We put forth a Fierzed hopping expansion for strong coupling Wilson fermions. As an application, we show that the strong coupling Schwinger model on parallelogram lattices with nonbacktracking Wilson fermions span, as a function of the lattice skewness angle, the ∆ = −1 critical line of 6-vertex models. This Fierzed formulation also applies to backtracking Wilson fermions, which as we describe ...

In recent work,N = 2 supersymmetry has been proposed as a tool for the analysis of itinerant, correlated fermions on a lattice. In this paper we extend these considerations to the case of lattice fermions with spin 1/2 . We introduce a model for correlated spin-1/2 fermions with a manifest N = 4 supersymmetry, and analyze its properties. The supersymmetric ground states that we find represent h...

The mass spectrum and the mixing of fundamental fermions are the most important unsolved problems of the particle physics. According to the Standard Model (SM), these masses and mixings arise from the interaction with the Higgs doublet via spontaneous symmetry breaking. In the framework of SM, fermions with the same quantum numbers (electric charge, weak isospin, etc.) are indistinguishable bef...

We discuss the behavior of free perfect staggered fermions and truncated versions thereof. The study includes flavor non-degenerate masses. We suggest a new blocking scheme, which provides excellent locality of the perfect lattice action. A truncation procedure adequate for the structure of staggered fermions is applied. We consider spectral and thermodynamic properties and compare truncated pe...

We develop a multichannel scattering theory for atom-atom collisions in quasi-1D geometries. We apply our general framework to the low energy scattering of two spin-polarized fermions and show that tightly confined fermions have infinitely strong interactions at a particular value of the 3D, free-space p-wave scattering volume. Moreover, we describe a mapping of this strongly interacting system...

However many obstacles seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. Which fermions and bosons could be related ? Is spontaneous supersymmetry breaking possible at all ? If yes, where is the corresponding spin1 2 Goldstone fermion ? Supersymmetric theories also involve Majorana fermions, unknown in Nature. And how could we define conserved quan...

We consider a recent proposal by Horváth et al. to address the question whether topological charge fluctuations in QCD are instanton dominated via the response of fermions using lattice fermions with exact chiral symmetry, the overlap fermions. Considering several volumes and lattice spacings we find strong evidence for chirality of a finite density of low-lying eigenvectors of the overlap-Dira...

We construct a perfect lattice action for staggered fermions by blocking from the continuum. The locality, spectrum and pressure of such perfect staggered fermions are discussed. We also derive a consistent fixed point action for free gauge fields and discuss its locality as well as the resulting static quark-antiquark potential. This provides a basis for the construction of (classically) perfe...

Most materials are either metals or insulators. When they are metals, their electronic properties are usually described by Landau's Fermi liquid theory. That is, they behave more or less like a free Fermi gas, with a few modifications due to electron-electron interactions. However, there exist a few metallic materials whose phenomenology does not fit within Fermi liquid theory. These are quasi-...

We study two-dimensional conformal field theories generated from a “symplectic fermion” — a free two-component fermion field of spin one — and construct the maximal local supersymmetric conformal field theory generated from it. This theory has central charge c = −2 and provides the simplest example of a theory with logarithmic operators. Twisted states with respect to the global SL(2, C)-symmet...