arXiv:1304.6877 · Physical Review B

Quantum phase transitions in multileg spin ladders with ring exchange

Sylvain Capponi, P. Lecheminant, Marion Moliner

Published Aug 19, 2013• 40 citations

Abstract

Four-spin exchange interaction has been raising intriguing questions regarding the exotic phase transitions it induces in two-dimensional quantum spin systems. In this context, we investigate the effects of a cyclic four-spin exchange in the quasi-1D limit by considering a general $N$-leg spin ladder. We show by means of a low-energy approach that depending on its sign, this ring exchange interaction can engender either a staggered or a uniform dimerization from the conventional phases of spin ladders. The resulting quantum phase transition is found to be described by the SU(2)${}_{N}$ conformal field theory. This result, as well as the fractional value of the central charge at the transition, is further confirmed by a large-scale numerical study performed by means of exact diagonalization and density matrix renormalization group approaches for $N\ensuremath{\le}4$.

DOI: 10.1103/physrevb.88.075132

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arXiv:1304.6877 · Physical Review B

Quantum phase transitions in multileg spin ladders with ring exchange

Sylvain Capponi, P. Lecheminant, Marion Moliner

Published Aug 19, 2013• 40 citations

arXiv HTML PDF

Abstract

N

-leg spin ladder. We show by means of a low-energy approach that depending on its sign, this ring exchange interaction can engender either a staggered or a uniform dimerization from the conventional phases of spin ladders. The resulting quantum phase transition is found to be described by the SU(2)

{}_{N}

conformal field theory. This result, as well as the fractional value of the central charge at the transition, is further confirmed by a large-scale numerical study performed by means of exact diagonalization and density matrix renormalization group approaches for

N\ensuremath{\le}4

DOI: 10.1103/physrevb.88.075132

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Phase diagram of a spin ladder with cyclic four-spin exchange

Andreas Martin Läuchli, Guido Schmid, Matthias Troyer

We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.

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Honda, Yasushi, Tsuyoshi Horiguchi

We investigate an $S=1/2$ two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by $J_4$ , by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by $J_{rung}$ and $J_{\rm leg}$ , respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet ( $S_{tot}^z=0$ ) and the triplet ( $S_{tot}^z=1$ ) states vanishes at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$ . This result is in contrast with the fact that the $S=1/2$ antiferromagnetic Heisenberg ladder, that is the case of $J_{rung} \neq J_{leg}, J_4=0$ , has a spin gap for all nonzero value of interchain interaction $J_{\rm rung}>0$ . We find a larger value of the correlation length for the spin-pair correlation function than a linear size $L$ of the system at $J_4/J_{\rm leg}=0.3$ and $J_{rung}=J_{leg}$ : the correlation length $ξ$ is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at $J_4/J_{leg}=0.3$ and $J_{rung}=J_{leg}$ . These results suggest that there is a quantum phase transition at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$ . We estimate a phase boundary where the spin gap vanishes in a $J_4/J_{leg}-J_{rung}/J_{leg}$ plane and obtain a consistent result with that by a perturbation theory for $J_{\rm rung}/J_{leg}>1$ .We investigate an $S=1/2$ two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by $J_4$, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by $J_{rung}$ and $J_{\rm leg}$, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet ($S_{tot}^z=0$) and the triplet ($S_{tot}^z=1$) states vanishes at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$. This result is in contrast with the fact that the $S=1/2$ antiferromagnetic Heisenberg ladder, that is the case of $J_{rung} \neq J_{leg}, J_4=0$, has a spin gap for all nonzero value of interchain interaction $J_{\rm rung}>0$. We find a larger value of the correlation length for the spin-pair correlation function than a linear size $L$ of the system at $J_4/J_{\rm leg}=0.3$ and $J_{rung}=J_{leg}$: the correlation length $ξ$ is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at $J_4/J_{leg}=0.3$ and $J_{rung}=J_{leg}$. These results suggest that there is a quantum phase transition at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$. We estimate a phase boundary where the spin gap vanishes in a $J_4/J_{leg}-J_{rung}/J_{leg}$ plane and obtain a consistent result with that by a perturbation theory for $J_{\rm rung}/J_{leg}>1$.

arXiv:cond-mat/0106426Jun 21, 20013 citations

N

{}_{N}

N\ensuremath{\le}4

We present the phase diagram of the

S=1/2

Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.

We study an

S=\frac{1}{2}

quantum-spin ladder system with four-spin cyclic exchange, using the density matrix renormalization group (DMRG) and exact diagonalization methods. Recently, the phase transition and its universality class in this system have been studied. However, controversies remain on whether the phase transition is second-order type or another type and on the nature of critical phenomena. In addition, there are several arguments concerning where the transition point is. Analyzing DMRG data, we use an approach to determine the ordered phase which appears after the phase transition. We find that the edge state appears under the open boundary condition by investigating excitation energies of states with higher magnetizations. We also estimate the correlation length and discuss the critical behavior.

k=2

SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.

We investigate an

S=1/2

two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by

J_4

, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by

J_{rung}

and

J_{\rm leg}

, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet (

S_{tot}^z=0

) and the triplet (

S_{tot}^z=1

) states vanishes at

J_4/J_{leg} \simeq 0.3

for

J_{rung}=J_{leg}

. This result is in contrast with the fact that the

S=1/2

antiferromagnetic Heisenberg ladder, that is the case of

J_{rung} \neq J_{leg}, J_4=0

, has a spin gap for all nonzero value of interchain interaction

J_{\rm rung}>0

. We find a larger value of the correlation length for the spin-pair correlation function than a linear size

L

of the system at

J_4/J_{\rm leg}=0.3

and

J_{rung}=J_{leg}

: the correlation length

ξ

is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at

J_4/J_{leg}=0.3

and

J_{rung}=J_{leg}

. These results suggest that there is a quantum phase transition at

J_4/J_{leg} \simeq 0.3

for

J_{rung}=J_{leg}

. We estimate a phase boundary where the spin gap vanishes in a

J_4/J_{leg}-J_{rung}/J_{leg}

plane and obtain a consistent result with that by a perturbation theory for

J_{\rm rung}/J_{leg}>1