scholarly journals Exact Integrability of the su(n) Hubbard Model

1998 ◽  
Vol 12 (02n03) ◽  
pp. 51-56 ◽  
Author(s):  
Z. Maassarani
Keyword(s):  
Hubbard Model ◽  
One Dimension ◽  
Baxter Equation ◽  
Conserved Quantities ◽  
R Matrix ◽  
Conserved Charges ◽  
Exact Integrability ◽  
Infinite Set

The bosonic su (n) Hubbard model was recently introduced. The model was shown to be integrable in one dimension by exhibiting the infinite set of conserved quantities. I derive the R-matrix and use it to show that the conserved charges commute among themselves. This new matrix is a nonadditive solution of the Yang–Baxter equation. Some properties of this matrix are derived.

scholarly journals Degenerate Sklyanin algebras

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Andrey Smirnov
Keyword(s):  
Difference Operators ◽  
Baxter Equation ◽  
Quantum Algebras ◽  
Rational Solutions ◽  
R Matrix ◽  
Gauge Transformations ◽  
Sklyanin Algebras ◽  
Sklyanin Algebra ◽  
The Difference

AbstractNew trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

Equilibrium and Dynamical Properties of the Boson Hubbard Model in One Dimension

2005 ◽  
Vol 140 (3-4) ◽  
pp. 313-332 ◽  
Author(s):  
R. T. Scalettar ◽  
G. Batrouni ◽  
P.J.H. Denteneer ◽  
F. Hébert ◽  
A. Muramatsu ◽  
...  
Keyword(s):  
Hubbard Model ◽  
One Dimension ◽  
Dynamical Properties ◽  
Boson Hubbard Model

Transfer Matrix of the Two-dimensional Ising Model

2020 ◽  
pp. 211-234
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Transfer Matrix ◽  
Functional Equations ◽  
Baxter Equation ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
R Matrix ◽  
Transfer Matrix Formalism ◽  
Lowest Eigenvalue

This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

FERMIONS AND LINK INVARIANTS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 493-532 ◽  
Author(s):  
L. Kauffman ◽  
H. Saleur
Keyword(s):  
Braid Group ◽  
Degrees Of Freedom ◽  
Knot Theory ◽  
Alexander Polynomial ◽  
Baxter Equation ◽  
Group Representations ◽  
R Matrix ◽  
Link Invariants ◽  
Linear Representations ◽  
State Models

This paper deals with various aspects of knot theory when fermionic degrees of freedom are taken into account in the braid group representations and in the state models. We discuss how the Ř matrix for the Alexander polynomial arises from the Fox differential calculus, and how it is related to the quantum group Uqgl(1,1). We investigate new families of solutions of the Yang Baxter equation obtained from "linear" representations of the braid group and exterior algebra. We study state models associated with Uqsl(n,m), and in the case n=m=1 a state model for the multivariable Alexander polynomial. We consider invariants of links in solid handlebodies and show how the non trivial topology lifts the boson fermion degeneracy that is present in S3. We use "gauge like" changes of basis to obtain invariants in thickened surfaces Σ×[0,1].

Sign in / Sign up

Export Citation Format

Share Document