71,007 research outputs found
Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
Here we present an efficient and numerically stable procedure for compressing
a correlation matrix into a set of local unitary single-particle gates, which
leads to a very efficient way of forming the matrix product state (MPS)
approximation of a pure fermionic Gaussian state, such as the ground state of a
quadratic Hamiltonian. The procedure involves successively diagonalizing
subblocks of the correlation matrix to isolate local states which are purely
occupied or unoccupied. A small number of nearest neighbor unitary gates
isolates each local state. The MPS of this state is formed by applying the
many-body version of these gates to a product state. We treat the simple case
of compressing the correlation matrix of spinless free fermions with definite
particle number in detail, though the procedure is easily extended to fermions
with spin and more general BCS states (utilizing the formalism of Majorana
modes). We also present a DMRG-like algorithm to obtain the compressed
correlation matrix directly from a hopping Hamiltonian. In addition, we discuss
a slight variation of the procedure which leads to a simple construction of the
multiscale entanglement renormalization ansatz (MERA) of a fermionic Gaussian
state, and present a simple picture of orthogonal wavelet transforms in terms
of the gate structure we present in this paper. As a simple demonstration we
analyze the Su-Schrieffer-Heeger model (free fermions on a 1D lattice with
staggered hopping amplitudes).Comment: 15 pages, 17 figure
Competition Between Stripes and Pairing in a t-t'-J Model
As the number of legs n of an n-leg, t-J ladder increases, density matrix
renormalization group calculations have shown that the doped state tends to be
characterized by a static array of domain walls and that pairing correlations
are suppressed. Here we present results for a t-t'-J model in which a diagonal,
single particle, next-near-neighbor hopping t' is introduced. We find that this
can suppress the formation of stripes and, for t' positive, enhance the
d_{x^2-y^2}-like pairing correlations. The effect of t' > 0 is to cause the
stripes to evaporate into pairs and for t' < 0 to evaporate into
quasi-particles. Results for n=4 and 6-leg ladders are discussed.Comment: Four pages, four encapsulated figure
A Renormalization Group Method for Quasi One-dimensional Quantum Hamiltonians
A density-matrix renormalization group (DMRG) method for highly anisotropic
two-dimensional systems is presented. The method consists in applying the usual
DMRG in two steps. In the first step, a pure one dimensional calculation along
the longitudinal direction is made in order to generate a low energy
Hamiltonian. In the second step, the anisotropic 2D lattice is obtained by
coupling in the transverse direction the 1D Hamiltonians. The method is applied
to the anisotropic quantum spin half Heisenberg model on a square lattice.Comment: 4 pages, 4 figure
The linear polarization of lunar thermal emission at 3.1 mm wavelength
Several observations of the distribution of linearly polarized lunar thermal emission were made at a wavelength of 3.1 mm with 4.88 m parabolic reflector from February to March 1971. A shadow corrected rough surface thermal emission model was least squares fitted to the data. Results indicate an effective lunar dielectric constant of 1.34 + or -.08 with surface roughness characterized by a standard deviation of surface slopes of 18 deg + or - 2 deg. A comparison of these results with previously published values at other wavelengths suggests that the effective lunar dielectric constant decreases with decreasing wavelength
Thermodynamics of the anisotropic Heisenberg chain calculated by the density matrix renormalization group method
The density matrix renormalization group (DMRG) method is applied to the
anisotropic Heisenberg chain at finite temperatures. The free energy of the
system is obtained using the quantum transfer matrix which is iteratively
enlarged in the imaginary time direction. The magnetic susceptibility and the
specific heat are calculated down to T=0.01J and compared with the Bethe ansatz
results. The agreement including the logarithmic correction in the magnetic
susceptibility at the isotropic point is fairly good.Comment: 4 pages, 3 Postscript figures, REVTeX, to appear in J. Phys. Soc.
Jpn. Vol.66 No.8 (1997
An Attempt to Calculate Energy Eigenvalues in Quantum Systems of Large Sizes
We report an attempt to calculate energy eigenvalues of large quantum systems
by the diagonalization of an effectively truncated Hamiltonian matrix. For this
purpose we employ a specific way to systematically make a set of orthogonal
states from a trial wavefunction and the Hamiltonian. In comparison with the
Lanczos method, which is quite powerful if the size of the system is within the
memory capacity of computers, our method requires much less memory resources at
the cost of the extreme accuracy.
In this paper we demonstrate that our method works well in the systems of
one-dimensional frustrated spins up to 48 sites, of bosons on a chain up to 32
sites and of fermions on a ladder up to 28 sites. We will see this method
enables us to study eigenvalues of these quantum systems within reasonable
accuracy.Comment: 17pages, 4figures(eps-files
A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm
It has proved difficult to extend the density matrix renormalization group
technique to large two-dimensional systems. In this Communication I present a
novel approach where the calculation is done directly in two dimensions. This
makes it possible to use an infinite system method, and for the first time the
fixed point in two dimensions is studied. By analyzing several related blocking
schemes I find that there exists an algorithm for which the local energy
decreases monotonically as the system size increases, thereby showing the
potential feasibility of this method.Comment: 5 pages, 6 figure
Observing the sky at extremely high energies with the Cherenkov Telescope Array: Status of the GCT project
The Cherenkov Telescope Array is the main global project of ground-based
gamma-ray astronomy for the coming decades. Performance will be significantly
improved relative to present instruments, allowing a new insight into the
high-energy Universe [1]. The nominal CTA southern array will include a
sub-array of seventy 4 m telescopes spread over a few square kilometers to
study the sky at extremely high energies, with the opening of a new window in
the multi-TeV energy range. The Gamma-ray Cherenkov Telescope (GCT) is one of
the proposed telescope designs for that sub-array. The GCT prototype recorded
its first Cherenkov light on sky in 2015. After an assessment phase in 2016,
new observations have been performed successfully in 2017. The GCT
collaboration plans to install its first telescopes and cameras on the CTA site
in Chile in 2018-2019 and to contribute a number of telescopes to the
subsequent CTA production phase.Comment: 8 pages, 7 figures, ICRC201
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