Integrability and duality in spin chains

Abstract

We construct a new, two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect non-interacting modes of different systems. We apply the new solution and duality to a Richardson-Gaudin model and generate a novel integrable system termed the $s$-$d$ wave Richardson-Gaudin-Kitaev interacting chain, interpolating $s$- and $d$- wave superconductivity. The phase diagram of this model has a topological phase transition that can be connected to the duality, where the occupancy of the non-interacting mode serves as a topological order parameter.

10 pages, 2 figures, typos added, reference added, footnote [58] added on page 2, changed phrasing on YBE, acknowledgements updated

References in corpus (20)

• On space of integrable quantum field theories
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Interacting anyons in topological quantum liquids: The golden chain
• An exact solution for the KPZ equation with flat initial conditions
• Crystallization of strongly interacting photons in a nonlinear optical fiber
• Probing the Excitations of a Lieb-Liniger Gas from Weak to Strong Coupling
• Dynamical structure factor of one-dimensional Bose gases: experimental signatures of beyond-Luttinger liquid physics
• Exact dynamics in the inhomogeneous central-spin model
• Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• On T-Duality and Integrability for Strings on AdS Backgrounds
• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• Universalities of thermodynamic signatures in topological phases
• Spin- and entanglement-dynamics in the central spin model with homogeneous couplings
• What is a particle-conserving Topological Superfluid?
• Competing interactions in semiconductor quantum dots
• Exact solution of the p+ip Hamiltonian revisited: duality relations in the hole-pair picture
• Ground-state Bethe root densities and quantum phase transitions
• Something interacting and solvable in 1d
• The symmetric six-vertex model and the Segre cubic threefold

Cited by in corpus (9)

• Yang-Baxter and the Boost: splitting the difference
• Classifying nearest-neighbour interactions and deformations of AdS
• From integrability to chaos in quantum Liouvillians
• Migdal-Eliashberg theory as a classical spin chain
• Something interacting and solvable in 1d
• Integrable Model of Topological SO(5) Superfluidity
• Integrable model of a $p$-wave bosonic superfluid
• Novel approach of exploring ASEP-like models through the Yang Baxter Equation
• Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases