Spin nematics correlations in bilinear-biquadraticS=1spin chains

Abstract

We report the existence of an extended critical, nondimerized region in the phase diagram of the bilinear-biquadratic spin-one chain. The dominant power law correlations are ferroquadrupolar i.e. spin nematic in character. Another known critical region is also characterized by dominant quadrupolar correlations, although with a different wave vector. Our results show that spin nematic correlations play an important role in quantum magnets with spin S ≥ 1 in regions between antiferromagnetic and ferromagnetic phases.PACS numbers: 75.10. Jm, 75.10.Pq, 75.40.Mg, 75.40.Cx The recent experimental demonstration [1] of the transition to a Mott insulating state of atoms in an optical lattice from a superfluid state has opened the way to novel realizations of effective quantum lattice models with widely tunable control parameters. Quantum magnetic systems can be realized by spinor atoms in an optical lattice, e.g.23 Na with a total S = 1 moment. Confining S = 1 atoms to an optical lattice there are two scattering channels for identical atoms with total spin S = 0, 2 which can be mapped to an effective bilinear and biquadratic spin interaction [2,3]:where we adopt the standard parametrization J = cos θ and J q = sin θ. In one dimension, the bilinearbiquadratic spin-one model has a rich phase diagram (see Fig. 1 In dimensions higher than one, the bilinear-biquadratic spin-one model is well understood in the relevant parameter regime. It exhibits a spin nematic phase with a finite spin quadrupole moment in the groundstate [10,11].In this Letter we propose a novel scenario for the phase diagram of the one-dimensional model in between the dimerized and the ferromagnetic phases. In particular, we substantiate the existence of an extended critical, nondimerized region with dominant spin nematic correlations using extensive numerical simulations. We further characterize a second extended critical phase between the Haldane and the ferromagnetic phase, as also having prevalent quadrupolar correlations, albeit with a different wavevector.The outline of this paper is as follows. In the first part we present various numerical results providing evidence for an extended critical phase without spontaneous dimerization for θ ∈ (−3π/4, −0.67π]. We show that the quintuplet gap vanishes over this whole interval and that the transition between the dimerized and the critical phase is of a generalized Beresinski-KosterlitzThouless (BKT) type. The absence of finite dimerization is discussed. We further determine conformal field theory parameters, such as scaling dimensions and the central charge for the critical region. Finally we address the second extended critical phase θ ∈ [+π/4, +π/2), which we exhibit to have prevailing quadrupolar correlations at wavevectors ±2π/3.Numerical techniques -Our results constitute the

Anyonic quantum spin chains: Spin-1 generalizations and topological stability

“…This critical phase can be described by a conformal field theory with central charge c = 2. There are characteristic quadrupolar (nematic) spin correlations 24 in this phase, as well as a three sublattice structure 25 resulting in soft modes at momenta K = 0, 2π/3, 4π/3. At the transition from the gapped Haldane phase to this critical nematic phase at θ 2,1 = π/2, the system has enhanced SU(3) symmetry.…”

“…The phase transitions from this phase to both the adjacent dimerized phase as well as the nematic phase are first order. In the vicinity of the transition between the dimerized and ferromagnetic phase, early analytical work 28 suggested the possibility of an intermediate nematic phase, which, however has later been found to not materialize 24,29,30 .…”

Renormalization algorithm for the calculation of spectra of interacting quantum systems

“…Since then, a few numerical works have dealt with this problem, [16][17][18][19] but this phase is yet not fully characterized.…”

Overscreened Kondo fixed point inS=1spin liquid

“…A gapless phase for spin-1 with bilinear and biquadratic interaction has been established for a certain range of couplings. [64][65][66][67] . A spin-half impurity in such a chain is expected to realize overscreened Kondo physics.…”