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Generalised Onsager Algebra in Quantum Lattice Models
- MathematicsSciPost Physics
- 2022
The Onsager algebra is one of the cornerstones of exactly solvable models in statistical mechanics. Starting from the generalised Clifford algebra, we demonstrate its relations to the graph…
65 References
Onsager's algebra and superintegrability
- Mathematics
- 1990
The author considers the irreducible representations of the Onsager algebra, and shows that for a finite system, possessing such an algebra leads to an Ising-like structure in the spectra of…
Dolan–Grady relations and noncommutative quasi-exactly solvable systems
- Mathematics, Physics
- 2003
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a…
New symmetries of the chiral Potts model
- Mathematics
- 2012
In this paper a hitherto unknown spectrum generating algebra, consisting of two coupled Temperley–Lieb algebras, is found in the three-state chiral Potts model. From this, we can construct new…
Free parafermions
- Physics
- 2013
The spectrum of the quantum Ising chain can be found by expressing the spins in terms of free fermions. An analogous transformation exists for clock chains with Zn?> symmetry, but is of less use…
Onsager’s algebra and the Dolan–Grady condition in the non‐self‐dual case
- Mathematics
- 1991
In this paper, it is shown that a pair of operators that satisfy the Dolan–Grady conditions generate an Onsager algebra even in the case that they are not self‐dual. Briefly considered will be the…
Exact solution of a cluster model with next-nearest-neighbor interaction
- Physics, MathematicsProgress of Theoretical and Experimental Physics
- 2020
A 1D cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model…