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Journal of Yangzhou University

Effect of the diagonal antiferromagnetic frustration on the two-leg ferromagnetic comb model

Yongjun Liu

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

By using exact diagonalization method and density matrix renormalization group method,the author studies the ground states of the two-leg spin-1/2 mixed comb model,of which the nearest-neighbor interaction is ferromagnetic(FM) and the diagonal next-nearest-neighbor interaction is antiferromagnetic(AF).The ground state energy and the total spin are analyzed.When α≤0.25,the ground states are simply FM.With the diagonal AF frustration increasing,the ground state transforms from FM state to a canted state region,and then to the S=0 AF state.Differently in the mixed ladder model,the ground state directly transforms from FM state to AF state.

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By using exact diagonalization method and density matrix renormalization group method,the author studies the ground states of the two-leg spin-1/2 mixed comb model,of which the nearest-neighbor interaction is ferromagnetic(FM) and the diagonal next-nearest-neighbor interaction is antiferromagnetic(AF).The ground state energy and the total spin are analyzed.When α≤0.25,the ground states are simply FM.With the diagonal AF frustration increasing,the ground state transforms from FM state to a canted state region,and then to the S=0 AF state.Differently in the mixed ladder model,the ground state directly transforms from FM state to AF state.
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.
Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.
The goal of this project is to study the ground-state properties of frustrated spin-1/2 two- and three-leg Heisenberg ladders, and to investigate possible effects of diagonal couplings on spin gaps. The ground-state and the first-excited-state energies of these two systems are calculated systematically by using the density matrix renormalization group method. The ground state phase diagrams for these two systems are obtained. For the frustrated two-leg ladder, we found that the spin gap is insensitive to the change of the FM diagonal coupling constant. This is in agreement with experimental suggestions. For the frustrated three-leg ladder, we conclusively proved that introducing AF diagonal couplings can not change the gapless property of the ground state.
We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearest-neighbor bonds in the leg direction, and on the nearest-neighbor bonds in the rung direction. A dynamical spin correlation function at zero temperature is calculated using the dynamical density-matrix renormalization-group method for possible magnetic phases, i.e., columnar-dimer and rung-singlet phases. The columnar-dimer phase is characterized by multispinon excitations with a spin gap, whereas the rung-singlet phase is dominated by the triplet excitation in the rung direction. One major difference found between these two phases appears in the spectral weight of magnetic excitations, in particular, the bonding and antibonding modes in the rung direction. Therefore, we can distinguish one phase from the other by the difference in the spectral weight. Furthermore, we examine the effect of frustration on both modes in the rung-singlet phase with a perturbation theory from the strong coupling limit. The antibonding mode is shown to be stable against frustration, and a wave number with minimum excitation energy is shifted from being commensurate to being incommensurate. In contrast, the bonding mode is merged into the continuum excitation of multiple triplet excitations by increasing frustration. By comparing our results with inelastic neutron scattering experiments for BiCu2{}_{2}2​PO6{}_{6}6​, the magnitude of the magnetic exchange interactions and the ground state will be determined.
We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J 1, a and J 1, b between nearest neighbor spins in the legs a and b , respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by J r and Δ J r , respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J 1, a J 1, b < 0 irrespective of the sign of J r . The phase diagrams on the Δ (0≤Δ<1) versus J 1, b plane in the cases of J 1, a = − 0.2 and J 1, a = 0.2 with J r = −1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state , when J 1, a + J 1, b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.
We study a mixed spin-(3/2, 1) ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction. The exactly solved Ising-chain model is employed to investigate the ground-state properties and thermodynamics of the low-dimensional ladder system. Our results show that the competition between different exchange couplings brings in a large variety of ground states characterized by various values of normalized magnetization equal to 0, 1/5, 2/5, 3/5, 1. Moreover, an interesting double-peak structure is also detected in the thermal dependence of magnetic susceptibility and specific heat when the frustration comes into play. It is shown that the double-peak phenomenon at zero-field for the case of AF 2 ground-state arises from the very strong antiferromagnetic rung coupling, while other cases are attributed to the excitations induced by temperature and external field around the phase boundary.