arXiv:1310.7074 · Journal of Physics A Mathematical and Theoretical

The τ2model and parafermions

R. J. Baxter

Published Jul 18, 2014• 25 citations

Abstract

Paul Fendley has recently found a 'parafermionic' way to diagonalize a simple solvable Hamiltonian associated with the chiral Potts model. Here we indicate how this method generalizes to the τ 2 model with open boundaries and make some comments.

DOI: 10.1088/1751-8113/47/31/315001

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arXiv:1310.7074 · Journal of Physics A Mathematical and Theoretical

The τ2model and parafermions

R. J. Baxter

Published Jul 18, 2014• 25 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1751-8113/47/31/315001

Related papers

Superintegrable chiral Potts model: Thermodynamic properties, an ?inverse? model, and a simple associated Hamiltonian

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Journal of Statistical PhysicsOct 1, 1989119 citations

Dissipative Fendley Models: Integrability, Parafermions, and the Fate of Topological Order under Open-System Dynamics A Non-Hermitian and Lindbladian Extension of Exactly Solvable Lattice Theories

Ijaz Durrani

Jan 1, 20260 citations

The challenge of the chiral Potts model

R. J. Baxter

Jan 1, 20056 citations

Parafermions in the τ2model

Helen Au-Yang, Jacques H. H. Perk

It has been shown recently by Baxter that the $τ_2(t_q)$ model with open boundary conditions can be solved by the "parafermionic" method of Fendley. In Baxter's paper there are several conjectures, which were formulated based on numerical short-chain calculations. Here we present the proof of two of them.It has been shown recently by Baxter that the $τ_2(t_q)$ model with open boundary conditions can be solved by the "parafermionic" method of Fendley. In Baxter's paper there are several conjectures, which were formulated based on numerical short-chain calculations. Here we present the proof of two of them.

arXiv:1402.0061Journal of Physics A Mathematical and TheoreticalJul 18, 201427 citations

Parafermions in the tau-2 model II

Helen Au-Yang, Jacques H. H. Perk

Many years ago Baxter introduced an inhomogeneous two-dimensional classical spin model, now called the $τ_2(t)$ model with free boundary conditions, and he specialized the resulting quantum spin-chain Hamiltonian in a special limit to a simple clock Hamiltonian. Recently, Fendley showed that this clock Hamiltonian can be expressed in terms of free "parafermions." Baxter followed this up by showing that this construction generalizes to the more general $τ_2(t)$ model, provided some conjectures hold. In this paper, we will compare the different notations and approaches enabling us to express the Hamiltonians in terms of projection operators as introduced by Fendley. By examining the properties of the raising operators, we are then able to prove the last unproven conjecture in Baxter's paper left in our previous paper. Thus the eigenvectors can all be written in terms of these raising operators.Many years ago Baxter introduced an inhomogeneous two-dimensional classical spin model, now called the $τ_2(t)$ model with free boundary conditions, and he specialized the resulting quantum spin-chain Hamiltonian in a special limit to a simple clock Hamiltonian. Recently, Fendley showed that this clock Hamiltonian can be expressed in terms of free "parafermions." Baxter followed this up by showing that this construction generalizes to the more general $τ_2(t)$ model, provided some conjectures hold. In this paper, we will compare the different notations and approaches enabling us to express the Hamiltonians in terms of projection operators as introduced by Fendley. By examining the properties of the raising operators, we are then able to prove the last unproven conjecture in Baxter's paper left in our previous paper. Thus the eigenvectors can all be written in terms of these raising operators.

arXiv:1606.06319Jun 20, 201610 citations

The Integrable Chiral Potts Model: Quantum Group Methods Applied to Superintegrable Case

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It has been shown recently by Baxter that the

τ_2(t_q)

model with open boundary conditions can be solved by the "parafermionic" method of Fendley. In Baxter's paper there are several conjectures, which were formulated based on numerical short-chain calculations. Here we present the proof of two of them.

Many years ago Baxter introduced an inhomogeneous two-dimensional classical spin model, now called the

τ_2(t)

model with free boundary conditions, and he specialized the resulting quantum spin-chain Hamiltonian in a special limit to a simple clock Hamiltonian. Recently, Fendley showed that this clock Hamiltonian can be expressed in terms of free "parafermions." Baxter followed this up by showing that this construction generalizes to the more general

τ_2(t)

model, provided some conjectures hold. In this paper, we will compare the different notations and approaches enabling us to express the Hamiltonians in terms of projection operators as introduced by Fendley. By examining the properties of the raising operators, we are then able to prove the last unproven conjecture in Baxter's paper left in our previous paper. Thus the eigenvectors can all be written in terms of these raising operators.