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Communications in Theoretical Physics

Quantum Phase Transitions and Dimerized Phases in Frustrated Spin Ladder

Rui Wen, Guanghua Liu, Guang-Shan Tian

Published Jun 1, 2011• 10 citations
Publisher

Abstract

In this paper, we study the phase diagram of a frustrated spin ladder model by applying the bosonization technique and the density-matrix renormalization-group (DMRG) algorithm. Effect of the intra-chain next-nearestneighbor (NNN) super-exchange interaction is investigated in detail and the order parameters are calculated to detect the emergence of the dimerized phases. We find that the intra-chain NNN interaction plays a key role in inducing dimerized phases.

DOI
10.1088/0253-6102/55/6/26

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In this paper, we study the phase diagram of a frustrated spin ladder model by applying the bosonization technique and the density-matrix renormalization-group (DMRG) algorithm. Effect of the intra-chain next-nearestneighbor (NNN) super-exchange interaction is investigated in detail and the order parameters are calculated to detect the emergence of the dimerized phases. We find that the intra-chain NNN interaction plays a key role in inducing dimerized phases.
Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J 2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J 2 = 0 is carefully analyzed.
In the present paper, by using the density-matrix renormalization-group technique, we investigate the existence of dimerized phases in a frustrated spin-1/2 ladder model. By calculating the two-rung localizable entanglement and, in particular, its first-order derivative in the ground state, we show that an intermediate columnar dimerized phase exists indeed in a narrow parameter region between the rung-singlet and the Haldane phases. Furthermore, by introducing an additional interchain next-nearest-neighbor exchange interaction, the stability of this phase can be greatly enhanced and a staggering dimerized phase also appears in the phase diagram. Our results confirm the previous conclusions derived by the bosonization methods.
This paper studies a spin ladder model which possesses frustrating interactions. By using both the bosonization and the density matrix renormalization group techniques, it shows that the intermediate columnar dimerized phase, which exists in a narrow parameter region of the so-called J 1 – J 2 model, vanishes if the interchain frustration is weak and anisotropic. Therefore, it concludes that the frustrating interaction indeed plays an important role in producing such a phase. As a complementary to our previous investigation, it reaches a more complete picture of the quantum phase transition in the frustrated spin ladder systems.
Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.
We revisit the phase diagram of the frustrated spin-1/2 ladder with two competing interchain antiferromagnetic exchanges, rung coupling ${J}_{\ensuremath{\perp}}$ and diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$. We suggest, based on the accurate renormalization-group analysis of the low-energy Hamiltonian of the ladder, that marginal interchain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line ${J}_{\ensuremath{\perp}}=2{J}_{\ifmmode\times\else\texttimes\fi{}}$. Following this insight we then suggest that changing these competing interchain exchanges from the previously considered antiferromagnetic to the ferromagnetic ones eliminates the issue of the marginal interactions altogether and dramatically expands the region of stability of the columnar dimer phase. This analytical prediction is convincingly confirmed by the numerical density-matrix renormalization-group and exact-diagonalization calculations as well as by the perturbative calculation in the strong rung-coupling limit. The phase diagram for ferromagnetic ${J}_{\ensuremath{\perp}}$ and ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is determined.