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Physical Review B

Phase transition of S=12 two-leg Heisenberg spin ladder systems with a four-spin interaction

Keigo Hijii, K. Nomura

Published Jul 23, 2009• 9 citations
Publisher

Abstract

We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the $k=2$ 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.

DOI
10.1103/physrevb.80.014426

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We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the k=2k=2k=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.
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We study a s=12s=\frac{1}{2}s=21​ Heisenberg spin ladder with four-spin exchange. Combining numerical results with conformal field theory, we find a phase transition with central charge c=32.c=\frac{3}{2}.c=23​. Since this system has an SU(2) symmetry, we can conclude that this critical theory is described by k=2k=2k=2 SU(2) Wess-Zumino-Witten model with Z2{Z}_{2}Z2​ symmetry breaking.
We present the phase diagram of the S=1/2S=1/2S=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.
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 NNN-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{}_{N}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 $N\ensuremath{\le}4$.
We study an S=12S=\frac{1}{2}S=21​ 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.
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