251 research outputs found
Excited states nonlinear integral equations for an integrable anisotropic spin 1 chain
We propose a set of nonlinear integral equations to describe on the excited
states of an integrable the spin 1 chain with anisotropy. The scaling
dimensions, evaluated numerically in previous studies, are recovered
analytically by using the equations. This result may be relevant to the study
on the supersymmetric sine-Gordon model.Comment: 15 pages, 2 Figures, typos correcte
Monopole Oscillations and Dampings in Boson and Fermion Mixture in the Time-Dependent Gross-Pitaevskii and Vlasov Equations
We construct a dynamical model for the time evolution of the boson-fermion
coexistence system. The dynamics of bosons and fermions are formulated with the
time-dependent Gross-Pitaevsky equation and the Vlasov equation. We thus study
the monopole oscillation in the bose-fermi mixture. We find that large damping
exists for fermion oscillations in the mixed system even at zero temperature.Comment: 16 pages text and 12 figure
Ladder operator for the one-dimensional Hubbard model
The one-dimensional Hubbard model is integrable in the sense that it has an
infinite family of conserved currents. We explicitly construct a ladder
operator which can be used to iteratively generate all of the conserved current
operators. This construction is different from that used for Lorentz invariant
systems such as the Heisenberg model. The Hubbard model is not Lorentz
invariant, due to the separation of spin and charge excitations. The ladder
operator is obtained by a very general formalism which is applicable to any
model that can be derived from a solution of the Yang-Baxter equation.Comment: 4 pages, no figures, revtex; final version to appear in Phys. Rev.
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Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction
We study a matrix product representation of the Bethe ansatz state for the
Lieb-Linger model describing the one-dimensional Bose gas with delta-function
interaction. We first construct eigenstates of the discretized model in the
form of matrix product states using the algebraic Bethe ansatz. Continuous
matrix product states are then exactly obtained in the continuum limit with a
finite number of particles. The factorizing -matrices in the lattice model
are indispensable for the continuous matrix product states and lead to a marked
reduction from the original bosonic system with infinite degrees of freedom to
the five-vertex model.Comment: 5 pages, 1 figur
Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model
By using the fact that Polychronakos-like models can be obtained through the
`freezing limit' of related spin Calogero models, we calculate the exact
spectrum as well as partition function of SU(m|n) supersymmetric Polychronakos
(SP) model. It turns out that, similar to the non-supersymmetric case, the
spectrum of SU(m|n) SP model is also equally spaced. However, the degeneracy
factors of corresponding energy levels crucially depend on the values of
bosonic degrees of freedom (m) and fermionic degrees of freedom (n). As a
result, the partition functions of SP models are expressed through some novel
q-polynomials. Finally, by interchanging the bosonic and fermionic degrees of
freedom, we obtain a duality relation among the partition functions of SP
models.Comment: Latex, 20 pages, no figures, minor typos correcte
Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
The thermodynamics of solvable isotropic chains with arbitrary spins is
addressed by the recently developed quantum transfer matrix (QTM) approach. The
set of nonlinear equations which exactly characterize the free energy is
derived by respecting the physical excitations at T=0, spinons and RSOS kinks.
We argue the implication of the present formulation to spinon character formula
of level k=2S SU(2) WZWN model .Comment: 25 pages, 8 Postscript figures, Latex 2e,uses graphicx, added figures
and detailed discussion
SO(4) Symmetry of the Transfer Matrix for the One-Dimensional Hubbard Model
The SO(4) invariance of the transfer matrix for the one-dimensional Hubbard
model is clarified from the QISM (quantum inverse scattering method) point of
view. We demonstrate the SO(4) symmetry by means of the fermionic R-matrix,
which satisfy the graded Yang-Baxter relation. The transformation law of the
fermionic L-operator under the SO(4) rotation is identified with a kind of
gauge transformation, which determines the corresponding transformation of the
fermionic creation and annihilation operators under the SO(4) rotation. The
transfer matrix is confirmed to be invariant under the SO(4) rotation, which
ensures the SO(4) invariance of the conserved currents including the
Hamiltonian. Furthermore, we show that the representation of the higher
conserved currents in terms of the Clifford algebra gives manifestly SO(4)
invariant forms.Comment: 20 pages, LaTeX file using citesort.st
Collective excitations of a trapped boson-fermion mixture across demixing
We calculate the spectrum of low-lying collective excitations in a mesoscopic
cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a
function of the boson-fermion repulsions. The cloud is under isotropic harmonic
confinement and its dynamics is treated in the collisional regime by using the
equations of generalized hydrodynamics with inclusion of surface effects. For
large numbers of bosons we find that, as the cloud moves towards spatial
separation (demixing) with increasing boson-fermion coupling, the frequencies
of a set of collective modes show a softening followed by a sharp upturn. This
behavior permits a clear identification of the quantum phase transition. We
propose a physical interpretation for the dynamical transition point in a
confined mixture, leading to a simple analytical expression for its location.Comment: revtex4, 9 pages, 8 postscript file
The determinant representation for quantum correlation functions of the sinh-Gordon model
We consider the quantum sinh-Gordon model in this paper. Using known formulae
for form factors we sum up all their contributions and obtain a closed
expression for a correlation function. This expression is a determinant of an
integral operator. Similar determinant representations were proven to be useful
not only in the theory of correlation functions, but also in the matrix models.Comment: 21 pages, Latex, no figure
On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3
Recently I quantized an elastica with Bernoulli-Euler functional in
two-dimensional space using the modified KdV hierarchy. In this article, I will
quantize a Willmore surface, or equivalently a surface with the Polyakov
extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation.
In other words, I show that the density of state of the partition function for
the quantized Willmore surface is expressed by volume of a subspace of the
moduli of the MNV equation.Comment: AMS-Tex Us
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