198 research outputs found
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
Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function
The asymptotics of the equal-time one-particle Green's function for the
half-filled one-dimensional Hubbard model is studied at finite temperature. We
calculate its correlation length by evaluating the largest and the second
largest eigenvalues of the Quantum Transfer Matrix (QTM). In order to allow for
the genuinely fermionic nature of the one-particle Green's function, we employ
the fermionic formulation of the QTM based on the fermionic R-operator of the
Hubbard model. The purely imaginary value of the second largest eigenvalue
reflects the k_F (= pi/2) oscillations of the one-particle Green's function at
half-filling. By solving numerically the Bethe Ansatz equations with Trotter
numbers up to N=10240, we obtain accurate data for the correlation length at
finite temperatures down into the very low temperature region. The correlation
length remains finite even at T=0 due to the existence of the charge gap. Our
numerical data confirm Stafford and Millis' conjecture regarding an analytic
expression for the correlation length at T=0.Comment: 7 pages, 6 figure
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
Screening and investigation of dye decolorization activities of basidiomycetes
ArticleJOURNAL OF BIOSCIENCE AND BIOENGINEERING. 105(1): 69-72 (2008)journal articl
Exact evaluation of density matrix elements for the Heisenberg chain
We have obtained all the density matrix elements on six lattice sites for the
spin-1/2 Heisenberg chain via the algebraic method based on the quantum
Knizhnik-Zamolodchikov equations. Several interesting correlation functions,
such as chiral correlation functions, dimer-dimer correlation functions, etc...
have been analytically evaluated. Furthermore we have calculated all the
eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a
result the exact von Neumann entropy for the reduced density matrix on six
lattice sites has been obtained.Comment: 33 pages, 4 eps figures, 3 author
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.
Let
Exact results for the sigma^z two-point function of the XXZ chain at Delta=1/2
We propose a new multiple integral representation for the correlation
function of the XXZ spin-1/2 Heisenberg chain in the
disordered regime. We show that for Delta=1/2 the integrals can be separated
and computed exactly. As an example we give the explicit results up to the
lattice distance m=8. It turns out that the answer is given as integer numbers
divided by 2^[(m+1)^2].Comment: 8 page
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.Comment: 17 page
Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet
We exactly evaluate the third neighbor correlator and all
the possible non-zero correlators <S^{alpha}_j S^{beta}_{j+1} S^{gamma}_{j+2}
S^{delta}_{j+3}> of the spin-1/2 Heisenberg antiferromagnet in the ground
state without magnetic field. All the correlators are expressed in terms of
certain combinations of logarithm ln2, the Riemann zeta function zeta(3),
zeta(5) with rational coefficients. The results accurately coincide with the
numerical ones obtained by the density-matrix renormalization group method and
the numerical diagonalization.Comment: 4 page
- …