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arXiv:hep-th/0006243 · Journal of Physics A Mathematical and General

Integrable laddert-Jmodel with staggered shift of the spectral parameter

Jan Ambjørn A, D. Arnaudon, A. Sedrakyan, Tigran Sedrakyan, P. Sorba

Published Jul 20, 2001• 15 citations
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Abstract

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.

DOI
10.1088/0305-4470/34/30/301

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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 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 (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
Abstract Yang–Baxter integrable vertex models with a generic Z 2 -staggering can be expressed in terms of composite R -matrices given in terms of the elementary R-matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices K ± . We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of commuting integrals of motion (in addition to the one including the Hamiltonian obtained from the usual transfer matrix), starting with the so-called quasi momentum operator. In this paper, we show that this quasi momentum operator can be obtained together with the Hamiltonian for both periodic and open models in a unified way from enlarged Yang–Baxter or reflection algebras in the composite picture. For the special case of the staggered six-vertex model, this allows constructing an integrable spectral flow between the two local cases.