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