Two-dimensional Fermion Model Research Articles

Two-dimensional nonlinear fermionic models in curved space with torsion

A completely integrable two-dimensional model of gravity with dynamical metric and torsion coupled to 2D massless Dirac matter is extended by inclusion of a nonlinear fermionic interaction. The classical equations of motion of this model are solved by considering perturbations up to second order. The Green function for the massless Dirac equation in this model is also calculated.

Dx2-y2 superconductivity in a model of correlated fermions.

A two-dimensional fermionic model with attractive interactions is discussed. Its form is motivated by the phenomenology of the underdoped high-{ital T}{sub {ital c}} cuprates, as discussed in previous literature. The exact solution to the two-particle problem leads to a bound state in the {ital d}{sub {ital x}{sup 2}{minus}{ital y}{sup 2}} subspace. Numerical techniques show that the model has strong {ital d}{sub {ital x}{sup 2}{minus}{ital y}{sup 2}} pairing correlations in the ground state at low fermionic density. Within a self-consistent random phase approximation diagrammatic study, the model has a {ital d}-wave superconducting (SC) phase. The density dependence of the critical temperature is calculated. We argue that in the context of {ital d}-wave SC this model fulfills the role that the attractive on-site Hubbard model has played for {ital s}-wave SC. We also show that another candidate, the attractive {ital t}-{ital U}-{ital V} model, is actually not useful as a toy model for {ital d}-wave SC for a variety of reasons. {copyright} {ital 1996 The American Physical Society.}

A partial resummation of diagrams in the two-dimensional lattice fermion model with Pauli-Villars regularization

The polarization operator and axial current are obtained by means of a partial resummation in the Schwinger two-dimensional lattice SLAC-fermion model with Pauli-Villars regularization. It is shown that the resummation procedure does not change the result obtained earlier in [1] for the fermion model under consideration.

Spin chains and chiral lattice fermions

The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter's corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by fermionized nearest-neighbor Heisenberg spin chain operators. The transformation properties of the local lattice fermion operators under a boost provide a natural and precise way of generalizing the chiral structure of a continuum Dirac field to the lattice. The resulting formulation differs from both the Wilson and staggered (Kogut-Susskind) prescriptions. In particular, an axial $Q_5$ rotation is sitewise local, while the vector charge rotation mixes nearest neighbors on even and odd sublattices.

Two-dimensional fermionic correlations in topologically nontrivial backgrounds.

By using a path-integral approach to the study of two-dimensional massless fermionic models in nontrivial sectors, we compute certain special correlation functions which are nonvanishing only when nontrivial topology is taken into account. In particular, we derive the first explicit expression for the so-called nonminimal Green's function. We introduce one specific topological charge distribution for which this correlation function takes a simple form. We also comment on the application of our results to the analysis of massive fermions in topological backgrounds.

GENERALIZED COSET CONSTRUCTION AND CONSTRAINED FERMIONIC MODELS

We present a path-integral formulation of two-dimensional constrained fermionic models which correspond to a generalized coset construction G=Hn/Hn-1/…/H1 for a descending chain of groups Hn⊃Hn-1⊃…⊃H1.

Ground state properties of the two-dimensional spin fermion model

Two dimensional spin-fermion model is studied by using the perturbation method and the spin wave approximation. Non-crossing diagrams are calculated using the dominant pole approximation. As a result, we see that the renormalization parameter z is reduced as z ∝ L −1 4 , where L is the linear dimension of the system, and the doped fermion becomes totally incoherent in the thermodynamic limit.

Dissolving of mesons and soliton baryons in 2-dimensional gauge theories

We analyse two-dimensional fermionic models with a nonabelian gauge and chiral symmetry in the largeN limit. We show that there is a transition temperature at which the chiral symmetry is restored. At this transition temperature the meson bound states and the chiral solitons, the baryons of the model, dissolve. We interpret this as a simultaneous chiral symmetry restoration and deconfinement transition.

Constrained Fermi systems and Virasoro algebras

We study constrained two-dimensional fermion models in the path-integral framework. We consider constraints on the fermion currents and on the energy-momentum tensor. We discuss how these constraints determine the structure of the Virasoro algebras.

Connection of some two-dimensional bosonic and fermionic models to scalar curvature.

It is found that the equations of motion of a variety of two-dimensional bosonic and fermionic models are a consequence of the constancy of the scalar curvature.

Path-integral bosonization for the Abelian Avan-de Vega two-dimensional model.

We study the bosonization of the Abelian version of the Avan-de Vega two-dimensional fermion model in the framework of path integrals.

Invalidity of the replica trick for a two-dimensional fermion model

Non-interacting fermions in a random potential are considered on a square lattice. Such a model was previously proposed as a description of the quenched thermodynamics of a disordered Ising model. The author compares in a perturbative approach the replica trick and a formal functional integral representation and find that they yield different results.

Symmetric quantum models from non-symmetric classical actions

Two-dimensional fermionic models with classical actions breaking Lorentz and/or flavour symmetry are studied in the large- N limit. It is shown that they both lead in the infrared limit to the same well-behaved theory which is the usual Gross-Neveu model.

Free-fermion, checkerboard andZ-invariant lattice models in statistical mechanics

It is shown that the two-dimensional free fermion model is equivalent to a checkerboard Ising model, which is a special case of the general ‘Z-invariant’ Ising model. Expressions are given for the partition function and local correlations in terms of those of the regular square lattice Ising model. Corresponding results are given for the self-dual Potts model, and the application of the methods to the three-dimensional Zamolodchikov model is discussed. The paper ends with a discussion of the critical and disorder surfaces of the checkerboard Potts model.

Soluble two-dimensional fermionic models with broken SU( N) symmetry

Two new families of broken SU( N) massless Thirring models are shown to be integrable by the Bethe ansatz. They correspond to asymmetric versions of the Coqblin-Schrieffer model of condensed matter if one of the particle chiralities has zero kinetic energy.