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Journal of the Physical Society of Japan

Effect of a Symmetry-Breaking Field on the Ground State of the Spin-1/2 Antiferromagnetic Linear Chain

Shigeyoshi Mori, Jong-Jae Kim, Isao Harada

Published Sep 15, 1995• 19 citations
Publisher

Abstract

We investigate the ground-state property of the one-dimensional spin-1/2 antiferromagnetic X X Z chain in a symmetry-breaking field, by means of numerical diagonalization method for finite-size spin systems combined with the phenomenological renormalization group method. It is found that, with increasing field, there occurs the ground-state phase transition from an ordered phase to a disordered phase, whose critical property belongs to the universality class of the transverse Ising model. The ground-state phase diagram is determined in two parameter regions; (i) an Ising-like region and (ii) an X Y -like region. Our inspection of the field dependence of the energy gap and the static spin structure factors reveals that the ordered phase in both regions exhibits the characteristics of Néel order. Quantum nature of the ground state is also briefly discussed.

DOI
10.1143/jpsj.64.3409

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We have studied the antiferromagnetic Ising chain in a transverse magnetic field hx{h}_{x}hx​ and uniform longitudinal field hz.{h}_{z}.hz​. Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in (hx,hz){(h}_{x}{,h}_{z})(hx​,hz​) plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in hz{h}_{z}hz​ the scaling behavior of the mass gap in the vicinity of the critical point (hx=1/2,hz=0){(h}_{x}{=1/2,h}_{z}=0)(hx​=1/2,hz​=0) is established. It is found that the form of the transition line near the classical multicritical point (hx=0,hz=1){(h}_{x}{=0,h}_{z}=1)(hx​=0,hz​=1) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.
We study the S =1 antiferromagnetic Heisenberg chain with the anisotropies E ∑ j [( S j x ) 2 -( S j y ) 2 ] and D ∑ j ( S j x ) 2 in a magnetic field H along z -axis, using numerical diagonalization up to N =14 and the finite-size scaling and phenomenological renormalization. We give the phase diagrams in the H E and H D planes repectively at T =0. It is found that a magnetic field breaking the axial symmetry of the Hamiltonian brings about canted Néel order for H c1 < H < H c2 , if the system has the Haldane gap. The two transitions at H c1 and H c2 are revealed to belong to the same universality class as the two-dimensional Ising model. In addition it is found that even if the system is in the large- D phase ( D > D c ≈1), the same transitions occur in the region where the value of D is about 1.0∼1.5.
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