Generalised Onsager Algebra in Quantum Lattice Models

Abstract

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 Temperley-Lieb algebra, and a generalisation of the Onsager algebra. We present a series of quantum lattice models as representations of the generalised Clifford algebra, possessing the structure of a special type of the generalised Onsager algebra. The integrability of those models is presented, analogous to the free fermionic eight-vertex model. We also mention further extensions of the models and physical properties related to the generalised Onsager algebras, hinting at a general framework that includes families of quantum lattice models possessing the structure of the generalised Onsager algebras.

arXiv comment25 pages, 2 figures

References in corpus (29)

• Onsager's Scars in Disordered Spin Chains
• Dualities and the phase diagram of the $p$-clock model
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Free parafermions
• The Bond-Algebraic Approach to Dualities
• Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
• Unified approach to Quantum and Classical Dualities
• A deformed analogue of Onsager's symmetry in the XXZ open spin chain
• A new current algebra and the reflection equation
• Free fermions in disguise
• sl(N) Onsager's Algebra and Integrability
• Free fermionic and parafermionic quantum spin chains with multispin interactions
• Free fermions behind the disguise
• Characterization of solvable spin models via graph invariants
• Yang-Baxter and the Boost: splitting the difference
• Onsager symmetries in $U(1)$-invariant clock models
• Integrable quantum spin chains with free fermionic and parafermionic spectrum
• Integrable hard rod deformation of the Heisenberg spin chains
• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• The alternating central extension of the $q$-Onsager algebra
• On the solutions to the multi-parametric Yang-Baxter equations
• Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models
• Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
• FRT presentation of classical Askey-Wilson algebras
• FRT presentation of the Onsager algebras
• Onsager algebra and algebraic generalization of Jordan-Wigner transformation
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• Quantum spin chains from Onsager algebras and reflection $K$-matrices
• A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain

Cited by in corpus (9)

• The proton structure in and out of muonic hydrogen
• Proof of absence of local conserved quantities in the mixed-field Ising chain
• Ising analogues of quantum spin chains with multispin interactions
• Integrable Quantum Circuits from the Star-Triangle Relation
• Random free-fermion quantum spin chain with multi-spin interactions
• Pivoting through the chiral-clock family
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Polynomially restricted operator growth in dynamically integrable models
• Parity anomaly from LSM: exact valley symmetries on the lattice