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At least 955 records · Page 53Linked to original sources
arXiv1996

Integrabilities of the long range t-J model of twisted boundary condition

The integrability of the one-dimensional long range supersymmetric t-J model has previously been established for both open systems and those closed by periodic boundary conditions through explicit construction of its integrals of motion. Recently the system has been extended to include the effect of magnetic flux, which gives rise to a closed chain with twisted boundary conditions. While the t-J model with twisted boundary conditions has been solved for the ground state and full energy spectrum, proof of its integrability has so far been lacking. In this letter we extend the proof of integrability of the long range supersymmetric t-J model and its SU(m|n) generalization to include the case of twisted boundary conditions.

solv-int↗
arXiv1997

Shock waves in one-dimensional Heisenberg ferromagnets

We use SU(2) coherent state path integral formulation with the stationary phase approximation to investigate, both analytically and numerically, the existence of shock waves in the one- dimensional Heisenberg ferromagnets with anisotropic exchange interaction. As a result we show the existence of shock waves of two types,"bright" and "dark", which can be interpreted as moving magnetic domains.

solv-int↗
arXiv1998

One-Dimensional XXZ Model for Particles Obeying Fractional Statistics

We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations show that fractional statistics, effectively, accounts for coupling an external gauge field to an integer statistics' system.

cond-mat.str-el↗
arXiv1998

Correlation amplitude for S=1/2 XXZ spin chain in the critical region

The density-matrix renormalization-group technique is used to calculate the spin correlation functions and of the one-dimensional S=1/2 XXZ model in the gapless regime. The numerical results for open chains of 200 spins are analyzed by comparing them with correlation functions calculated from a low-energy field theory. This gives precise estimates of the amplitudes of the correlation functions in the thermodynamic limit. The exact amplitude recently conjectured by Lukyanov and Zamolodchikov and the logarithmic correction in the Heisenberg model are confirmed numerically.

cond-mat.stat-mech↗
arXiv1999

Ground State and Excitations of Spin Chain with Orbital Degeneracy

The one dimensional Heisenberg model in the presence of orbital degeneracy is studied at the SU(4) symmetric viewpoint by means of Bethe ansatz. Following Sutherland's previous work on an equivalent model, we discuss the ground state and the low-lying excitations more extensively in connection to the spin systems with orbital degeneracy. We show explicitly that the ground state is a SU(4) singlet. We study the degeneracies of the elementary excitations and the spectra of the generalized magnons consisting of these excitations. We also discuss the complex 2-strings in the context of the Bethe ansatz solutions.

cond-mat.str-el↗
arXiv1999

Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $ $ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.

cond-mat.stat-mech↗
arXiv1999

Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems

The algebraic structure and the relationships between the eigenspaces of the Calogero-Sutherland model (CSM) and the Sutherland model (SM) on a circle are investigated through the Cherednik operators. We find an exact connection between the simultaneous non-symmetric eigenfunctions of the $A_{N-1}$ Cherednik operators, from which the eigenfunctions of the CSM and SM are constructed, and the monomials. This construction, not only, allows one to write down a harmonic oscillator algebra involving the Cherednik operators, which yields the raising and lowering operators for both of these models, but also shows the connection of the CSM with free oscillators and the SM with free particles on a circle. We also point out the subtle differences between the excitations of the CSM and the SM.

hep-th↗
arXiv1997

Exact Solution of selfconsistent Vlasov equation

An analytical solution of the selfconsistent Vlasov equation is presented. The time evolution is entirely determined by the initial distribution function. The largest Lyapunov exponent is calculated analytically. For special parameters of the model potential positive Lyapunov exponent is possible. This model may serve as a check for numerical codes solving selfconsistent Vlasov equations. The here presented method is also applicable for any system with analytical solution of the Hamilton equation for the formfactor of the potential.

physics.plasm-ph↗
arXiv1996

Dynamical Generation of Extended Objects in a $1+1$ Dimensional Chiral Field Theory: Non-Perturbative Dirac Operator Resolvent Analysis

We analyze the $1+1$ dimensional Nambu-Jona-Lasinio model non-perturbatively. In addition to its simple ground state saddle points, the effective action of this model has a rich collection of non-trivial saddle points in which the composite fields $\sigx=\lag\barψψ\rag$ and $\pix=\lag\barψi\gam_5ψ\rag$ form static space dependent configurations because of non-trivial dynamics. These configurations may be viewed as one dimensional chiral bags that trap the original fermions (``quarks") into stable extended entities (``hadrons"). We provide explicit expressions for the profiles of these objects and calculate their masses. Our analysis of these saddle points is based on an explicit representation we find for the diagonal resolvent of the Dirac operator in a $\{\sigx, \pix\}$ background which produces a prescribed number of bound states. We analyse in detail the cases of a single as well as two bound states. We find that bags that trap $N$ fermions are the most stable ones, because they release all the fermion rest mass as binding energy and become massless. Our explicit construction of the diagonal resolvent is based on elementary Sturm-Liouville theory and simple dimensional analysis and does not depend on the large $N$ approximation. These facts make it, in our view, simpler and more direct than the calculations previously done by Shei, using the inverse scattering method following Dashen, Hasslacher, and Neveu. Our method of finding such non-trivial static configurations may be applied to other $1+1$ dimensional field theories.

