( M ) and S U q ( M ) quantum spin chains undergo ( M -2) times field-induced phase transitions at zero temperature.
The zero-temperature magnetization curve of the S =1 antiferromagnetic XXZ chain with partial integrability is studied by the Bethe ansatz, combined with a numerical renormalization-group method. We find a magnetic first-order phase transition; the magnetization curve shows a discontinuity at a critical field h c . Due to the partial integrability, the low-field curve and the high-field curve each correspond to a part of the magnetization curve of the S=12S=\frac12S=21​XXZ chain. We conclude that the obtained magnetization curve is exact in the whole range of the magnetic field.
The ground-state magnetization curve around the critical magnetic field Hc{H}_{c}Hc​ of quantum spin chains with a spin gap is investigated. We propose a size scaling method to estimate the critical exponent \ensuremath{\delta} defined as $m\ensuremath{\sim}|H\ensuremath{-}{H}_{c}{|}^{1/\ensuremath{\delta}}$ from finite cluster calculation. The applications of the method to the S=1S=1S=1 antiferromagnetic chain and S=1/2S=1/2S=1/2 bond-alternating chain lead to a common conclusion that $\ensuremath{\delta}=2.$ The same result is derived for both edges of the magnetization plateau of the S=3/2S=3/2S=3/2 antiferromagnetic chain with single-ion anisotropy.
We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain in magnetic fields, using the density-matrix renormalization-group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process $(M\ensuremath{-}H$ curve): the saturation field, the lower critical field associated with excitation gap, and the field at the middle-field cusp singularity. We calculate magnetization, susceptibility, and specific heat of the zigzag chain in magnetic fields at finite temperatures, and then discuss how the calculated quantities reflect the low-lying excitations of the system related with the critical behaviors in the $M\ensuremath{-}H$ curve.
The S=1 quantum spin chain with equal Heisenberg and biquadratic exchange was shown by Sutherland to be integrable. In this paper the equations obtained by Sutherland are solved numerically to obtain the behaviour at zero temperature in a magnetic field. It is found that there is an additional phase change at a lower field than the spin flop field. This new phase change marks the boundary between a regime in which the ground state contains only atoms with S z =1, 0 and one in which 1, 0 and -1 are present. The form of the elementary excitations in the two regimes is discussed and the possibility of a similar phase change in the pure Heisenberg model is considered.
We study the magnetic properties of one-dimensional multicomponent quantum system in the presence of external fields at zero temperature. We show a general method of calculating the differentiation of energy with respect to the sum of integration of root-density distribution functions in terms of the dressed energy and the dressed charge matrix. Using these analytic formulas, we investigate the ground-state magnetic properties of the SU (M) quantum spin chain. It has been already shown that the magnetization curve versus magnetic field of the SU (M) spin chain undergoes multiple phase transitions. These correspond to discontinuities of the magnetic susceptibility. Introducing imaginary fields and taking zero limit of the imaginary fields, we calculate the critical field h_e and the magnetic susceptibility at h_e.|絶対零度における1次元多成分量子系の磁気的性質を調べた。SU(M)量子スピン鎖の磁化曲線は折れ曲がり構造をとることがすでに示されている。我々の考えた方法を用いて折れ曲がりの起こる臨界磁場とそこにおける磁化率を求めた。