Contributor info: Dr Marius de Leeuw

Luke Corcoran, Marius de Leeuw

SciPost Phys. Core 7, 045 (2024) · published 26 July 2024 | Toggle abstract · pdf

We complete the classification of 4×4 regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer matrices that have a non-trivial Jordan block structure. One model corresponds to a non-diagonalisable integrable deformation of the XXX spin chain.

Marius de Leeuw, Ana Lucia Retore

SciPost Phys. 15, 241 (2023) · published 15 December 2023 | Toggle abstract · pdf

In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and R-matrix of the three-loop SU(2) sector in N=4 SYM. We show that all known integrable long-range deformations of the 6-vertex models of this type can be obtained from a Lax operator and an R-matrix. Finally we discuss what happens at higher loops and highlight some general structures that these models exhibit.

Marius de Leeuw, Chiara Paletta, Balázs Pozsgay

SciPost Phys. 15, 071 (2023) · published 28 August 2023 | Toggle abstract · pdf

In this paper we present a new integrable deformation of the Hubbard model. Our deformation gives rise to a range 3 interaction term in the Hamiltonian which does not preserve spin or particle number. This is the first non-trivial medium range deformation of the Hubbard model that is integrable. Our model can be mapped to a new integrable nearest-neighbour model via a duality transformation. The resulting nearest-neighbour model also breaks spin conservation. We compute the $R$-matrices for our models, and find that there is a very unusual dependence on the spectral parameters in terms of the elliptic amplitude.

Marius de Leeuw, Chiara Paletta, Anton Pribytok, Ana L. Retore, Paul Ryan

SciPost Phys. 11, 069 (2021) · published 27 September 2021 | Toggle abstract · pdf

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in \cite{deLeeuw:2019zsi}. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16×16 solutions which exhibit su(2)+su(2) symmetry, which include the one-dimensional Hubbard model and the S-matrix of the AdS5 x S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.