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Chinese Physics B

Frustration and intermediate dimerized phase in spin ladder system

Shi Dong, Rui Wen, Guanghua Liu, Tian Guang-Shan

Published Jul 1, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/19/7/077503

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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.
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.
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.
A two-leg spin-1/2 ladder with diagonal interactions is investigated numerically. We focus our attention on the possibility of columnar dimer phase, which was recently predicted based on a reformulated bosonization theory. By using density matrix renormalization group technique and exact diagonalization method, we calculate columnar dimer order parameter, spin correlation on a rung, string order parameters, and scaled excitation gaps. Carefully using various finite-size scaling techniques, our results show no support for the existence of columnar dimer phase in the spin ladder under consideration.
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.
We revisit the phase diagram of the frustrated s=1/2s=1/2s=1/2 spin ladder with antiferromagnetic rung and diagonal couplings. In particular, we reexamine the evidence for the columnar dimer phase, which has been predicted from analytic treatment of the model and has been claimed to be found in numerical calculations. By performing density-matrix renormalization-group (DMRG) calculations on long ladders, keeping a large number of states within the DMRG, and carrying out careful scaling in number of states kept and system size, we calculate the behavior of the dimer order parameter as a function of frustration strength. We find no positive numerical evidence for a finite dimer order parameter in the thermodynamic limit anywhere in the parameter regime in which the columnar dimer phase is expected to appear. Conservative error estimates in the scaling of our data place stringent limits on the maximum possible value of the dimer order parameter and the maximum possible extent of the parameter regime in which a sufficiently weak dimer phase could still exist.