Riesz transforms associated to Schr\"odinger operators with negative potentials

The goal of this paper is to study the Riesz transforms \na A^{-1/2} where $A$ is the Schr\"odinger operator -\D-V, V\ge 0, under different conditions on the potential $V$. We prove that if $V$ is strongly subcritical, \na A^{-1/2} is bounded on $L^p(\R^N)$, $N\ge3$, for all $p\in(p_0';2]$ where $p_0'$ is the dual exponent of $p_0$ where $2<\frac{2N}{N-2

Efficient calculation of imaginary time displaced correlation functions in the projector auxiliary field quantum Monte-Carlo algorithm

The calculation of imaginary time displaced correlation functions with the auxiliary field projector quantum Monte-Carlo algorithm provides valuable insight (such as spin and charge gaps) in the model under consideration. One of the authors and M. Imada [F.F. Assaad and M. Imada, J. Phys. Soc. Jpn. 65 189 (1996).] have proposed a numerically stable method to compute those quantities. Although precise this method is expensive in CPU time. Here, we present an alternative approach which is an order of magnitude quicker, just as precise, and very simple to implement. The method is based on the observation that for a given auxiliary field the equal time Green function matrix, $G$, is a projector: $G^2 = G$.Comment: 4 papes, 1 figure in eps forma

Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions

We show that the two recently proposed methods to compute Renyi entanglement entropies in the realm of determinant quantum Monte Carlo methods for fermions are in principle equivalent, but differ in sampling strategies. The analogy allows to formulate a numerically stable calculation of the entanglement spectrum at strong coupling. We demonstrate the approach by studying static and dynamical properties of the entanglement hamiltonian across the interaction driven quantum phase transition between a topological insulator and quantum antiferromagnet in the Kane-Mele Hubbard model. The formulation is not limited to fermion systems and can readily be adapted to world-line based simulations of bosonic systems.Comment: 8 pages, 5 figure

Coupled analysis of material flow and die deflection in direct aluminum extrusion

The design of extrusion dies depends on the experience of the designer. After the die has\ud been manufactured, it is tested during an extrusion trial and machined several times until it works\ud properly. The die is designed by a trial and error method which is an expensive process in terms\ud of time and the amount of scrap. In order to decrease the time and the amount of scrap, research is\ud going on to replace the trial pressing with finite element simulations. The goal of these simulations\ud is to predict the material flow through the die. In these simulations, it is required to calculate the\ud material flow and the tool deformation simultaneously. Solving the system of equations concerning\ud the material flow and the tool deformation becomes more difficult with increasing the complexity\ud of the die. For example the total number of degrees of freedom can reach a value of 500,000 for\ud a flat die. Therefore, actions must be taken to solve the material flow and the tool deformation\ud simultaneously and faster. This paper describes the calculation of a flat die deformation used in the\ud production of a U-shape profile with a coupled method. In this calculation an Arbitrary Lagrangian\ud Eulerian and Updated Lagrangian formulation are applied for the aluminum and the tool finite\ud element models respectively. In addition, for decreasing the total number of degrees of freedom,\ud the stiffness matrix of the tool is condensed to the contact nodes between the aluminum and the tool\ud finite element models. Finally, the numerical results are compared with experiment results in terms\ud of extrusion force and the angular deflection of the tongue

The Fractional Quantum Hall Effect on a Lattice

Starting from the Hofstadter butterfly, we define lattice versions of Landau levels as well as a continuum limit which ensures that they scale to continuum Landau levels. By including a next-neighbor repulsive interaction and projecting onto the lowest lattice Landau level, we show that incompressible ground states exist at filling fractions, $\nu = 1/3, 2/5$ and $3/7$. Already for values of $l_0/a \sim 2$ where $l_0$ ($a$) is the magnetic length (lattice constant), the lattice version of the $\nu = 1/3$ state reproduces with nearly perfect accuracy the the continuum Laughlin state. The numerical data strongly suggests that at odd filling fractions of the lowest lattice Landau level, the lattice constant is an irrelevant length scale. We find a new relation between the hierarchy of incompressible states and the self-similar structure of the Hofstadter butterfly.Comment: 11 pages, Latex, 3 compressed and uuencoded postscript figures appended, FFA-94-0