Green's Functions from Quantum Cluster Algorithms

We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a cluster algorithm for the partition function has been constructed. To explain the idea, we consider the quantum XY model and compute its two point Green's function in various ways, showing that all of them are equivalent. We also provide numerical evidence confirming the analytic arguments. Similar techniques are applicable to other models. In particular, in the recently constructed quantum link models, the new technique allows us to construct improved estimators for Wilson loops and may lead to a very precise determination of the glueball spectrum.Comment: 15 pages, LaTeX, with four figures. Added preprint numbe

High Efficiency Detection of Argon Scintillation Light of 128nm Using LAAPDs

The possibility of efficient collection and detection of vacuum ultraviolet light as emitted by argon, krypton, and xenon gas is studied. Absolute quantum efficiencies of large area avalanche photodiodes (LAAPDs) are derived at these wavelengths. VUV light of wavelengths down to the 128nm of Ar emission is shown to be detectable with silicon avalanche photodiodes at quantum efficiencies above 42%. Flexible Mylar foil overcoated with Al+MgF$_2$ is measured to have a specular reflectivity of $\sim$91% at argon emission wavelength. Low-pressure argon gas is shown to emit significant amounts of non-UV radiation. The average energy expenditure for the creation of non-UV photons in argon gas at this pressure is measured to be below 378 eV.Comment: 5 pages, 4 figures, Talk given at IEEE 2005 Nuclear Science Symposium and Medical Imaging Conference, Puerto Ric

Non-perturbative Renormalization Constants using Ward Identities

We extend the application of vector and axial Ward identities to calculate $b_A$, $b_P$ and $b_T$, coefficients that give the mass dependence of the renormalization constants of the corresponding bilinear operators in the quenched theory. The extension relies on using operators with non-degenerate quark masses. It allows a complete determination of the $O(a)$ improvement coefficients for bilinears in the quenched approximation using Ward Identities alone. Only the scale dependent normalization constants $Z_P^0$ (or $Z_S^0$) and $Z_T$ are undetermined. We present results of a pilot numerical study using hadronic correlators.Comment: 3 pages. Makefile and sources included. Talk presented at LATTICE98 (matrixelement

Kosterlitz-Thouless Universality in a Fermionic System

A new extension of the attractive Hubbard model is constructed to study the critical behavior near a finite temperature superconducting phase transition in two dimensions using the recently developed meron-cluster algorithm. Unlike previous calculations in the attractive Hubbard model which were limited to small lattices, the new algorithm is used to study the critical behavior on lattices as large as $128\times 128$. These precise results for the first time show that a fermionic system can undergo a finite temperature phase transition whose critical behavior is well described by the predictions of Kosterlitz and Thouless almost three decades ago. In particular it is confirmed that the spatial winding number susceptibility obeys the well known predictions of finite size scaling for $T<T_c$ and up to logarithmic corrections the pair susceptibility scales as $L^{2-\eta}$ at large volumes with $0\leq\eta\leq 0.25$ for $0\leq T\leq T_c$.Comment: Revtex format; 4 pages, 2 figure

Topological Phases in Neuberger-Dirac operator

The response of the Neuberger-Dirac fermion operator D=\Id + V in the topologically nontrivial background gauge field depends on the negative mass parameter $m_0$ in the Wilson-Dirac fermion operator $D_w$ which enters $D$ through the unitary operator $V = D_w (D_w^{\dagger} D_w)^{-1/2}$. We classify the topological phases of $D$ by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise

Quantum Link Models with Many Rishon Flavors and with Many Colors

Quantum link models are a novel formulation of gauge theories in terms of discrete degrees of freedom. These degrees of freedom are described by quantum operators acting in a finite-dimensional Hilbert space. We show that for certain representations of the operator algebra, the usual Yang-Mills action is recovered in the continuum limit. The quantum operators can be expressed as bilinears of fermionic creation and annihilation operators called rishons. Using the rishon representation the quantum link Hamiltonian can be expressed entirely in terms of color-neutral operators. This allows us to study the large N_c limit of this model. In the 't Hooft limit we find an area law for the Wilson loop and a mass gap. Furthermore, the strong coupling expansion is a topological expansion in which graphs with handles and boundaries are suppressed.Comment: Lattice2001(theorydevelop), poster by O. Baer and talk by B. Schlittgen, 6 page

State-recycling and time-resolved imaging in topological photonic lattices

Photonic lattices - arrays of optical waveguides - are powerful platforms for simulating a range of phenomena, including topological phases. While probing dynamics is possible in these systems, by reinterpreting the propagation direction as "time," accessing long timescales constitutes a severe experimental challenge. Here, we overcome this limitation by placing the photonic lattice in a cavity, which allows the optical state to evolve through the lattice multiple times. The accompanying detection method, which exploits a multi-pixel single-photon detector array, offers quasi-real time-resolved measurements after each round trip. We apply the state-recycling scheme to intriguing photonic lattices emulating Dirac fermions and Floquet topological phases. In this new platform, we also realise a synthetic pulsed electric field, which can be used to drive transport within photonic lattices. This work opens a new route towards the detection of long timescale effects in engineered photonic lattices and the realization of hybrid analogue-digital simulators.Comment: Comments are welcom