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Chinese Physics Letters

Spin-Peierls Instability in the Ferromagnetic Heisenberg Ladder

Yin-Jie Xu, Hui Zhao, Yuguang Chen, Yonghong Yan

Published Mar 1, 2013• 2 citations
Publisher

Abstract

A two-leg S = 1/2 spin ladder with ferromagnetic rung coupling is investigated to reveal the phase transition between the Haldane and columnar dimer phase. The elastic lattice with the elastic force K is introduced into the system, which induces unstable spin chains towards the spontaneous dimerization. When the rung coupling is strong enough, the dimerization along the legs is suppressed and the spin ladder undergoes a phase transition. The dimerization amplitude is calculated self-consistently by the density-matrix renormalization group method. To determine the phase transition boundary, the spin gap, the columnar dimer order parameter and the block-block entanglement entropy are calculated. Our results show that the phase boundary between the columnar dimer phase and Haldane phase follows the power law J t ∼ K −α .

DOI
10.1088/0256-307x/30/3/037503

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A two-leg S = 1/2 spin ladder with ferromagnetic rung coupling is investigated to reveal the phase transition between the Haldane and columnar dimer phase. The elastic lattice with the elastic force K is introduced into the system, which induces unstable spin chains towards the spontaneous dimerization. When the rung coupling is strong enough, the dimerization along the legs is suppressed and the spin ladder undergoes a phase transition. The dimerization amplitude is calculated self-consistently by the density-matrix renormalization group method. To determine the phase transition boundary, the spin gap, the columnar dimer order parameter and the block-block entanglement entropy are calculated. Our results show that the phase boundary between the columnar dimer phase and Haldane phase follows the power law J t ∼ K −α .
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.
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.
Because the three-leg ladder behaves like a renormalized single Heisenberg chain, we argue that a spin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons. Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state below the spin-Peierls transition temperature forms into the columnar dimerized phase instead of the staggered one. This contrasts with the argument based on antiferromagnetism. A physical argument based rather on spin bonding into singlets could explain why the columnar configuration is favored. No quantum criticality (gaplessness) can occur in the columnar arrangement of the dimerized chains.
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.
We study the ground-state properties of three-leg S = 1/2 Heisenberg tube with antiferromagnetic interleg couplings J ⊥ (> 0). The spin gap, dimerization-order parameter, and Berry phase are calculated with the density-matrix renormalization group method. We find that the system is spontaneously dimerized and all the spin excitations are gapped whether intraleg couplings J || are antiferromagnetic or ferromagnetic. Also, the phase diagram is divided into three regimes according to topological configuration of the spin-singlet pairs: (i) Haldane-gap-like regime for J ⊥ / J || < 0, (ii) intraleg-singlet regime 0 < J ⊥ J || ≤ 5, and (iii) intrarung-singlet regime for J ⊥ J || ≥ 5.