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Register a new userStable particles in anisotropic spin-1 chains
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Added by
Lorenzo Campos Venuti
Publication date
2006
fields
Physics
and research's language is
English
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Motivated by field-theoretic predictions we investigate the stable excitations that exist in two characteristic gapped phases of a spin-1 model with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a region close to the phase boundary where a stable breather exists besides the stable particles, that form the Haldane triplet at the Heisenberg isotropic point. The numerical data, obtained by means of the Density Matrix Renormalization Group, confirm this picture in the so-called large-D phase for which we give also a quantitative analysis of the bound states using standard perturbation theory. However, the situation turns out to be considerably more intricate in the Haldane phase where, to the best of our data, we do not observe stable breathers contrarily to what could be expected from the sine-Gordon model, but rather only the three modes predicted by a novel anisotropic extension of the Non-Linear Sigma Model studied here by means of a saddle-point approximation.
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Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 $XXZ$ chain with single-ion anisotropy $D$. We demonstrate that the Haldane phase between large-$D$ and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-$D$ and antiferromagnetic phases with central charge $c=1/2$, which terminates at a critical end-point where $c=7/10$. Calculating the critical exponents of the order parameter, neutral gap and spin-spin-correlation function, we find $beta=1/8$ (1/24), $ u=1$ (5/9), and $eta=1/4$ (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.
We construct a new, two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect non-interacting modes of different systems. We apply the new solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the $s$-$d$ wave Richardson-Gaudin-Kitaev interacting chain, interpolating $s$- and $d$- wave superconductivity. The phase diagram of this model has a topological phase transition that can be connected to the duality, where the occupancy of the non-interacting mode serves as a topological order parameter.
By means of a numerical analysis using a non-Abelian symmetry realization of the density matrix renormalization group, we study the behavior of vector chirality correlations in isotropic frustrated chains of spin S=1 and S=1/2, subject to a strong external magnetic field. It is shown that the field induces a phase with spontaneously broken chiral symmetry, in line with earlier theoretical predictions. We present results on the field dependence of the order parameter and the critical exponents.
We study spontaneous dimerization transitions in a Heisenberg spin-1 chain with additional next-nearest neighbor (NNN) and 3-site interactions using extensive numerical simulations and a conformal field theory analysis. We show that the transition can be second order in the WZW SU(2)$_2$ or Ising universality class, or first-order. We argue that these features are generic because of a marginal operator in the WZW SU(2)$_2$ model, and because of two topologically distinct non-dimerized phases with or without edge states. We also provide explicit numerical evidence of conformal towers of singlets inside the spin gap at the Ising transition. Implications for other models are briefly discussed.
Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited mode, in stark contrast with three massive excitations previously observed in the structurally similar Haldane-gap material NDMAP [A. Zheludev et al., Phys. Rev. B 68, 134438 (2003)].
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