Quantum information analysis of the phase diagram of the half-filled extended Hubbard model

We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and small on-site Coloumb repulsion and a spin-density-wave at small nearest-neighbor and large on-site Coloumb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first-order at strong coupling to second-order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent, unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.Comment: 8 pages, 7 figure

Elementary Secondary Education Act, Title II Non-Print Expenditures for 1965-1966 in Washington State Public Schools

The purpose of doing this study was to compile, categorize, report and evaluate the data concerning the purchases of non-print materials by Washington State Public Schools with Federal funds provided through Title II Elementary and Secondary Education Act of 1965. The data was collected from Title II applications submitted by Washington State Public Schools to the State Department of Public Instruction as of June 12, 1967

Uniform and staggered magnetizations induced by Dzyaloshinskii-Moriya interactions in isolated and coupled spin 1/2 dimers in a magnetic field

We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin 1/2 dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the ${\bf D}$ vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes {\it perpendicular} to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of $0.35 g\mu_B$ in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of inter-dimer coupling in the context of ladders with Density Matrix Renormalization Group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on Cu$_{2}$(C$_{5}$H$_{12}$N$_{2}$)$_{2}$Cl$_{4}$.Comment: 8 pages, 9 figure

Smoothing and Rothe's method for Stefan problems in enthalpy form

AbstractThe classical two-phase Stefan problem as well as its weak variational formulation model the connection between the different phases of the considered material by interface conditions at the occurring free boundary or by a jump of the enthalpy. One way to treat the corresponding discontinuous variational problems consists in its embedding into a family of continuous ones and applying some standard techniques to the chosen approximation problems. The aim of the present paper is to analyze a semi-discretization via Rothe's method and its convergence behavior in dependence of the smoothing parameter. While in Grossmann et al. (Optimization, in preparation) the treatment of the Stefan problem is based on the given variable, i.e. the temperature, here first a transformation via the smoothed enthalpy is applied. Numerical experiments indicate a higher stability of the discretization by Rothe's method. In addition, to avoid inner iterations a frozen coefficient approach as common in literature is used