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理论物理通讯：英文版

Soliton Lattice State of Spin—1／2 Antiferromagnetic Chain in an External Magnetic Field

WANGZhi-Guo, ZHANGYu-Mei

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

One-dimensional spin-1-2 anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure.The magnetization and the energy of the ground state which depend on the external magnetic field are calculated.For the case of anisotropic parameter △＞△0,increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state,until to an another critical field where the ground state changes to the canted state phase.Therefore,with increasing external magnetic field,the ground state experiences four different phases successively,namely,antiferromagnetic Ising,soliton lattice state canted state,and magnetization saturated phases.When △＜△0,the soliton lattice state phase does not appear,with increasing external field,the paramagnetic phase smoothly evolves into the canted state phase,finally reaches magnetization saturated phase.

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Physical review. B, Condensed matter•Aug 1, 1992•9 citations
One-dimensional spin-1-2 anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure.The magnetization and the energy of the ground state which depend on the external magnetic field are calculated.For the case of anisotropic parameter △＞△0,increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state,until to an another critical field where the ground state changes to the canted state phase.Therefore,with increasing external magnetic field,the ground state experiences four different phases successively,namely,antiferromagnetic Ising,soliton lattice state canted state,and magnetization saturated phases.When △＜△0,the soliton lattice state phase does not appear,with increasing external field,the paramagnetic phase smoothly evolves into the canted state phase,finally reaches magnetization saturated phase.
Soliton Lattice State of Spin-12\frac{1}{2}21​ Antiferromagnetic Chain in an External Magnetic Field
One-dimensional spin- anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure. The magnetization and the energy of the ground state which depend on the external magnetic field are calculated. For the case of anisotropic parameter , increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state, until to an another critical field where the ground state changes to the canted state phase. Therefore, with increasing external magnetic field, the ground state experiences four different phases successively, namely, antiferromagnetic Ising, soliton lattice state canted state, and magnetization saturated phases. When , the soliton lattice state phase does not appear, with increasing external field, the paramagnetic phase smoothly evolves into the canted state phase, finally reaches magnetization saturated phase.
In this work we study the Heisenberg XXZ antiferromagnetic model for spin S and dimension d in the presence of an external longitudinal magnetic field. First, we essay a variational approach which uses as trial function a version of the analytic expression for the ground state given by the paired nonmagnetic excitation (PNME) theory [M. Lagos and G. G. Cabrera, Solid State Commun. 67, 221 (1988); Phys. Rev. B 38, 659 (1988)], generalized in order to incorporate the external field. The ground-state energy, sublattice magnetization, and magnetic susceptibility are obtained. Subsequently, we solve the problem numerically for a chain of 12 spins (S=1 and S=3/2) using the Lancz\"os method [E. Dagotto and A. Moreo, Phys. Rev. D 31, 865 (1985)]. The two approaches give excellent concordance over a wide range of the parameters of the model. We show that our analytic trial function represents accurately the ground state of the system for anisotropies ranging from the Ising limit to the almost isotropic Heisenberg model for all values of the field. Moreover, it accounts for the several antiferromagnetic and ferromagnetic phases occurring for different values of the magnetic field with the same precision. The critical fields of the transitions are predicted correctly. Also, results for various spin values S in two and three dimensions are presented.
The critical properties of the one-dimensional spin-1/2 transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility was used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J_{2}, we calculated the fidelity susceptibility as a function of the transverse field B_{x} and the longitudinal field B_{z}. The phase diagram in the (B_{x},B_{z})-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For B_{x}<1, we observed an antiferromagnetic phase for small values of B_{z} and a paramagnetic phase for large values of B_{z}. For B_{x}>1 and low B_{z}, we found a disordered phase that undergoes a second-order phase transition to a paramagnetic phase for large values of B_{z}.
We calculate energies and wave functions of S=1 antiferromagnetic Heisenberg chains with single-ion anisotropy in a symmetry-breaking external magnetic field. From results for the string correlation function for low-lying excited states we identify these states as solitons with respect to the hidden string order. For finite anisotropic chains we investigate the transition to the fully magnetized state at high magnetic fields and conclude that Bose condensation in an external magnetic field occurs also for the anisotropic chain.
We present a variational approach to the Heisenberg antiferromagnetic model for spin 1/2 and anisotropic exchange, with an external longitudinal and transverse magnetic field. In the one-dimensional case, we calculate exactly with our trial function the expectation values of energy, sublattice magnetization, and magnetic susceptibility. On minimizing the energy, we obtain several phases, which depend on the strength of the field and anisotropy parameter. Subsequently we approach the problem numerically and solve it for a chain of 12 spins using the Lanczos method. The two approaches are in excellent concordance, particularly for the critical fields of the transitions, over a wide range of the parameters of the model. Beside its precision and mathematical simplicity, the method has the important advantage of accounting for the different magnetic phases and their transitions with a single trial function that has a compact mathematical expression. The formalism is expected to work better in higher dimensions, but the corresponding calculations are omitted because of the lack of numerical field-dependent data with which to compare.