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International Journal of Modern Physics A

INTEGRABLE N-LEG LADDER MODELS

D. Arnaudon, A. Sedrakyan, Tigran Sedrakyan

Published May 1, 2004• 3 citations
Publisher

Abstract

We construct integrable spin chains with the inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of coupled Yang–Baxter equations. This construction yields the P-leg integrable ladder Hamiltonians. We analyse the corresponding quantum group symmetry.

DOI
10.1142/s0217751x04020282

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We construct integrable spin chains with the inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The integrability of the model is based on a set of coupled Yang–Baxter equations. This construction yields the P-leg integrable ladder Hamiltonians. We analyse the corresponding quantum group symmetry.
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.
A detailed study of an S = ½ spin ladder model is given. The ladder consists of plaquettes formed by nearest-neighbor rungs with all possible SU (2)-invariant interactions. For properly chosen coupling constants, the model is shown to be integrable in the sense that the quantum Yang-Baxter equation holds and one has an infinite number of conserved quantities. The R -matrix and L -operator associated with the model Hamiltonian are given in a limiting case. It is shown that after a simple transformation, the model can be solved via a Bethe ansatz. The phase diagram of the ground state is exactly derived using the Bethe ansatz equation.
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.