Related papers: Bosonization and the lattice: the $d=2$ Gross-Neve…
We review our results for the simulation of the 2--d lattice Gross--Neveu model in a fermion loop representation. Possible extensions of our techniques to other models and higher dimensions are discussed, as well as the limitations of…
Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is \emph{exactly\/}…
In this work we present two correspondences between the massless Gross-Neveu model with one or two coupling constants in 1+1 dimensions and nonrelativistic field theories in 3+1 dimensions. It is shown that on a mean-field level the…
We suggest a method of bosonizing any D=2 theory. We demonstrate how it works with the examples of the Thirring and the Schwinger models, known results are reproduced. This method, being applied to the Gross-Neveu model, yields nonlinear…
The (discrete) Gross-Neveu model is studied in a lattice realization with an N-component Majorana Wilson fermion field. It has an internal O(N) symmetry in addition to the euclidean lattice symmetries. The discrete chiral symmetry for…
We construct a Hamiltonian lattice regularisation of the $N$-flavour Gross-Neveu model that manifestly respects the full $\mathsf{O}(2N)$ symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field…
The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more…
We analytically investigate the 2-dimensional Gross-Neveu model at finite temperature and density using Wilson fermion action. The relation between the phase structure on the lattice and that in the continuum is clarified.
In this paper we present a schema for describing dualities between physical theories (Sections 2 and 3), and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory (Sections…
Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making…
We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent…
An effective quantum field theory of the 2D Hubbard model on a square lattice near half-filling is presented and studied. This effective model describes so-called nodal and antinodal fermions, and it is derived from the lattice model using…
We introduce in this paper two dimensional lattice models whose continuum limit belongs to the $N=2$ series. The first kind of model is integrable and obtained through a geometrical reformulation, generalizing results known in the $k=1$…
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum…
In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…
The Gross-Neveu model is a quantum field theory model of Dirac fermions in two dimensions with a quartic interaction term. Like Yang-Mills theory in four dimensions, the model is scaling critical (i.e. renormalizable but not…
Many of the exciting features of the Standard Model of the elementary particles are inherently non-perturbative. A theoretical understanding of many physics aspects beyond the Standard Model of elementary particles also requires a…
The massless Gross-Neveu and chiral Gross-Neveu models are well known examples of integrable quantum field theories in 1+1 dimensions. We address the question whether integrability is preserved if one either replaces the four-fermion…
Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions…
A local quantum bosonic model on a lattice is constructed whose low energy excitations are gravitons described by linearized Einstein action. Thus the bosonic model is a quantum theory of gravity, at least at the linear level. We find that…