Related papers: On integrability of the one-dimensional Hubbard mo…
The representation of the Hubbard operators in terms of the spin$-\frac{1}{2}$ operators and the fermion operator with spin$-\frac{1}{2}$ is proposed. In the low-energy limit this representation is reduced to the representation following…
We construct invertible spectral parameter dependent Yang-Baxter solutions ($R$-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic (representation independent). They are constructed using…
We construct the XX and Hubbard-like models based on unitary superalgebras gl(N|M) generalizing Shastry's and Maassarani's approach. We introduce the R-matrix of the gl(N|M) XX-type model; the one of the Hubbard-like model is defined by…
For any algebra two families of coloured Yang-Baxter operators are constructed, thus producing solutions to the two-parameter quantum Yang-Baxter equation. An open problem about a system of functional equations is stated. The matrix forms…
By using the supersymmetric version of the Faddeev-Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In this approach the Hubbard ${\hat X}$-operators are used as field variables. In…
I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local…
The symmetries, especially those related to the $R$-transformation, of the reflection equation(RE) for two-component systems are analyzed. The classification of solutions to the RE for eight-, six- and seven-vertex type $R$-matrices is…
We construct XX- and Hubbard- like models based on unitary superalgebras gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N|M) XX model and that of the Hubbard model defined…
A rigorous result about Hubbard model obtained by C.N.Yang [Phys.Rev.Lett.63,2144(1989)] is generalized to two kinds of extended Hubbard models. One is the Hubbard model in two-dimensional triangular lattice, and the other is the Hubbard…
The application of functional integral methods and the Hubbard--Stratonovich transformation to the Hubbard model is discussed. For the attractive case, using a simple gauge transformation of the superconducting order parameter field, the…
Two new one-dimensional fermionic models depending on two independent parameters are formulated and solved exactly by the Bethe-ansatz method. These models connect continuously the integrable Hubbard and supersymmetric t-J models.
We consider the symmetry resolved R\'enyi entropies in the one dimensional tight binding model, equivalent to the spin-1/2 XX chain in a magnetic field. We exploit the generalised Fisher-Hartwig conjecture to obtain the asymptotic behaviour…
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower…
We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…
We reanalyze the Hubbard-I approximation by showing that it is equivalent to an effective Hamiltonian describing Fermionic charge fluctuations, which can be solved by Bogoliubov transformation. As the most important correction in the limit…
We construct a hyperbolic modular double -- an algebra lying in between the Faddeev modular double for $U_q(sl_2)$ and the elliptic modular double. The intertwining operator for this algebra leads to an integral operator solution of the…
We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The…
We classify all fundamental integrable spin chains with two-dimensional local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form R(u,v)=R(u-v) and…
In this paper we continue the development of quantum holonomy theory, which is a candidate for a fundamental theory based on gauge fields and non-commutative geometry. The theory is build around the QHD(M) algebra, which is generated by…
In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay,…