Physical review. B, Condensed matter

Kosterlitz-Thouless transition in a quantum spin-1 Heisenberg chain

Juan Pablo Neirotti, Mário J. de Oliveira

Published Feb 1, 1999• 2 citations

Abstract

A density-matrix renormalization-group study of the Kosterlitz-Thouless transition in the anisotropic antiferromagnetic spin-1 Heisenberg chain is presented. The numerical value of the critical anisotropic parameter is found to be, within statistical errors, in agreement with the numerical value conjectured by Alcaraz and Moreo.

DOI: 10.1103/physrevb.59.3303

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Physical review. B, Condensed matter

Kosterlitz-Thouless transition in a quantum spin-1 Heisenberg chain

Juan Pablo Neirotti, Mário J. de Oliveira

Published Feb 1, 1999• 2 citations

Publisher

Abstract

DOI: 10.1103/physrevb.59.3303

Related papers

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D. Peters, Ian P. McCulloch, Walter Selke

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Quantum anisotropic Heisenberg chains with superlattice structure: A DMRG study

Jereson Silva-Valencia, J. C. Xavier, E. Miranda

Using the density matrix renormalization group technique, we study spin superlattices composed of a repeated pattern of two spin- $\frac{1}{2}\phantom{\rule{0.3em}{0ex}}XXZ$ chains with different anisotropy parameters. The magnetization curve can exhibit two plateaus, a nontrivial plateau with the magnetization value given by the relative sizes of the subchains and another trivial plateau with zero magnetization. We find good agreement of the value and the width of the plateaus with the analytical results obtained previously. In the gapless regions away from the plateaus, we compare the finite-size spin gap with the predictions based on bosonization and find reasonable agreement. These results confirm the validity of the Tomonaga-Luttinger liquid superlattice description of these systems.Using the density matrix renormalization group technique, we study spin superlattices composed of a repeated pattern of two spin-$\frac{1}{2}\phantom{\rule{0.3em}{0ex}}XXZ$ chains with different anisotropy parameters. The magnetization curve can exhibit two plateaus, a nontrivial plateau with the magnetization value given by the relative sizes of the subchains and another trivial plateau with zero magnetization. We find good agreement of the value and the width of the plateaus with the analytical results obtained previously. In the gapless regions away from the plateaus, we compare the finite-size spin gap with the predictions based on bosonization and find reasonable agreement. These results confirm the validity of the Tomonaga-Luttinger liquid superlattice description of these systems.

arXiv:cond-mat/0501419Physical Review BJan 12, 200517 citations

We numerically investigate the critical behavior of the spin-

(1,\frac{1}{2})

Heisenberg ferrimagnet with anisotropic exchange coupling in a magnetic field. A quantized magnetization plateau as a function of the field, appearing at a third of the saturated magnetization, is stable over the whole antiferromagnetic coupling region. The plateau vanishes in the ferromagnetic coupling region via the Kosterlitz-Thouless transition. Comparing the quantum and classical magnetization curves, we elucidate what are essential quantum effects.

A Kosterlitz-Thouless phase transition in the ground state of an antiferromagnetic spin-

\frac{1}{2}

Heisenberg chain with nearest and next-nearest-neighbor interactions is re-investigated from a different perspective: An unequivocal correspondence is found between components of the scalar product

\langle Ψ_0| Ψ_0 \rangle

and geometrical objects. One can classify these objects according to whether any two of them can be transformed into each other in a continuous way (belong to the same homotopy class). A finite size scaling of the "connection term``

\langle Ψ_0|\partial Ψ_0 \rangle

with respect to chain length (16, 18, 20, 22, 24 spins) for each homotopy class of above mentioned objects leads to the critical value of

λ

with rather high accuracy.

In this paper we study a frustrated antiferromagnetic isotropic Heisenberg S=1 quantum spin chain H=${\ensuremath{\sum}}_{\mathrm{i}}$

{\mathbf{S}}_{\mathrm{i}}

{\mathbf{S}}_{\mathrm{i}+1}

+\ensuremath{\alpha}${\ensuremath{\sum}}_{\mathrm{i}}$

{\mathbf{S}}_{\mathrm{i}}

{\mathbf{S}}_{\mathrm{i}+2}

, using a variational ansatz starting from valence bond states and the density-matrix renormalization group. We find both methods to give results in very good qualitative and good quantitative agreement, which clarify the phase diagram as follows: At ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{D}}$=0.284(1), there is a disorder point of the first kind, marking the onset of incommensurate spin-spin correlations in the chain. At ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{L}}$=0.3725(25) there is a Lifshitz point, at which the excitation spectrum is found to develop a particular doubly degenerate structure. These points are the quantum remnants of the transition from antiferromagnetic to spiral order in the classical frustrated chain. At ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{T}}$=0.7444(6) there is a first-order phase transition from an Affleck-Kennedy-Lieb-Tasaki (AKLT) phase characterized by nonvanishing string order to a phase which can be understood as a next-nearest-neighbor generalization of the AKLT model. At the transition, the string order parameter shows (to numerical precision) a discontinuous jump of 0.085 to zero; the correlation length and the gap are both finite at the transition. The problem of edge states in open frustrated chains is discussed at length.

Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic

S=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.

Using the density matrix renormalization group technique, we study spin superlattices composed of a repeated pattern of two spin-

\frac{1}{2}\phantom{\rule{0.3em}{0ex}}XXZ

chains with different anisotropy parameters. The magnetization curve can exhibit two plateaus, a nontrivial plateau with the magnetization value given by the relative sizes of the subchains and another trivial plateau with zero magnetization. We find good agreement of the value and the width of the plateaus with the analytical results obtained previously. In the gapless regions away from the plateaus, we compare the finite-size spin gap with the predictions based on bosonization and find reasonable agreement. These results confirm the validity of the Tomonaga-Luttinger liquid superlattice description of these systems.