Related papers: Colored Bosonic Models and Matrix Coefficients
We consider chiral, generally nonlinear density waves in one dimension, modelling the bosonized edge modes of a two-dimensional fermionic topological insulator. Using the coincidence between bosonization and Lie-Poisson dynamics on an…
We propose a model for Quantum Chromodynamics, obtained by ignoring the angular dependence of the gluon fields, which could qualitatively describe systems containing one heavy quark. This leads to a two dimensional gauge theory which has…
We introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in finite lattice. We introduce the $L$-operator related with the $U_q(sl_2)$ $R$-matrix, and…
In this paper, we prove a conjecture of Broadhurst and Zudilin \cite{BZ17} concerning a divisibility property of the Fourier coefficients of a meromorphic modular form using the generalization of the Shimura lift by Borcherds…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
We study the connection between the three-color model and the polynomials $q_n(z)$ of Bazhanov and Mangazeev, which appear in the eigenvectors of the Hamiltonian of the XYZ spin chain. By specializing the parameters in the partition…
While internal space-time symmetries of relativistic particles are dictated by the little groups of the Poincar\'e group, it is possible to construct representations of the little group for massive particles starting from harmonic…
In this paper we analyze the quantum homological invariants (the Poincar\'e polynomials of the $\mathfrak{sl}_N$ link homology). In the case when the dimensions of homologies of appropriate topological spaces are precisely known, the…
We study the chromatic quasisymmetric class function of a linearized combinatorial Hopf monoid. Given a linearized combinatorial Hopf monoid $H$, and an $H$-structure $h$ on a set $N$, there are proper colorings of $h$, generalizing graph…
A fully self-consistent calculation of the bosonic dynamics of the Hubbard model is developed within the Composite Operator Method. From one side we consider a basic set of fermionic composite operators (Hubbard fields) and calculate the…
A fully self-consistent calculation of the bosonic dynamics of the Hubbard model is developed within the Composite Operator Method. From one side we consider a basic set of fermionic composite operators (Hubbard fields) and calculate the…
We construct model wavefunctions for the collective modes of fractional quantum Hall systems. The wavefunctions are expressed in terms of symmetric polynomials characterized by a root partition and a "squeezed" basis, and show excellent…
The fundamental fermion representations of causal spinor fields have previously been demonstrated to describe free Dirac fermions, as well as incorporate \emph{only} the observed degrees of freedom for local gauge invariance. In this paper,…
We study the groundstates of cold atomic gases on rotating optical lattices, as described by the Bose-Hubbard model in a uniform effective magnetic field. Mapping the bosons to composite fermions leads to the prediction of quantum Hall…
The "color-flavor transformation", conceived as a kind of generalized Hubbard-Stratonovich transformation, is a variant of the Wegner-Efetov supermatrix method for disordered electron systems. Tailored to quantum systems with disorder…
We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…
We study the properties of the Luttinger-Ward functional (LWF) in a simplified Hubbard-type model without time or spatial dimensions, but with $N$ identical replicas located on a single site. The simplicity of this $(0+0)d$ model permits an…
We discuss the theory of mixtures of Bosonic and Fermionic atoms in periodic potentials at zero temperature. We derive a general Bose--Fermi Hubbard Hamiltonian in a one--dimensional optical lattice with a superimposed harmonic trapping…
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal…
We study incompressible ground states of bosons in a two-dimensional rotating square optical lattice. The system can be described by the Bose-Hubbard model in an effective uniform magnetic field present due to the lattice rotation. To study…