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arXiv:1005.0711 · Physical Review B

Quantum phase transitions in three-leg spin tubes

D. Charrier, Sylvain Capponi, Masaki Oshikawa, Pierre Pujol

Published Aug 6, 2010• 23 citations
arXivHTMLPDF

Abstract

We investigate the properties of a three-leg quantum spin tube using several techniques such as the density-matrix renormalization-group (DMRG) method, strong-coupling approaches and the nonlinear sigma model. For integer $S$, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of $2S$ phase transitions. They can be accurately identified by the behavior of a nonlocal string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions is further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases $S=1$. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first-order phase transition but at the close proximity of a tricritical point separating a gapless and a first-order transition line in the phase diagram of the quantum spin tube.

DOI
10.1103/physrevb.82.075108

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We investigate the properties of a three-leg quantum spin tube using several techniques such as the density-matrix renormalization-group (DMRG) method, strong-coupling approaches and the nonlinear sigma model. For integer SSS, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of 2S2S2S phase transitions. They can be accurately identified by the behavior of a nonlocal string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions is further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases S=1S=1S=1. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first-order phase transition but at the close proximity of a tricritical point separating a gapless and a first-order transition line in the phase diagram of the quantum spin tube.
We study the ground-state properties of three-leg S = 1/2 Heisenberg tube with antiferromagnetic interleg couplings J ⊥ (> 0). The spin gap, dimerization-order parameter, and Berry phase are calculated with the density-matrix renormalization group method. We find that the system is spontaneously dimerized and all the spin excitations are gapped whether intraleg couplings J || are antiferromagnetic or ferromagnetic. Also, the phase diagram is divided into three regimes according to topological configuration of the spin-singlet pairs: (i) Haldane-gap-like regime for J ⊥ / J || < 0, (ii) intraleg-singlet regime 0 < J ⊥ J || ≤ 5, and (iii) intrarung-singlet regime for J ⊥ J || ≥ 5.
We investigate quantum phase transitions of the S=12S=\frac{1}{2}S=21​ three-leg antiferromagnetic spin tube with asymmetric interchain (rung) exchange interactions. On the basis of the electron tube system, we propose a useful effective theory to give the global phase diagram of the asymmetric spin tube. In addition, using other effective theories we raise the reliability of the phase diagram. The density-matrix renormalization-group and the numerical diagonalization analyses show that the finite spin gap appears in a narrow region around the rung-symmetric line, in contrast to a recent paper by Nishimoto and Arikawa, [Phys. Rev. B 78, 054421 (2008)]. The numerical calculations indicate that this global phase diagram obtained by use of the effective theories is qualitatively correct. In the gapless phase on the phase diagram, the numerical data are fitted by a finite-size scaling in the c=1c=1c=1 conformal field theory. We argue that all the phase transitions between the gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless universality class.
We investigate the S = 1/2 three-leg spin tube, which is the simplest spin nanotube, using the density matrix renormalization group (DMRG) and the numerical exact diagonalization (ED), conbined with a finite-size scaling analysis. Particularly, we intruduce the lattice distortion from the regular triangle unit to the isosceles one. In our previous works, we revealed that the S = 1/2 isosceles triangle spin tube exhibits following exotic quantum phenomena: the quantum phase transition between the spin gapped and gapless spin liquid phases, the 1/3 magnetization plateau due to two different mechanisms, and a new phase between the two plateau phases where the translational symmetry is spontaneously broken. We briefly review these results and show our new calculation of the expectation value of the magnetization at each site to specify the spin structure in the new field induced phase.
We study the ground-state phase diagram of a frustrated spin-1/2 four-leg tube. Using a variety of complementary techniques, namely, density matrix renormalization group, exact diagonalization, Schwinger boson mean-field theory, quantum Monte Carlo, and series expansion, we explore the parameter space of this model in the regime of all-antiferromagnetic exchange. In contrast to unfrustrated four-leg tubes, we uncover a rich phase diagram. Apart from the Luttinger liquid fixed point in the limit of decoupled legs, this comprises several gapped ground states, namely, a plaquette, an incommensurate, and an antiferromagnetic quasispin-2 chain phase. The transitions between these phases are analyzed in terms of total energy and static structure factor calculations and are found to be of (weak) first order. Despite the absence of long-range order in the quantum case, remarkable similarities to the classical phase diagram are uncovered, with the exception of the icommensurate regime, which is strongly renormalized by quantum fluctuations. In the limit of large leg exchange, the tube exhibits a deconfinement crossover from gapped magnon-like excitations to spinons.
We study quantum phase transitions in the asymmetric variation of the three-leg Heisenberg tube for half-odd-integer spin, with a modulation of one of the rung exchange couplings ${J}_{\ensuremath{\perp}}^{\ensuremath{'}}$ while the other two are kept constant ${J}_{\ensuremath{\perp}}$. We focus on the strong rung-coupling regime ${J}_{\ensuremath{\perp}}\ensuremath{\gg}{J}_{\ensuremath{\parallel}}$, where ${J}_{\ensuremath{\parallel}}$ is the leg coupling, and analyze the effective spin-orbital model with a transverse crystal field in detail. Applying the Abelian bosonization to the effective model, we find that the system is in the dimer phase for the general half-odd-integer-spin cases without the rung modulation; the phase transition between the dimer and Tomonaga-Luttinger-liquid phases induced by the rung modulation is of the SU(2)-symmetric Berezinskii-Kosterlitz-Thouless type. Moreover, we perform a level spectroscopy analysis for the effective model for spin-1/2 using exact diagonalization, to determine the precise transition point $|{J}_{\ensuremath{\perp}}^{\ensuremath{'}}\ensuremath{-}{J}_{\ensuremath{\perp}}|/{J}_{\ensuremath{\parallel}}\ensuremath{\sim}0.283$ in the strong rung-coupling limit. The presence of the dimer phase in a small but finite region is also confirmed by a density-matrix renormalization group calculation on the original spin-tube model.
Using density-matrix renormalization group calculations, we investigate the general phase diagram of the frustrated two-leg ladder with Heisenberg interactions along legs, rungs, and diagonals. We confirm that all antiferromagnetic gapped states belong to the same universality class as the Haldane phase. In a three-dimensional phase diagram, we determine a continuous surface with singularities in the string-order parameter or its first derivative, corresponding to a transition between two Haldane phases with different topological order. Some parts of this transition surface are critical with zero gap and vanishing string-order parameter. In the complementary parts, the transition is first order with finite gap and string order. The boundary of this surface with the ferromagnetic region is a critical end line, when the surface is critical, and a triple line anywhere else. Part of this boundary coincides with the exactly soluble model proposed by Dmitriev, Krivnov, and Ovchinnikov [Phys. Rev. B 56, 5985 (1997)].