Some properties of frustrated spin systems: extensions and applications of Lieb-Schupp approach

Lieb and Schupp have obtained, using certain version of ``spin-reflection positivity'' method, a number of ground-state properties for frustrated Heisenberg models. One group of these results is related to singlet nature of ground state and it needs an assumption of reflection symmetry present in the system. In this paper, it is shown that the result holds also for other symmetries (inversion etc.). The second Lieb-Schupp result is relation between ground-state energies of certain systems. In the paper, this relation is applied to multidimensional models on various lattices.Comment: 15 pages, 8 eps figures, revtex

Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), we study a frustrated $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice. The classical $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice has N\'eel order for $J_2 J_1/6$, it exhibits a one-parameter family of degenerate incommensurate spin spiral ground states where the spiral wave vector can point in any direction. Spin wave fluctuations at leading order lift this accidental degeneracy in favor of specific wave vectors, leading to spiral order by disorder. For spin $S=1/2$, quantum fluctuations are, however, likely to be strong enough to melt the spiral order parameter over a wide range of $J_2/J_1$. Over a part of this range, we argue that the resulting state is a valence bond solid (VBS) with staggered dimer order - this VBS is a nematic which breaks lattice rotational symmetry. Our arguments are supported by comparing the spin wave energy with the energy of the dimer solid obtained using a bond operator formalism. Turning to the effect of thermal fluctuations on the spiral ordered state, any nonzero temperature destroys the magnetic order, but the discrete rotational symmetry of the lattice remains broken resulting in a thermal analogue of the nematic VBS. We present arguments, supported by classical Monte Carlo simulations, that this nematic transforms into the high temperature symmetric paramagnet via a thermal phase transition which is in the universality class of the classical 3-state Potts (clock) model in 2D. We discuss the possible relevance of our results for honeycomb magnets, such as Bi$_3$M$_4$O$_{12}$(NO$_3$) (with M=Mn,V,Cr), and bilayer triangular lattice magnets.Comment: Slightly revise

Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group

In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets, symmetries, and collective dynamics. This last item allows to study integrability as inherited from a system on the whole cotangent bundle, leading in a natural way to the AKS theory for integrable systems

Inhomogeneity Induces Resonance Coherence Peaks in Superconducting BSCCO

In this paper we analyze, using scanning tunneling spectroscopy, the density of electronic states in nearly optimally doped BSCCO in zero field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a 2 xi_0 * 2 xi_0 patch with an enhanced or supressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.Comment: 4 pages, 3 figure

Suppression of Dimer Correlations in the Two-Dimensional J1J_1-J2J_2 Heisenberg Model: an Exact Diagonalization Study

We present an exact diagonalization study of the ground state of the spin-half $J_1{-}J_2$ model. Dimer correlation functions and the susceptibility associated to the breaking of the translational invariance are calculated for the $4\times 4$ and the $6\times 6$ clusters. These results -- especially when compared to the one dimensional case, where the occurrence of a dimerized phase for large enough frustration is well established -- suggest either a homogeneous spin liquid or, possibly, a dimerized state with a rather small order parameter

Thermodynamics of the quantum easy-plane antiferromagnet on the triangular lattice

The classical XXZ triangular-lattice antiferromagnet (TAF) shows both an Ising and a BKT transition, related to the chirality and the in-plane spin components, respectively. In this paper the quantum effects on the thermodynamic quantities are evaluated by means of the pure-quantum self-consistent harmonic approximation (PQSCHA), that allows one to deal with any spin value through classical MC simulations. We report the internal energy, the specific heat, and the in-plane correlation length of the quantum XX0 TAF, for S=1/2, 1, 5/2. The quantum transition temperatures turn out to be smaller the smaller the spin, and agree with the few available theoretical and numerical estimates.Comment: 4 pages,3 postscript figure

Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large $U$. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.Comment: 4 pages, 2 figure

A Recursive Method of the Stochastic State Selection for Quantum Spin Systems

In this paper we propose the recursive stochastic state selection method, an extension of the recently developed stochastic state selection method in Monte Carlo calculations for quantum spin systems. In this recursive method we use intermediate states to define probability functions for stochastic state selections. Then we can diminish variances of samplings when we calculate expectation values of the powers of the Hamiltonian. In order to show the improvement we perform numerical calculations of the spin-1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. Examining results on the ground state of the 21-site system we confide this method in its effectiveness. We also calculate the lowest and the excited energy eigenvalues as well as the static structure factor for the 36-site system. The maximum number of basis states kept in a computer memory for this system is about 3.6 x 10**7. Employing a translationally invariant initial trial state, we evaluate the lowest energy eigenvalue within 0.5 % of the statistical errors.Comment: 14 pages, 1 figur