From Perturbation Theory to Confinement: How the String Tension is built up

We study the spatial volume dependence of electric flux energies for SU(2) Yang-Mills fields on the torus with twisted boundary conditions. The results approach smoothly the rotational invariant Confinement regime. The would-be string tension is very close to the infinite volume result already for volumes of $(1.2 \ {\rm fm.})^3$. We speculate on the consequences of our result for the Confinement mechanism.Comment: 6p, ps-file (uuencoded). Contribution to Lattice'93 Conference (Dallas, 1993). Preprint INLO-PUB 18/93, FTUAM-93/4

Instanton classical solutions of SU(3) fixed point actions on open lattices

We construct instanton-like classical solutions of the fixed point action of a suitable renormalization group transformation for the SU(3) lattice gauge theory. The problem of the non-existence of one-instantons on a lattice with periodic boundary conditions is circumvented by working on open lattices. We consider instanton solutions for values of the size (0.6-1.9 in lattice units) which are relevant when studying the SU(3) topology on coarse lattices using fixed point actions. We show how these instanton configurations on open lattices can be taken into account when determining a few-couplings parametrization of the fixed point action.Comment: 23 pages, LaTeX, 4 eps figures, epsfig.sty; some comments adde

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Calorons with non-trivial holonomy on and off the lattice

We discuss recent solutions for SU(2) calorons with non-trivial holonomy at higher charge, both through analytic means and using cooling, as well as extensive lattice studies for SU(3).Comment: 12 pages, 16 figures in 34 parts, 4 talks presented at Lattice 2004(topology

Coupling single molecule magnets to quantum circuits

In this work we study theoretically the coupling of single molecule magnets (SMMs) to a variety of quantum circuits, including microwave resonators with and without constrictions and flux qubits. The main results of this study is that it is possible to achieve strong and ultrastrong coupling regimes between SMM crystals and the superconducting circuit, with strong hints that such a coupling could also be reached for individual molecules close to constrictions. Building on the resulting coupling strengths and the typical coherence times of these molecules (of the order of microseconds), we conclude that SMMs can be used for coherent storage and manipulation of quantum information, either in the context of quantum computing or in quantum simulations. Throughout the work we also discuss in detail the family of molecules that are most suitable for such operations, based not only on the coupling strength, but also on the typical energy gaps and the simplicity with which they can be tuned and oriented. Finally, we also discuss practical advantages of SMMs, such as the possibility to fabricate the SMMs ensembles on the chip through the deposition of small droplets.Comment: 23 pages, 12 figure

Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator (MPDO) valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.Comment: v1: 11 pages, 1 figure. v2: very minor changes. About to appear in Journal of Mathematical Physic

Metal-insulator transition in Nd1−x_{1-x}Eux_{x}NiO3_{3} compounds

Polycrystalline Nd$_{1-x}$Eu$_{x}$NiO$_3$ ($0 \leq x \leq 0.5$) compounds were synthesized in order to investigate the character of the metal-insulator (MI) phase transition in this series. Samples were prepared through the sol-gel route and subjected to heat treatments at $\sim$1000 $^\circ$C under oxygen pressures as high as 80 bar. X-ray Diffraction (XRD) and Neutron Powder Diffraction (NPD), electrical resistivity $\rho(T)$, and Magnetization $M(T)$ measurements were performed on these compounds. The results of NPD and XRD indicated that the samples crystallize in an orthorhombic distorted perovskite structure, space group $Pbnm$. The analysis of the structural parameters revealed a sudden and small expansion of $\sim$0.2% of the unit cell volume when electronic localization occurs. This expansion was attributed to a small increase of $\sim$0.003 \AA{} of the average Ni-O distance and a simultaneous decrease of $\sim$$- 0.5^\circ$ of the Ni-O-Ni superexchange angle. The $\rho(T)$ measurements revealed a MI transition occurring at temperatures ranging from $T_{\rm MI}\sim 193$ to 336 K for samples with $x = 0$ and 0.50, respectively. These measurements also show a large thermal hysteresis in NdNiO$_{3}$ during heating and cooling processes suggesting a first-order character of the phase transition at $T_{\rm MI}$. The width of this thermal hysteresis was found to decrease appreciably for the sample Nd$_{0.7}$Eu$_{0.3}$NiO$_{3}$. The results indicate that cation disorder associated with increasing substitution of Nd by Eu is responsible for changing the first order character of the transition in NdNiO$_{3}$.Comment: 19 pages, 9 figure

QCD vacuum structure

Several issues related to the structure of the QCD vacuum are reviewed. We concentrate mostly on results concerning instantons and center vortices.Comment: Lattice 2000 (Plenary), 8 pages, 2 figures; typos corrected, hep-numbers of references updated, one figure replaced by black and whit