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Progress of Theoretical Physics Supplement

Finite-Field Ground State of anS= 1 Anisotropic Antiferromagnetic Chain

Takashi Tonegawa, Kouichi Okunishi, Tôru Sakai, Makoto Kaburagi

Published Jan 1, 2005• 7 citations
Publisher

Abstract

We investigate, using numerical methods, the finite-field ground-state properties of an S = 1 anisotropic antiferromagnetic chain described by the Hamiltonian . It is found that the magnetization jump anomaly (a first-order phase transition) appears in the ground-statemagnetization curve when Δ = 5.0 and −1.50 ≲ D ≲ 1.05; in a certain region of D, the jump starts from a finite value of the magnetization m per spin. We also find that the a second-order phase transition between commensurate and incommensurate gapless phases takes place in the finite-field ground state. The critical point of this transition as well as the values of m at the onset and end of the magnetization jump is summarized in the m versus D phase diagram.

DOI
10.1143/ptps.159.77

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We investigate, using numerical methods, the finite-field ground-state properties of an S = 1 anisotropic antiferromagnetic chain described by the Hamiltonian . It is found that the magnetization jump anomaly (a first-order phase transition) appears in the ground-statemagnetization curve when Δ = 5.0 and −1.50 ≲ D ≲ 1.05; in a certain region of D, the jump starts from a finite value of the magnetization m per spin. We also find that the a second-order phase transition between commensurate and incommensurate gapless phases takes place in the finite-field ground state. The critical point of this transition as well as the values of m at the onset and end of the magnetization jump is summarized in the m versus D phase diagram.
The ground-state magnetization process of the S=1S=1S=1 antiferromagnetic chain with the easy-axis single-ion anisotropy described by negative DDD is investigated. It is numerically found that a phase transition between two different gapless phases occurs at an intermediate magnetic field between the starting and saturation points of the magnetization for $\ensuremath{-}1.49<D<\ensuremath{-}0.35.$ The transition is similar to the spin flopping, but it is second order and not accompanied with any significant anomalous behaviors in the magnetization curve. We also present the phase diagrams in the $m\ensuremath{-}D$ and $H\ensuremath{-}D$ planes which reveal a possible re-entrant transition.
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Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic S=1S=1S=1 Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid phases as well as the spin-liquid and ferromagnetic phases. Analyzing spin-correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.
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.
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