256 research outputs found
Fermionic R-Operator and Integrability of the One-Dimensional Hubbard Model
We propose a new type of the Yang-Baxter equation (YBE) and the decorated
Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were
introduced recently as a tool to treat the integrability of the fermion models.
Using the YBE and the DYBE for the XX fermion model, we construct the fermionic
R-operator for the one-dimensional (1D) Hubbard model. It gives another proof
of the integrability of the 1D Hubbard model. Furthermore a new approach to the
SO(4) symmetry of the 1D Hubbard model is discussed.Comment: 25 page
Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries
The one-dimensional Hubbard model with open boundary conditions is exactly
solved by means of algebraic Bethe ansatz. The eigenvalue of the transfer
matrix, the energy spectrum as well as the Bethe ansatz equations are obtained.Comment: Only LaTex file; no figur
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
Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain
We study the Emptiness Formation Probability (EFP) for the spin 1/2 XXZ spin
chain. EFP P(n) detects a formation of ferromagnetic string of the length n in
the ground state. It is expected that EFP decays in a Gaussian way for large
strings P(n) ~ n^{-gamma} C^{-n^2}. Here, we propose the explicit expressions
for the rate of Gaussian decay C as well as for the exponent gamma. In order to
confirm the validity of our formulas, we employed an ab initio simulation
technique of the density-matrix renormalization group to simulate XXZ spin
chain of sufficient length. Furthermore, we performed Monte-Carlo integration
of the Jimbo-Miwa multiple integral for P(n). Those numerical results for P(n)
support our formulas fairly definitely.Comment: 9 pages, 2 figure
Lax pair for SU(n) Hubbard model
For one dimensional SU(n) Hubbard model, a pair of Lax operators are derived,
which give a set of fundamental equations for the quantum inverse scattering
method under both periodic and open boundary conditions. This provides another
proof of the integrability of the model under periodic boundary condition.Comment: Latex file, 7 pages, little change adde
Fermionic R-Operator and Algebraic Structure of 1D Hubbard Model: Its application to quantum transfer matrix
The algebraic structure of the 1D Hubbard model is studied by means of the
fermionic R-operator approach. This approach treats the fermion models directly
in the framework of the quantum inverse scattering method. Compared with the
graded approach, this approach has several advantages. First, the global
properties of the Hamiltonian are naturally reflected in the algebraic
properties of the fermionic R-operator. We want to note that this operator is a
local operator acting on fermion Fock spaces. In particular, SO(4) symmetry and
the invariance under the partial particle hole transformation are discussed.
Second, we can construct a genuinely fermionic quantum transfer transfer matrix
(QTM) in terms of the fermionic R-operator. Using the algebraic Bethe Ansatz
for the Hubbard model, we diagonalize the fermionic QTM and discuss its
properties.Comment: 22 pages, no 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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Integrable variant of the one-dimensional Hubbard model
A new integrable model which is a variant of the one-dimensional Hubbard
model is proposed. The integrability of the model is verified by presenting the
associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue
that the new model possesses the SO(4) algebra symmetry, which contains a
representation of the -pairing SU(2) algebra and a spin SU(2) algebra.
Additionally, the algebraic Bethe ansatz is studied by means of the quantum
inverse scattering method. The spectrum of the Hamiltonian, eigenvectors, as
well as the Bethe ansatz equations, are discussed
Analytic Bethe Ansatz for 1-D Hubbard model and twisted coupled XY model
We found the eigenvalues of the transfer matrices for the 1-D Hubbard model
and for the coupled XY model with twisted boundary condition by using the
analytic Bethe Ansatz method. Under a particular condition the two models have
the same Bethe Ansatz equations. We have also proved that the periodic 1-D
Hubbard model is exactly equal to the coupled XY model with nontrivial twisted
boundary condition at the level of hamiltonians and transfer matrices.Comment: 22 pages, latex, no figure
A variational approach for the Quantum Inverse Scattering Method
We introduce a variational approach for the Quantum Inverse Scattering Method
to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake
this in a manner which does not rely on any prior knowledge of integrability
through the existence of a set of conserved operators. The procedure is
conducted in the framework of Hamiltonians describing the crossover between the
low-temperature phenomena of superconductivity, in the
Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC).
The Hamiltonians considered describe systems with interacting Cooper pairs and
a bosonic degree of freedom. We obtain general exact solvability requirements
which include seven subcases which have previously appeared in the literature.Comment: 18 pages, no eps figure
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