5 citations · 12 across the 15 of their papers we have counts for
17 papers
Superintegrable systems in curved spaces via coalgebras and deformed Racah algebras
Samuel Jimenez-Swain, Ian Marquette, Yao-Zhong Zhang
We determine the Poisson algebras generated by partial Casimirs of undeformed and non-standard -deformed coalgebras, respectively. The derivation is performed…
Geometric construction of superintegrable Poisson projection chains via Poisson centralizers
Kai Jiang, Guorui Ma, Ian Marquette +2
We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra of a complex semisim…
Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces
Kai Jiang, Guorui Ma, Ian Marquette +2
We provide a method for formulating superintegrable magnetic geodesic flows on reductive homogeneous spaces , with a compact semisimple Lie group and a closed subgro…
New quasi-exactly solvable systems from SUSYQM and Bethe Ansatz
Siyu Li, Ian Marquette, Yao-Zhong Zhang
We give a systematic construction of new quasi-exactly solvable systems via Bethe ansatz and supersymmetric quantum mechanics (SUSYQM). Methods based on the intertwining of superch…
Subalgebra chains and nuclear physics: Commutant approach and construction of polynomial algebras
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this paper, we review a new approach to study subalgebra chains in the context of nuclear physics. This approach does not rely on explicit r…
Polynomial deformations of and unified algebraic framework for solutions of a class of spin models
Siyu Li, Ian Marquette, Yao-Zhong Zhang
We introduce novel polynomial deformations of the Lie algebra . We construct their finite-dimensional irreducible representations and the corresponding differential operator…
Polynomial algebra from the Lie algebra reduction chain : The supermultiplet model
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
The supermultiplet model, based on the reduction chain , is revisited through the lens of commutants within unive…
On the construction of polynomial Poisson algebras: a novel grading approach
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this work, we refine recent results on the explicit construction of polynomial algebras associated with commutants of subalgebras in enveloping algebras of Lie algebras by consi…
Stäckel transform, coupling constant metamorphosis and algebraization of quasi-exactly solvable systems
Siyu Li, Ian Marquette, Yao-Zhong Zhang
We generalize the notions of the Stäckel transform and the coupling constant metamorphosis to quasi-exactly solvable systems. We discover that for a variety of one-dimensional and…
Exact physical quantities of the spin chain model with generic open boundary conditions
Pengcheng Lu, Junpeng Cao, Wen-Li Yang +2
We study the quantum integrable spin chain model associated with the twisted algebra (or simply the model) under generic open boundary conditions. The Hamil…
Exact surface energies and boundary excitations of the Izergin-Korepin model with generic boundary fields
Pengcheng Lu, Junpeng Cao, Wen-Li Yang +2
The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra symmetry. Applying the method, we derive the homogeneous ze…
Polynomial Poisson Algebras and Superintegrable Systems from Cartan centralisers of Types , and
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this work, we construct explicit formulas for the generators of the Cartan centralisers of complex semisimple Lie algebras and , the case being already know…
T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature
Pengcheng Lu, Junpeng Cao, Wen-Li Yang +2
We study the thermodynamics of the antiperiodic XXZ chain with anisotropy parameter η=iπ/3 by means of the t-W method. We parameterize the eigenvalues of both the transfer matrix a…
Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries
Jiasheng Dong, Pengcheng Lu, Junpeng Cao +3
We investigate the thermodynamic limit and exact surface energy of the isotropic spin-1 Heisenberg chain with integrable generic open boundary conditions by a novel Bethe ansatz me…
Bethe ansatz solutions and hidden algebraic structure for a class of quasi-exactly solvable systems
Siyu Li, Ian Marquette, Yao-Zhong Zhang
The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed pr…
On polynomial symmetry algebras underlying superintegrable systems in Darboux spaces
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
We review three different approaches to polynomial symmetry algebras underlying superintegrable systems in Darboux spaces. The first method consists of using deformed oscillator al…
Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions…