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Physical review. B, Condensed matter

Low-energy properties of spin-1/2 two-leg antiferromagnetic Heisenberg ladders with ferromagnetic diagonal coupling

Ningsheng Zhu, Xiaoqun Wang, Changfeng Chen

Published Dec 11, 2000• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.63.012401

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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×\else\texttimes\fi.{J}_{\ifmmode\times\else\texttimes\fi{}}.J\ifmmode×\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⊥{J}_{\ensuremath{\perp}}J\ensuremath⊥​ and the diagonal coupling J\ifmmode×\else\texttimes\fi{J}_{\ifmmode\times\else\texttimes\fi{}}J\ifmmode×\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⊥{J}_{\ensuremath{\perp}}J\ensuremath⊥​ to the leg coupling constant J\ensuremath∥{J}_{\ensuremath{\Vert}}J\ensuremath∥​ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.
Using the density matrix renormalization group method, we determine the phase diagram of a frustrated bond-alternating S = 1/2 Heisenberg ladder with ferro-antiferromagnetic couplings at zero temperature. With the interactions between spins along the rungs set, we identify three spin-gapped phases (the Haldane phase, the singlet phase and the dimer phase) in the whole parameter range. The analysis of our data shows that two-leg spin bond-alternating ladders have a rich phase diagram if both rung and diagonal couplings are taken into account.
The ground state and low lying excitation of the spin 1/2 Heisenberg ladder with antiferromagnetic leg (JJJ) and ferromagnetic rung (−λJ,λ>0-λJ, λ>0−λJ,λ>0) interaction is studied by means of the density matrix renormalization group method. It is found that the state remains in the Haldane phase even for small λ∼0.02λ\sim 0.02λ∼0.02 suggesting the continuous transition to the gapless phase at λ=0λ= 0λ=0. The critical behavior for small λλλ is studied by the finite size scaling analysis. The result is consistent with the recent field theoretical prediction.
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.
Using density-matrix renormalization group calculations, we investigate the general phase diagram of the frustrated two-leg ladder with Heisenberg interactions along legs, rungs, and diagonals. We confirm that all antiferromagnetic gapped states belong to the same universality class as the Haldane phase. In a three-dimensional phase diagram, we determine a continuous surface with singularities in the string-order parameter or its first derivative, corresponding to a transition between two Haldane phases with different topological order. Some parts of this transition surface are critical with zero gap and vanishing string-order parameter. In the complementary parts, the transition is first order with finite gap and string order. The boundary of this surface with the ferromagnetic region is a critical end line, when the surface is critical, and a triple line anywhere else. Part of this boundary coincides with the exactly soluble model proposed by Dmitriev, Krivnov, and Ovchinnikov [Phys. Rev. B 56, 5985 (1997)].
We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-12\frac{1}{2}21​ rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-type nondegenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-12\frac{1}{2}21​ ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material FeIIFeIII{\text{Fe}}^{\text{II}}{\text{Fe}}^{\text{III}}FeIIFeIII (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.
Using the density matrix renormalization group method we have studied the ground-state phase diagram of a spin-1/2 frustrated three-leg antiferromagnetic Heisenberg ladder, and identified two phases corresponding to the spin-3/2 chain and the standard spin ladder. Varying the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ leads to a quantum phase transition from one ground state to the other, but does not alter the gapless nature of the excitation spectra. On the phase boundary, the degenerate ground states form a chiral spin liquid with a central charge c=2.c=2.c=2. The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.