68,680 research outputs found
Polynomial Expansion Monte Carlo Study of Frustrated Itinerant Electron Systems: Application to a Spin-ice type Kondo Lattice Model on a Pyrochlore Lattice
We present the benchmark of the polynomial expansion Monte Carlo method to a
Kondo lattice model with classical localized spins on a geometrically
frustrated lattice. The method enables to reduce the calculation amount by
using the Chebyshev polynomial expansion of the density of states compared to a
conventional Monte Carlo technique based on the exact diagonalization of the
fermion Hamiltonian matrix. Further reduction is brought by a real-space
truncation of the vector-matrix operations. We apply the method to the model
with spin-ice type Ising spins on a three-dimensional pyrochlore lattice, and
carefully examine the convergence in terms of the order of polynomials and the
truncation distance. We find that, in a wide range of electron density at a
relatively weak Kondo coupling compared to the noninteracting bandwidth, the
results by the polynomial expansion method show good convergence to those by
the conventional method within reasonable numbers of polynomials. This enables
us to study the systems up to 4x8^3 = 2048 sites, while the previous study by
the conventional method was limited to 4x4^3 = 256 sites. On the other hand,
the real-space truncation is not helpful in reducing the calculation amount for
the system sizes that we reached, as the sufficient convergence is obtained
when most of the sites are involved within the truncation distance. The
necessary truncation distance, however, appears not to show significant system
size dependence, suggesting that the truncation method becomes efficient for
larger system sizes.Comment: 13 pages, 9 figures, accepted for publication in Computer Physics
Communication
Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Coupled problems with various combinations of multiple physics, scales, and
domains are found in numerous areas of science and engineering. A key challenge
in the formulation and implementation of corresponding coupled numerical models
is to facilitate the communication of information across physics, scale, and
domain interfaces, as well as between the iterations of solvers used for
response computations. In a probabilistic context, any information that is to
be communicated between subproblems or iterations should be characterized by an
appropriate probabilistic representation. Although the number of sources of
uncertainty can be expected to be large in most coupled problems, our
contention is that exchanged probabilistic information often resides in a
considerably lower dimensional space than the sources themselves. In this work,
we thus use a dimension-reduction technique for obtaining the representation of
the exchanged information. The main subject of this work is the investigation
of a measure-transformation technique that allows implementations to exploit
this dimension reduction to achieve computational gains. The effectiveness of
the proposed dimension-reduction and measure-transformation methodology is
demonstrated through a multiphysics problem relevant to nuclear engineering
Progress on Polynomial Identity Testing - II
We survey the area of algebraic complexity theory; with the focus being on
the problem of polynomial identity testing (PIT). We discuss the key ideas that
have gone into the results of the last few years.Comment: 17 pages, 1 figure, surve
Q-operators in the six-vertex model
In this paper we continue the study of -operators in the six-vertex model
and its higher spin generalizations. In [1] we derived a new expression for the
higher spin -matrix associated with the affine quantum algebra
. Taking a special limit in this -matrix we obtained
new formulas for the -operators acting in the tensor product of
representation spaces with arbitrary complex spin.
Here we use a different strategy and construct -operators as integral
operators with factorized kernels based on the original Baxter's method used in
the solution of the eight-vertex model. We compare this approach with the
method developed in [1] and find the explicit connection between two
constructions. We also discuss a reduction to the case of finite-dimensional
representations with (half-) integer spins.Comment: 18 pages, no figure
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