388 research outputs found
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
X-ray scattering from crystalline SiO2 in the thermal oxide layers on vicinal Si(111) surfaces
Shimura, T., Misaki, H. & Umeno, M. (1996). Acta Cryst. A52, C465, https://doi.org/10.1107/S0108767396080932
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
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
Fast and stable method for simulating quantum electron dynamics
A fast and stable method is formulated to compute the time evolution of a
wavefunction by numerically solving the time-dependent Schr{\"o}dinger
equation. This method is a real space/real time evolution method implemented by
several computational techniques such as Suzuki's exponential product, Cayley's
form, the finite differential method and an operator named adhesive operator.
This method conserves the norm of the wavefunction, manages periodic conditions
and adaptive mesh refinement technique, and is suitable for vector- and
parallel-type supercomputers. Applying this method to some simple electron
dynamics, we confirmed the efficiency and accuracy of the method for simulating
fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure
Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-S
The spin-1 Uimin-Lai-Sutherland (ULS) isotropic chain model is expressed in
terms of fermions and the equivalence of the fermionic representation to the
supersymmetric t-J model is established directly at the level of
Hamiltonians.The spin-S ULS model is fermionized and the Hamiltonian of the
corresponding generalisation of the t-J model is written down.Comment: 16 page
Solution of the quantum inverse problem
We derive a formula that expresses the local spin and field operators of
fundamental graded models in terms of the elements of the monodromy matrix.
This formula is a quantum analogue of the classical inverse scattering
transform. It applies to fundamental spin chains, such as the XYZ chain, and to
a number of important exactly solvable models of strongly correlated electrons,
such as the supersymmetric t-J model or the the EKS model.Comment: 37 pages, AMS-Latex, AMS-Font
Finding Exponential Product Formulas of Higher Orders
In the present article, we review a continual effort on generalization of the
Trotter formula to higher-order exponential product formulas. The exponential
product formula is a good and useful approximant, particularly because it
conserves important symmetries of the system dynamics. We focuse on two
algorithms of constructing higher-order exponential product formulas. The first
is the fractal decomposition, where we construct higher-order formulas
recursively. The second is to make use of the quantum analysis, where we
compute higher-order correction terms directly. As interludes, we also have
described the decomposition of symplectic integrators, the approximation of
time-ordered exponentials, and the perturbational composition.Comment: 22 pages, 9 figures. To be published in the conference proceedings
''Quantum Annealing and Other Optimization Methods," eds. B.K.Chakrabarti and
A.Das (Springer, Heidelberg
The Schr\"oder functional equation and its relation to the invariant measures of chaotic maps
The aim of this paper is to show that the invariant measure for a class of
one dimensional chaotic maps, , is an extended solution of the Schr\"oder
functional equation, , induced by them. Hence, we give an
unified treatment of a collection of exactly solved examples worked out in the
current literature. In particular, we show that these examples belongs to a
class of functions introduced by Mira, (see text). Moreover, as a new example,
we compute the invariant densities for a class of rational maps having the
Weierstrass functions as an invariant one. Also, we study the relation
between that equation and the well known Frobenius-Perron and Koopman's
operators.Comment: 9 page
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