cond-mat↗
arXiv1997

Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics

We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to the standard nonperiodic case where either one or neither (but not both) of the isospectral pair has a zero mode. Thus it is possible to have supersymmetry unbroken and yet also have a vanishing Witten index. We present some explicit exactly soluble examples for which the isospectral potentials have identical band spectra, and which are ``self-isospectral'' in the sense that the potentials have identical shape, but are translated by one half period relative to one another.

hep-th↗
arXiv1998

The Geometrodynamics of Sine-Gordon Solitons

The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and construct the transformation to more standard ``Schwarzchild-like'' coordinates. For N=1 and 2, we find explicit closed form solutions to the dilaton equations of motion in soliton coordinates, and find the relationship between the soliton parameters and the black hole mass. Remarkably, the black hole mass is non-negative for arbitrary soliton parameters. In the one-soliton case the coordinates are shown to cover smoothly a region containing the whole interior of the black hole as well as a finite neighbourhood outside the horizon. A Hamiltonian analysis is performed for slicings that approach the soliton coordinates on the interior, and it is shown that there is no boundary contribution from the interior. Finally we speculate on the sine-Gordon solitonic origin of black hole statistical mechanics.

hep-th↗
arXiv1994

On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices

We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase space of this map. Using dimensionality properties of separatrix manifolds of the mapping we show the persistence of NLE solutions under perturbations of the system, provided NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam chains we rigorously prove the existence of NLE solutions.

solv-int↗
arXiv1996

Farey Tree and the Frenkel-Kontorova Model

We solved the Frenkel-Kontorova model with the potential $V(u)= -\frac{1}{2} |λ|(u-{\rm Int}[u]-\frac{1}{2})^2$ exactly. For given $|λ|$, there exists a positive integer $q_c$ such that for almost all values of the tensile force $σ$, the winding number $ω$ of the ground state configuration is a rational number in the $q_c$-th level Farey tree. For fixed $ω=p/q$, there is a critical $λ_c$ when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey tree. A kind of ``commensurate-incommensurate'' transition occurs at critical values of $σ$ when two sizes of molecules co-exist. ``Soliton'' in the usual sense does not exist but induces a transformation of one size of molecules into the other.

solv-int↗
arXiv1996

On the integrability of the square-triangle random tiling model

It is shown that the square-triangle random tiling model is equivalent to an asymmetric limit of the three colouring model on the honeycomb lattice. The latter model is known to be the O(n) model at T=0 and corresponds to the integrable model connected to the affine $A_2^{(1)}$ Lie algebra. Thus it is shown that the weights of the square-triangle random tiling satisfy the Yang-Baxter equation, albeit in a singular limit of a more general model. The three colouring model for general vertex weights is solved by algebraic Bethe Ansatz.

solv-int↗
arXiv1996

Small-amplitude excitations in a deformable discrete nonlinear Schroedinger equation

A detailed analysis of the small-amplitude solutions of a deformed discrete nonlinear Schrödinger equation is performed. For generic deformations the system possesses "singular" points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicinity of the singular points are described by the Toda-lattice equation while away from the singular points are described by the Korteweg-de Vries equation. Depending on the value of the deformation parameter and of the background level several kinds of solutions are possible. In particular we delimit the regions in the parameter space in which dark solitons are stable in contrast with regions in which bright pulses on nonzero background are possible. On the boundaries of these regions we find that shock waves and rapidly spreading solutions may exist.

solv-int↗
arXiv1996

Scaling Limit of the Ising Model in a Field

The dilute A_3 model is a solvable IRF (interaction round a face) model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A_3. It can be regarded as a solvable version of an Ising model at the critical temperature in a magnetic field. One therefore expects the scaling limit to be governed by Zamolodchikov's integrable perturbation of the c=1/2 conformal field theory. Indeed, a recent thermodynamic Bethe Ansatz approach succeeded to unveil the corresponding E_8 structure under certain assumptions on the nature of the Bethe Ansatz solutions. In order to check these conjectures, we perform a detailed numerical investigation of the solutions of the Bethe Ansatz equations for the critical and off-critical model. Scaling functions for the ground-state corrections and for the lowest spectral gaps are obtained, which give very precise numerical results for the lowest mass ratios in the massive scaling limit. While these agree perfectly with the E_8 mass ratios, we observe one state which seems to violate the assumptions underlying the thermodynamic Bethe Ansatz calculation. We also analyze the critical spectrum of the dilute A_3 model, which exhibits massive excitations on top of the massless states of the Ising conformal field theory.

hep-th↗
arXiv1997

Inelastic Collision and Switching of Coupled Bright Solitons in Optical Fibers

By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrodinger equation (Manakov model) using the Hirota method, we find that the solitons exhibit certain novel inelastic collision properties, which have not been observed in any other (1+1) dimensional soliton system so far. In particular, we identify the exciting possibility of switching solitons between modes by changing the phase. However, the standard elastic collision property of solitons is regained with specific choices of parameters.

solv-int↗