Universal Hubbard models with arbitrary symmetry (original) (raw)

Generalised integrable Hubbard models

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 "coupling" two independent XX models. In both cases, we show that the R-matrices satisfy the Yang-Baxter equation. We derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine its symmetries. A perturbative calculation "à la Klein and Seitz" is performed. Some explicit examples are worked out. We give a description of the two-particle scattering.

Fusion for the one-dimensional Hubbard model

Journal of Physics A: Mathematical and Theoretical, 2015

We discuss a formulation of the fusion procedure for integrable models which is suitable for application to non-standard R-matrices. It allows for construction of bound state R-matrices for AdS/CFT worldsheet scattering or equivalently for the one-dimensional Hubbard model. We also discuss some peculiar cases that arise in these models.

The Yangian symmetry of the Hubbard model

Physics Letters A, 1994

We discovered new hidden symmetry of the one-dimensional Hubbard model. We show that the one-dimensional Hubbard model on the infinite chain has the infinitedimensional algebra of symmetries. This algebra is a direct sum of two sl(2)-Yangians. This Y (sl(2)) ⊕ Y (sl(2)) symmetry is an extension of the well-known sl(2) ⊕ sl(2) . The deformation parameters of the Yangians are equal up to the signs to the coupling constant of the Hubbard model hamiltonian.

Super-Hubbard models and applications

Journal of High Energy Physics, 2007

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 by coupling two independent XX models. In both cases, we show that the R-matrices satisfy the Yang-Baxter equation, we derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine the symmetry of the Hamiltonian. Explicit examples are worked out. In the cases of the gl(1|2) and gl(2|2) Hubbard models, a perturbative calculation at two loopsà la Klein and Seitz is performed.

Quantum deformations of the one-dimensional Hubbard model

Journal of Physics A: Mathematical and Theoretical, 2008

The centrally extended superalgebra psu(2|2) R 3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation U q (psu(2|2) R 3) and derive the fundamental R-matrix. From the latter we deduce an integrable spin-chain Hamiltonian with three independent parameters and the corresponding Bethe equations to describe the spectrum on periodic chains. We relate our Hamiltonian to a two-parametric Hamiltonian proposed by Alcaraz and Bariev which can be considered a quantum deformation of the one-dimensional Hubbard model.

Structure of the Hilbert-space of the infinite-dimensional Hubbard model

The European Physical Journal B, 1999

The user has requested enhancement of the downloaded file. arXiv:cond-mat/9810318v1 [cond-mat.str-el] Abstract. An iterative procedure for the explicit construction of the nontrivial subspace of all symmetryadapted configurations with non-zero weight in the ground-state of the ∞-dimensional Hubbard model is developed on the basis of a symmetrized representation of the transition operators on a sequence of Bethe-Lattices of finite depth. The relation ship between these operators and the well known mapping of the ∞-dimensional Hubbard model onto an effective impurity problem coupled to a (self-consistent) bath on non-interacting electrons is given. As an application we calculate the properties of various Hubbard stars and give estimates for the half-filled Hubbard model with up to 0.1% accuracy.

New eigenstates of the 1-dimensional Hubbard model

Nuclear Physics B, 1992

Carrying Out a program proposed by C.N. Yang, we prove that all 'regular" (as defined in the paper) Bethe-Ansatz states of the 1-dimensional Hubbard model on a lattice of finite length L are lowest-weight vectors of an SO(4) algebra. Thus new eigenstates can be obtained by acting with the SO(4) raising Operators Ofl the Bethe-Ansatz states. In a following publication we will show that the SO(4) structure in combination with the Bethe Ansatz leads to a complete set of eigenfunctions for the 1-dimensional Hubbard model (asymptotically for large but finite lattice lengths L).

Canonical representation for electrons and its application to the Hubbard model

Physical Review B, 2008

A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible and constraint-free. Importantly, it simplifies the Hubbard interaction. On a bipartite lattice, the Hubbard model is reduced to a form in which the exchange interaction emerges simply by decoupling the Pauli subsystem from the spinless fermion bath. This exchange correctly reproduces the large U superexchange. Also derived, for U = ±∞, is the Hamiltonian to study Nagaoka ferromagnetism. In this representation, the infinite-U Hubbard problem becomes elegant and easier to handle. Interestingly, the ferromagnetism in Hubbard model is found to be related to the gauge invariance of the spinless fermions. Generalization of this representation for the multicomponent fermions, a new representation for bosons, the notion of a 'soft-core' fermion, and some interesting unitary transformations are introduced and discussed in the appendices.