Temperley-Lieb-Jones Algebraic Structures in Higher Spin Chain Models

We investigate the Temperley-Lieb-Jones algebraic structures in isomorphic higher spin chain modgls with nearest neighbour interactions and SU(2) symmetry. The Ternperley-Lieb-Jones algebraic constructions for such chains of spins from 1 to 7/2 are presented. For the case of spin-1 we also give the Temperley-Lieb-Jones algebraic representations related to the anisomorphic spin chain with q-deformed SU_q(2) symmetry. Their related spin chain Harniltonians with SU(2) and SU_q(2) symmetries as well as the corresponding solutions of Yang-Baxter equation are also discussed.     

Translational Symmetry Breaking and Soliton Sectors for Massive Quantum Spin Models in 1 + 1 Dimensions

We consider the classification of pure infinite volume ground states and that of soliton sectors for 1+1 dimensional massive quantum spin models. We obtain a proof that non-translationally invariant ground state cannot exist for a class of translationally invariant Hamiltonians including the spin 1 AKLT (Affleck Kennedy Lieb Tasaki) antiferromagnetic spin model. We also obtain a complete classification of soliton sectors (up to unitary equivalence) for certain massive models (e.g. ferromagnetic XXZ models). Received: 13 January 1997 / Accepted: 11 March 1997     

High—Dimensional Integrable Models with Infinitely Dimensional Virasoro—Type Symmetry Algebra

Using every realization of the Virasoro-type symmetry algebra[σ(f1),σ(f2)]=σ(f1f2-f2f1),we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries,By means of a concrete realization ,many(3 1)-dimensional equations which possess Kac-Moody-Virasoro-type infinite dimensional symmetry algebras are obtained.     

The qs-Hermite Polynomial and the Representations of Heisenberg and Quantum Heisenberg Algebra

By introducing a pair of canonical conjugate two-parameter deformed operators D_qs, X_qs,we can naturally obtain the form of qs-analogous Taylor series for an arbitrary analytic function, and explicitly construct the realizations of Heisenberg and two-parameter deformed quantum Heisenberg algebra by means of the operators D_qs and X_qs, and it is shown that the qs-analogous Hermite polynomials are the representations of Heisenberg and the quantum Heisen berg algebra.     

Symmetry breaking in Heisenberg antiferromagnets

We extend Griffith's theorem on symmetry breaking in quantum spin systems to the situation where the order operator and the Hamiltonian do not commute with each other. The theorem establishes that the existence of a long range order in a symmetric (non-pure) infinite-volume state implies the existence of a symmetry breaking in the state obtained by applying an infinitesimal symmetry-breaking field. The theorem is most meaningful when applied to a class of quantum antiferromagnets where the existence of a long range order has been proved by the Dyson-Lieb-Simon method. We also present a related theorem for the ground states. It is an improvement of the theorem by Kaplan, Horsch and von der Linden. Our lower bounds on the spontaneous staggered magnetization in terms of the long range order parameter take into account the symmetry of the system properly, and are likely to be saturated in general models.     

Thermal Spin Squeezing as a Signature of Thermal Global Entanglement in Heisenberg Models

We study thermal spin squeezing (TSS) and thermal global entanglement (TGE) in a general Heisenberg spin chain, in the presence of Dzyaloshinskii-Moriya interaction and an external magnetic field. We derive an inequality associating the squeezing parameter and the global concurrence, which establishes (TSS) as a signature of (TGE). The inequality reduces to equality for particular symmetric chains which also associates TSS with bipartite entanglement in such systems. We also check the results by presenting two numerical examples.     

Thermal Spin Squeezing as a Signature of Thermal Global Entanglement in Heisenberg Models

We study thermal spin squeezing (TSS) and thermal global entanglement (TGE) in a general Heisenberg spin chain, in the presence of Dzyaloshinskii-Moriya interaction and an external magnetic field. We derive an inequality associating the squeezing parameter and the global concurrence, which establishes (TSS) as a signature of (TGE). The inequality reduces to equality for particular symmetric chains which also associates TSS with bipartite entanglement in such systems. We also check the results by presenting two numerical examples.     

Superdiffusivity of Asymmetric Exclusion Process in Dimensions One and Two

We prove that the diffusion coefficient for the asymmetric exclusion process diverges at least as fast as t ^1/4 in dimension d=1 and (logt)^1/2 in d=2. The method applies to nearest and non-nearest neighbor asymmetric exclusion processes.     

R-Deformed Heisenberg Algebra, Quantum Mechanics, and Virasoro Algebra

We review the R-deformed Heisenberg algebra and its Fock space representation.We construct the R-deformed quantum mechanics in N dimensions, and proposea new R-deformed Virasoro algebra.     

Cyclic Cohomology and Hopf Algebra Symmetry

Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their actions on algebras allows the expansion of the range of applications of cyclic cohomology. It is the goal of this Letter to illustrate these recent developments, with special emphasis on the application to transverse index theory, and point towards future directions. In particular, we highlight the remarkable accord between our framework for cyclic cohomology of Hopf algebras on the one hand and both the algebraic as well as the analytic theory of quantum groups on the other, manifest in the construction of the modular square.     

(3 + 1)-Dimensional Integrable Models Possessing Infinite Dimensional Virasoro-Type Symmetry Algebra

Using a series of concrfte reGzations of the centerless Virasoro-type symmetry algebra [σ(ƒ₂(t), σ(ƒ₁(t))] = σ(ƒ₁ƒ₂ - ƒ₂ƒ₁), various (3+1)-dimensional integrable equations under the condition that they possess Kac-Moody-Virasoro-type infinite dimensional symmetry algebra are obtained.     

Spin diffusion in a Heisenberg spin glass

Using a combination of analytic and Monte Carlo techniques we obtain estimates for the spin diffusion constant and spin conductivity in a classical simple cubic Heisenberg spin glass which has a Gaussian distribution of exchange interactions between nearest neighbors.     

The Inhomogeneous Quantum Invariance Group of The Two Parameter Deformed Boson Algebra

We consider two parameter deformed boson algebra and investigate the inhomogeneous invariance quantum group of this system. We find the R-matrix which collects all information about the non-commuting structure of the quantum group. We extend our study to the d-dimensional case.     

Symmetry Group Analysis for Perfect Fluid Inhomogeneous Cosmological Models in General Relativity

In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between expansion scalar and shear scalar. For this, Lie group analysis is used to identify the generator (isovector fields) that leave the given system of PDEs (Einstein’s field equations) invariant for the models under consideration. A new class of exact solutions of Einstein’s field equation have been obtained for inhomogeneous space-time. The physical behaviors and geometric aspects of the derived models have been discussed in detail.