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Physical review. B, Condensed matter

Spin-1 XXZ chains in a staggered magnetic field

匡良 塚野, K. Nomura

Published Apr 1, 1998• 9 citations
Publisher

Abstract

Phase transitions of the spin-1 $\mathrm{XXZ}$ chain with a single-ion anisotropy in a staggered magnetic field are studied. We obtain interesting phase diagrams consisting of ferromagnetic, partially ferromagnetic, $XY,$ antiferromagnetic (AF) and large-$D$ phases. By using the twist-boundary-condition method, a Gaussian critical line is found between the AF phase and the large-$D$ phase. A multicritical point lies among the $XY,$ AF and large-$D$ phases. An Ashkin-Teller type of bifurcation does not appear.

DOI
10.1103/physrevb.57.r8087

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Journal of the Physical Society of Japan•Oct 15, 1996•138 citations
Phase transitions of the spin-1 XXZ\mathrm{XXZ}XXZ chain with a single-ion anisotropy in a staggered magnetic field are studied. We obtain interesting phase diagrams consisting of ferromagnetic, partially ferromagnetic, XY,XY,XY, antiferromagnetic (AF) and large-DDD phases. By using the twist-boundary-condition method, a Gaussian critical line is found between the AF phase and the large-DDD phase. A multicritical point lies among the XY,XY,XY, AF and large-DDD phases. An Ashkin-Teller type of bifurcation does not appear.
Phase diagram of S=1 XXZ chain in a staggered magnetic field is obtained numerically. The Berezinskii-Kosterlitz-Thouless transition between the XY and the antiferromagnetic phases is studied by the level-spectroscopy. Moreover we find that there is no distinction between the Haldane and the antiferromagnetic phases, since the Gaussian critical line does not appear, in contrast to the S=1/2S=1/2S=1/2 case. It is expected that some hidden Z2×Z2Z_2\times Z_2Z2​×Z2​ symmetry breaking happens not only in the Haldane phase but also in the antiferromagnetic one.
The phase diagram of the XXZ chain is calculated under the influence of homogeneous and staggered magnetic fields. The model has a rich phase structure with three types of phases. A fully ferromagnetic phase, an antiferromagnetic phase and a massless phase with partial ferromagnetic and antiferromagnetic order. This massless phase's critical fluctuations are governed by a conformal field theory with central charge c=1. When the sigma z -anisotropy Delta is zero the model is exactly integrable through a Jordan-Wigner fermionization and our results are analytic. For Delta not=0 our analysis is done numerically using lattice sizes up to M=20. Our results show that for -1<or= Delta < square root (2/2) the staggered magnetic field perturbation is relevant, whereas for square root (2/2)< Delta <or=1 it is irrelevant. In the region of relevant perturbations, we show that the massive continuum field theory associated with the model, has the same mass spectrum as the sine-Gordon model.
We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.
One-dimensional S=1S=1S=1 XXZ\mathrm{XXZ}XXZ chains with uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite-size systems. The numerical data are analyzed using conformal field theory, the level spectroscopy, phenomenological renormalization-group, and finite-size scaling method. We thus present a quantitatively reliable ground-state phase diagram of this model. The ground states of this model contain the Haldane phase, large-D phase, N\'eel phase, two XY\mathrm{XY}XY phases, and the ferromagnetic phase. There are four different types of transitions between these phases: the Brezinskii-Kosterlitz-Thouless-type transitions, the Gaussian-type transitions, the Ising-type transitions, and the first-order transitions. The locations of these critical lines are accurately determined.
Exotic criticality in the dimerized spin-1 XXZXXZXXZ chain with single-ion anisotropy
We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-DDD, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.
Ground-state properties of the spin-1 antiferromagnetic Heisenberg chain with bond alternation and uniaxial single-ion-type anisotropy, which is described by the Hamiltonian \({\cal H}_0 = \sum_{\ell=1}^N\{1-(-1)^\ell\alpha\}{\mib S}_\ell\cdot{\mib S}_{\ell+1} + D\sum_{\ell=1}^N\;(S_\ell^z)^2\) (0.0 ≤α≤1.0, -∞< D < ∞), are studied. An exact diagonalization method by means of the Lanczös technique is used. The ground-state phase diagram on the α versus D plane at the thermodynamic limit is determined by analyzing the Binder parameters associated with Néel order and z -direction string order for finite-size ( N = 6, 8, …, 16) chains. It is found that there exists a multicritical point at which the Haldane, Néel, and singlet-dimer phases meet and that the singlet-dimer phase and the large- D phase belong to the same unique phase. The ground-state magnetization curves at the thermodynamic limit for various values of α and D are obtained for the system described by the Hamiltonian, H 0 plus the Zeeman term - H ∑ ℓ=1 N S ℓ z . The results show that the 1/2-plateau appears in the magnetization curve at least when D ≥0.0 and 0.0≲α≤1.00.0\lesssim\alpha \leq 1.00.0≲α≤1.0.