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Journal of the Physical Society of Japan

High-Field Phase Transitions in Integrable Quantum Spin Chains

Hirohito Kiwata, Yasuhiro Akutsu

Published Dec 15, 1994• 11 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.63.4269

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Modern Physics Letters B•Dec 30, 1997•1 citation
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.
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.
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 effect of the external electric field and/or the external strain on the low-temperature behavior of the quantum spin chain model is studied. The external electric field or the strain can cause the quantum magnetic structural phase transition between two magnetically ordered phases with different order parameters. Such a quantum critical point can be observed in the special behavior of the low-temperature specific heat: At the critical value the low-temperature specific heat manifests linear in temperature behavior instead of the exponentially small one for other values of the field. The magnetic susceptibility also manifests the special behavior, in which quantum phase transitions are revealed.
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。
We study the quantum critical behavior in the antiferromagnetic Heisenberg chain and two-leg Heisenberg ladder resulting from the application of an external magnetic field. In each of these systems a finite-temperature crossover line between two different ferromagnetic phases ends with a quantum critical point at zero temperature. Using the bond-mean-field theory, we calculate the field dependence of the magnetization and the mean-field spin bond parameters in both systems. For the Heisenberg chain, we recover the existing exact results and show in addition that the saturation of the zero-temperature magnetization at the field hc=2J{h}_{c}=2Jhc​=2J is accompanied by a quantum phase transition, where the bond parameter vanishes. Here JJJ is the exchange coupling constant along the chain. For the two-leg ladder, we also recover the known results, like the two magnetization plateaus, and show that at the upper critical field, which corresponds to the appearance of the saturation magnetization plateau, the chain and rung spin bond parameters vanish. The identification of the order parameters that govern the field-induced quantum criticality in the systems we study here constitutes an original contribution. Because no long-range order, which breaks symmetry, characterizes the bond order, the latter could be a proposal for the so-called hidden order. We calculate analytically the bond parameters in both systems as functions of the field in the low- and high-field limits at zero temperature. At nonzero temperatures, the calculation of the magnetization and bond parameters is carried out by solving the mean-field equations numerically.
We study the magnetization process of the S=1 XXZ chain with biquadratic exchange interaction at zero temperature. This system can be regarded as a quantum lattice gas composed of "particles" with Sz=0, ±1. We introduce an approximate nested Bethe ansatz (ANBA) to examine the possibility of phase transition induced by the magnetic field. In the high-magnetization region σ≥σ0 for certain σ0, the ANBA gives the exact ground state energies. For σ<σ0 the ANBA gives approximate solutions. The analysis shows that a phase transition occurs at σ0 across which the magnetic susceptibility changes discontinuously. Comparing with the finite-size diagonalization, we argue that σ0 is the exact critical magnetization.