We introduce a separability condition for the states of fermion lattice systems. It shares similar characterizations about the state correlation between a pair of disjoint subsystems with that for the tensor-product systems. We propose two seemingly natural non-separable degrees for the fermion lattice system based on our generalization of the entanglement of formation to an arbitrary, namely n...

 The two-dimensional structure of graphene, consisting of an isotropic hexagonal lattice of carbon atoms, shows fascinating electronic properties, such as a gapless energy band and Dirac fermion behavior of electrons at fermi surface. Anisotropy can be induced in this structure by electrochemical pressure. In this article, by using tight-binding method, we review anisotropy effects in the elect...

Let γ be an automorphism of a fermion-boson C∗-system. If γ commutes with an arbitrary asymptotically abelian group of automorphisms, then it preserves the fermion grading symmetry.

We prove unbroken symmetry of grading transformations multiplying all fermion field operators by −1. We give a criterion of spontaneously symmetry breaking for general quasi-local systems with any statistics called macroscopic spontaneously symmetry breaking, or for short MSSB. It is formulated based on our thermodynamical viewpoint that each pair of distinct phases (appeared in spontaneous sym...

A system of strongly interacting fermions in a solid state is discussed. As an example, a structure of singlet and triplet coupled 2-particle states and their excitation spectra are investigated. It is shown that an account of intersite fermion interaction leads to new boson modes. Their number depends on dimensionality of a system. It is shown also that a reasonable choice of Hamiltonian param...

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zerotemperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green’s function and the density-density correlation function both for a...