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arXiv:cond-mat/0112249 · Physical review. B, Condensed matter

Quantum criticalities in a two-leg antiferromagnetic S=12 ladder induced by a staggered magnetic field

Y. J. Wang, Fabian H. L. Eßler, Michele Fabrizio, A. A. Nersesyan

Published Jul 2, 2002• 41 citations
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Abstract

We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descriptions to determine the dynamical response functions, the staggered spin susceptibility, and the string order parameter.

DOI
10.1103/physrevb.66.024412

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We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descriptions to determine the dynamical response functions, the staggered spin susceptibility, and the string order parameter.
This study addresses low-energy properties of two-leg spin-1 ladders with antiferromagnetic (AF) intrachain coupling under a uniform or staggered external field HHH, and a few of their modifications. The generalization to spin-SSS ladders is also discussed. In the strong AF rung(interchain)-coupling ${J}_{\ensuremath{\perp}}$ region, degenerate perturbation theory applied to spin-SSS ladders predicts 2S2S2S critical curves in the parameter space $({J}_{\ensuremath{\perp}},H)$ for the staggered-field case, in contrast to 2S2S2S finite critical regions for the uniform-field case. All critical areas belong to a universality with central charge c=1c=1c=1. On the other hand, we employ Abelian and non-Abelian bosonization techniques in the weak rung-coupling region. They show that in the spin-1 ladder, a sufficiently strong uniform field engenders a c=1c=1c=1 critical state regardless of the sign of ${J}_{\ensuremath{\perp}}$, whereas the staggered field is expected not to yield any singular phenomena. From the bosonization techniques, new field-theoretical expressions of string order parameters in the spin-1 systems are also proposed.
In the weak-coupling regime of the continuous theories, two sets of one-loop renormalization-group equations are derived and solved to disclose the phase diagrams of the antiferromagnetic generalized two-leg spin-12\frac{1}{2}21​ ladder under the effect of (I) a staggered external magnetic field and (II) an explicit dimerization. In model (I), the splitting of the SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ critical line into U(1)U(1)U(1) and Z2{Z}_{2}Z2​ critical surfaces is observed, while in model (II), two critical surfaces arising from their underlying critical lines with SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ and Z2{Z}_{2}Z2​ characteristics merge into an SU(2)1\mathrm{SU}{(2)}_{1}SU(2)1​ critical surface on the line where the model attains its highest symmetry.
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent α\alphaα. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken Neel phase at αc∼2.1\alpha_c\sim 2.1αc​∼2.1. We find evidence that the transition is second order with a dynamic critical exponent z=1z=1z=1 and ν≈1.2\nu\approx 1.2ν≈1.2. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- bound states of spinons across the legs. We obtained the momentum resolved spin dynamic structure factor numerically and found that the triplon band is well defined at high energies and adiabatically connected to the magnon dispersion. However, at low energies it emerges as the lower edge of continuum of excitations that shifts to high energies across the transition. We further discuss the possibility of deconfined criticality in this model.
Field-induced quantum (zero temperature) criticality described using parameters that are not associated with a symmetry-breaking long-range order is found in the spin-12\frac{1}{2}21​ antiferromagnetic three-leg Heisenberg ladder. These parameters represent the spin bond order, which is a consequence of the probability for spins on adjacent sites to be bound in a singletlike arrangement. They underwent two phase transitions, one at the lower critical field hc1{h}_{c1}hc1​ and the other at the upper critical field hc2{h}_{c2}hc2​. The field dependence of these bond parameters and of the magnetization is calculated for several values of the rung coupling in all regimes. This yields the coupling field phase diagram. It is found that the rung coupling must exceed a threshold value for the plateau, at one third of the saturation magnetization, to appear. The results obtained here within the bond mean-field theory compare well with existing numerical data.
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Recent experiments have revealed the role of the staggered Dzyaloshinskii-Moriya interaction in the magnetized phase of an antiferromagnetic spin-1∕21∕21∕2 two-leg ladder compound under a uniform magnetic field. We derive a low-energy effective field theory describing a magnetized two-leg ladder with a weak staggered Dzyaloshinskii-Moriya interaction. This theory predicts the persistence of the spin gap in the magnetized phase, in contrast to standard two-leg ladders, and the presence of bound states in the excitation spectrum. Such bound states are observable in Raman scattering measurements. These results are then extended to intermediate Dzyaloshinskii-Moriya interaction using exact diagonalizations.