arXiv:cond-mat/9710083 · Modern Physics Letters B

Exact Integrability of the su (n) Hubbard Model

Z. Maassarani

Published Feb 10, 1998• 24 citations

Abstract

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.

DOI: 10.1142/s0217984998000081

Related papers

The Yang–Baxter integrability of the critical Ising chain

Akash Sinha, T. Clark Justin, Pramod Padmanabhan +1 more

Abstract We demonstrate that the one-dimensional critical transverse field Ising model (TFIM) is Yang–Baxter integrable. This is achieved by constructing commuting transfer matrices derived from an R-matrix that satisfies the Yang–Baxter equation with additive spectral parameters. The R-matrix is nonlocal because it is expressed in terms of Majorana fermions. It is also non-regular. Nevertheless, we show that the quantum inverse scattering method can still be suitably adapted. Using the boost operator method, we recursively obtain the conserved quantities in the infinite volume. Among the conserved charges, we identify the Kramers–Wannier duality and other non-invertible symmetries for the periodic TFIM.

arXiv:2506.03668Journal of Statistical Mechanics Theory and ExperimentOct 1, 20253 citations

YANG-BAXTER AND KAC-MOODY ALGEBRAS IN FIELD THEORY WITH SOLITONS

Hector J. de Vega

The integrability of some important physical systems with a finite number of degrees of freedom relies on purely algebraic properties. One can solve the Coulomb potential and the harmonic oscillator both classically and quantum mechanically, using the appropriate dynamical algebra only [1]. Integrable systems with an infinite number of degrees of freedom are those with an infinite number of conserved quantities. They exhibit loop algebras, Yang-Baxter algebras and Kac-Moody algebras as symmetries. The investigation of theories has shown in recent years that Yang-Baxter algebras are the basic concepts of integrability [2]. The commutativity of a family of transfer matrices both in field theory and statistical mechanics follows directly from the Yang-Baxter algebra of monodromy matrices. Since the transfer matrix is a generating functional of local and non-local charges (including the hamiltonian) one gets an infinite set of commuting and conserved quantities. So, we can say that the theory is integrable. We are using the word integrable in the large sense explained above. Moreover, theories can be often explicitly solved to a large extent [2, 3]. In this brief report I will concentrate on a specific class of field theories. A complete account can be found in refs. 4-7. This class

Talk given atJan 1, 19850 citations

Hubbard Models as Fusion Products of Free Fermions

Z. Maassarani

A class of recently introduced su (n) "free-fermion" models has recently been used to construct generalized Hubbard models. I derive an algebra defining the "free-fermion" models and give new classes of solutions. I then introduce a conjugation matrix and give a new and simple proof of the corresponding decorated Yang–Baxter equation. This provides the algebraic tools required to couple in an integrable way two copies of free-fermion models. Complete integrability of the resulting Hubbard-like models is shown by exhibiting their L and R matrices. Local symmetries of the models are discussed. The diagonalization of the free-fermion models is carried out using the algebraic Bethe Ansatz.

arXiv:cond-mat/9711142International Journal of Modern Physics BJul 30, 19989 citations

Ladder Operator for the One-Dimensional Hubbard Model

Jon Links, Huan-Qiang Zhou, Ross H. McKenzie +1 more

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

arXiv:cond-mat/0011368Physical Review LettersMay 28, 200135 citations

The su(n) Hubbard model

Z. Maassarani

The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I indroduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that make it the su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the transfer matrix commutes with the hamiltonian. While the model is integrable in one dimension, it provides a generalization of the Hubbard hamiltonian in any dimension.

Jul 26, 201321 citations

Fermionic R -Operator and Integrability of the One-Dimensional Hubbard Model

有希子梅野, Masahiro Shiroishi, Miki Wadati

We propose a new type of the Yang-Baxter equation (YBE) and the decorated Yang-Baxter equation (DYBE). Those relations for the fermionic R-operator were introduced recently as a tool to treat the integrability of the fermion models. Using the YBE and the DYBE for the XX fermion model, we construct the fermionic R-operator for the one-dimensional (1D) Hubbard model. It gives another proof of the integrability of the 1D Hubbard model. Furthermore a new approach to the SO(4) symmetry of the 1D Hubbard model is discussed.

arXiv:cond-mat/9806144Journal of the Physical Society of JapanJul 15, 199828 citations