Theoretical Physics Seminar: Rob Klabbers

  • Date: –15:00
  • Location: Zoom:
  • Lecturer: Rob Klabbers (Nordita and Royal Inst. Tech., Stockholm)
  • Contact person: Luca Cassia
  • Seminarium

Title: How coordinate Bethe ansatz works for Inozemtsev model

Abstract: Three decades ago, Inozemtsev discovered an isotropic long-range spin chain with elliptic pair potential that interpolates between the Heisenberg and Haldane–Shastry spin chains while admitting an exact solution throughout, based on a connection with the elliptic quantum Calogero–Sutherland model. Though Inozemtsev’s spin chain is widely believed to be quantum integrable, the underlying algebraic reason for its exact solvability is not yet well understood. As a step in this direction in arxiv:2009.14513 we introduced a refinement of Inozemtsev’s ‘extended coordinate Bethe ansatz’ and clarify various aspects of the model’s exact spectrum and its limits.
I will discuss this refinement and show how it improves our control over the model. For example, in the new coordinates, the energy becomes close to additive. Moreover, both the Bethe-ansatz equations and the energy become elliptic functions, allowing for a lifting of the spectral problem to the elliptic curve, effectively rationalising it as one might expect for an isotropic spin chain. Direct comparison with the limiting models is now also possible: I will showcase the relation with the regular Bethe ansatz for the XXX chain and the Haldane-Shastry spectrum. In particular, I will show that the Inozemtsev model links the scattering states of the Heisenberg model to the Yangian highest-weight states of Haldane Shastry, while Heisenberg bound states become affine descendants in the Haldane-Shastry spectrum.