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Integrable Ladder t-J Model with Staggered Shift of the Spectral Parameter

Published Jan 31, 2013• 10 citations
OpenAlex

Abstract

The generalization of the Yang-Baxter equations (YBE) in the presence of Z2 grading along both chain and time directions is presented and an integrable model of t − J type with staggered disposition along a chain of shifts of the spectral parameter is constructed. The Hamiltonian of the model is computed in fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. In the thermodynamic limit, the lowest energy of the model is formed by the quarter filling of the states by fermions instead of usual half filling. 1

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Non-perturbative Quantum Effects•Sep 25, 2000•2 citations
The generalization of the Yang-Baxter equations (YBE) in the presence of Z2 grading along both chain and time directions is presented and an integrable model of t − J type with staggered disposition along a chain of shifts of the spectral parameter is constructed. The Hamiltonian of the model is computed in fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. In the thermodynamic limit, the lowest energy of the model is formed by the quarter filling of the states by fermions instead of usual half filling. 1
The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented and an integrable model of t-J type with staggered disposition along a chain of shifts of the spectral parameter is constructed. The Hamiltonian of the model is computed in fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zig-zag ladder model. The Algebraic Bethe Ansatz technique is applied and the eigenstates, along with eigenvalues of the transfer matrix of the model are found. In the thermodynamic limit, the lowest energy of the model is formed by the quarter filling of the states by fermions instead of usual half filling.
The generalization of the Yang-Baxter equations in the presence of ℤ 2 grading along both chain and time directions is presented and an integrable model of t - J type with staggered disposition of shifts of the spectral parameter along the chain is constructed. The Hamiltonian of the model is computed in the fermionic formulation. It involves three neighbour site interactions and therefore can be considered as a zigzag ladder model. The algebraic Bethe ansatz technique is applied and the eigenstates as well as the eigenvalues of the transfer matrix of the model are found. It is argued that in the thermodynamic limit the lowest energy of the model is formed by the quarter filling of the states by fermions instead of the usual half filling.
The theory of constructing integrable systems using solutions to the Yang-Baxter equation (YBE) is well established. The conserved operators can be obtained by a series expansion for the family of commuting transfer matrices. Another approach is to use the ladder operator, which permits a recursive method through repeated commutators, to obtain the conserved operators. The ladder operator for models where the solution of the YBE has the difference property is well known. Recently it has been shown that a ladder operator exists for the Hubbard model, which does not have the difference property, and the present work extends this to a general theory for the construction of the ladder operator for any integrable system obtained through the YBE, with the XYh model as an example. The existence of ladder operators for integrable models constructed from other variants of the YBE, such as closed chains with quantum algebra symmetry and the Heisenberg model with single site impurity, is also considered.
New solvable vertex models can be easily obtained by staggering the spectral parameter in already known ones. This simple construction reveals some surprises: for appropriate values of the staggering, highly non-trivial continuum limits can be obtained. The simplest case of staggering with period 2 (the case) for the six-vertex model was shown to be related, in one regime of the spectral parameter, to the critical antiferromagnetic Potts model on the square lattice, and has a non-compact continuum limit. Here we study the other regime: in the very anisotropic limit, it can be viewed as a zig–zag spin chain with spin anisotropy. From the Bethe–Ansatz solution, we obtain the central charge c = 2, the conformal spectrum and the continuum partition function, corresponding to one free boson and two Majorana fermions. Finally, moving in more physical territory, we obtain a massive integrable deformation of the model on the lattice. Interestingly, its scattering theory is a massive version of the one for the flow between minimal models. The corresponding field theory is argued to be a complex version of the C (2) 2 Toda theory.