322 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
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
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
Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy
We consider spatially two dimensional Madelung fluid whose irrotational
motion reduces into the Schr\"odinger equation for a single free particle. In
this respect, we regard the former as a direct generalization of the latter,
allowing a rotational quantum flow. We then ask for the most likely wave
function possessing a given average energy by maximizing the Shannon
information entropy over the quantum probability density. We show that there
exists a class of solutions in which the wave function is self-trapped,
rotationally symmetric, spatially localized with finite support, and spinning
around its center, yet stationary. The stationarity comes from the balance
between the attractive quantum force field of a trapping quantum potential
generated by quantum probability density and the repulsive centrifugal force of
a rotating velocity vector field. We further show that there is a limiting case
where the wave function is non-spinning and yet still stationary. This special
state turns out to be the lowest stationary state of the ordinary Schr\"odinger
equation for a particle in a cylindrical tube classical potential.Comment: 19 page
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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