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arXiv:cond-mat/0504125 · Journal of the Physical Society of Japan

Emergence of Long Period Antiferromagnetic Orders from Haldane Phase in S=1 Heisenberg Chains with D-Modulation

Kazuo Hida, Wei Chen

Published Jul 1, 2005• 12 citations
arXivHTMLPDF

Abstract

The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Neel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Neel orders. The investigation of the model with longer period D-modulation also confirms this picture.

DOI
10.1143/jpsj.74.2090

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The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Neel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Neel orders. The investigation of the model with longer period D-modulation also confirms this picture.
We investigate ground-state and low-lying excited states of the S = 1 antiferromagnetic Heisenberg chain with exchange anisotropy, single-ion anisotropy and biquadratic exchange and with free boundary conditions. We present an approximate mapping of the S = 1 model to an effective S = 1/2 chain in an external magnetic field, which can be solved exactly in several limiting cases. We obtain results for the phase diagram, correlation functions and the excitation spectrum. The transition to the Haldane phase is related to the condensation of the lowest soliton modes and the hidden order parameter of the Haldane phase is identified as transverse long-range order in the effective S = 1/2 chain.
The ground state properties of the high spin Heisenberg chains with alternating single site anisotropy are investigated by means of the numerical exact daigonaization and DMRG method. It is found that the ferrimagnetic state appears between the Haldane phase and period doubled Néel phase for the integer spin chains. On the other hand, the transition from the Tomonaga-Luttinger liquid state into the ferrimagnetic state takes place for the half-odd-integer spin chains. In the ferrimagnetic phase, the spontaneous magnetization varies continuously with the modulation amplitude of the single site anisotropy. Eventually, the magnetization is locked to fractional values of the saturated magnetization. These fractional values satisfy the Oshikawa-Yamanaka-Affleck condition. The local spin profile is calculated to reveal the physical nature of each state. In contrast to the case of frustration induced ferrimagnetism, no incommensurate magnetic superstructure is found.
The ground state properties of the high spin Heisenberg chains with alternating single site anisotropy are investigated by means of the numerical exact daigonaization and DMRG method.It is found that the ferrimagnetic state appears between the Haldane phase and period doubled Néel phase for the integer spin chains.On the other hand, the transition from the Tomonaga-Luttinger liquid state into the ferrimagnetic state takes place for the half-odd-integer spin chains.In the ferrimagnetic phase, the spontaneous magnetization varies continuously with the modulation amplitude of the single site anisotropy.Eventually, the magnetization is locked to fractional values of the saturated magnetization.These fractional values satisfy the Oshikawa-Yamanaka-Affleck condition.The local spin profile is calculated to reveal the physical nature of each state.In contrast to the case of frustration induced ferrimagnetism, no incommensurate magnetic superstructure is found.
The ground-state phase diagram of S=2S=2S=2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-DDD, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
The ground state of the ferromagnetic-antiferromagnetic alternating spin-1/2 Heisenberg chain is studied with Ising-type anisotropy on the ferromagnetic bond. This model tends to the spin-1 antiferromagnetic Heisenberg chain with on-site anisotropy in the limit of strong ferromagnetic bond. It is found that the Haldane-gap phase, the large-D phase, and the two types of N\'eel phases appear as the ground state of this model. The duality relations between these four phases are proved for several limiting cases. The string order parameter characterizing the large-D phase is introduced based on these duality relations. The ground-state phase diagram is determined by the numerical diagonalization of the finite-size system.
The ground-state phase diagram of a frustrated S=1 Heisenberg spin chain with uniaxial single-ion-type anisotropy is studied using the infinite-system density-matrix renormalization-group method. Particular attention is paid to "chiral" phases, in which the long-range order parameter is a vector chirality. It is found that, in addition to the Haldane, large-D (LD), and double-Haldane phases, the phase diagram includes three different chiral phases, i.e., the gapless chiral, chiral-Haldane, and chiral-LD phases. These chiral phases are distinguished from each other by the energy gap and the string long-range order.