3.7k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- ARC Centre of Excellence for Engineered Quantum SystemsAU357 papers
- Centre National de la Recherche ScientifiqueFR333 papers
- Australian National UniversityAU332 papers
- University College LondonGB296 papers
- University of MichiganUS282 papers
- Australian Astronomical ObservatoryAU271 papers
- University of PortsmouthGB270 papers
- Institució Catalana de Recerca i Estudis AvançatsES269 papers
- Fermi National Accelerator LaboratoryUS266 papers
- Ludwig-Maximilians-Universität MünchenDE258 papers
- Institute for High Energy PhysicsES252 papers
- Centro de Investigaciones Energéticas, Medioambientales y TecnológicasES250 papers
139 papers · 1 filter
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…
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…
Polynomially Superintegrable Hamiltonians Separating in Cartesian Coordinates
Ian Marquette, Anthony Parr
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdeterminati…
Einstein metrics on homogeneous superspaces
Yang Zhang, Mark D. Gould, Artem Pulemotov +1
This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces.…
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…
Graded colour Lie superalgebras for solving Lévy-Leblond equations
Mitchell Ryan
The Lévy-Leblond equation with free potential admits a symmetry algebra that is a -graded colour Lie superalgebra (see arXiv:1609.08224). We exten…
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…
Special function models of indecomposable representations: The Laguerre Case
Sébastien Bertrand, Ian Marquette, Willard Miller +1
In this paper, we point out connections between certain types of indecomposable representations of and generalizations of well-known orthogonal polynomials. Those represent…
Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
Ian Marquette, Anthony Parr
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method express…
Polynomial algebras from commutants: Classical and Quantum aspects of
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
We review some aspects of the Racah algebra , including the closure relations, pointing out their role in superintegrability, as well as in the description of the symmetry al…
The ghost algebra and the dilute ghost algebra
Madeline Nurcombe
We introduce the ghost algebra, a two-boundary generalisation of the Temperley-Lieb (TL) algebra, using a diagrammatic presentation. The existing two-boundary TL algebra has a basi…
The Lie algebra of the lowest transitively differential group of degree three
Alfred Michel Grundland, Ian Marquette
We investigate the real Lie algebra of first-order differential operators with polynomial coefficients, which is subject to the following requirements. (1) The Lie algebra should a…
Non-Hermitian superintegrable systems
Francisco Correa, Luis Inzunza, Ian Marquette
A non-Hermitian generalisation of the Marsden--Weinstein reduction method is introduced to construct families of quantum -symmetric superintegrable models over an …
Polynomial algebras from Lie algebra reduction chains
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
We reexamine different examples of reduction chains of Lie algebras in order to show how the polynomials determining the commutant with respect…
Infinite dimensional representations of cubic and quintic algebras and special functions
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we intr…
Integrable models from singly generated planar algebras
Xavier Poncini, Jorgen Rasmussen
Not all planar algebras can encode the algebraic structure of a Yang--Baxter integrable model described in terms of a so-called homogeneous transfer operator. In the family of subf…
Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +1
Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians a…
Critical site percolation on the triangular lattice: From integrability to conformal partition functions
Alexi Morin-Duchesne, Andreas Klümper, Paul A. Pearce
Critical site percolation on the triangular lattice is described by the Yang-Baxter solvable dilute loop model with crossing parameter specialized to , cor…