Seminar “Modern Mathematical Physics”

Date and Time: Wednesday, 28 October 2020, at 3:00 PM

Venue: Online conference on Zoom, Bogoliubov Laboratory of Theoretical Physics

Seminar topic: «Conformal field theory and Richardson-Gaudin models»

Speaker: Marcin Piatek

Abstract:

Conformal field theory in two dimensions (2d CFT) yields an effective description of critical phenomena in two-dimensional statistical systems and describes the worldsheet dynamics of relativistic strings. Two-dimensional CFT has also found use in condensed matter physics, in particular as a tool to study states of the fractional quantum Hall effect. For instance, the Laughlin wave functions can be represented by certain conformal blocks calculated within a free field realization. Interestingly, as has been observed by Sierra around 2000, an idea of representing quantum states by conformal blocks of a certain WZW model works great, when it is applied to characterize eigenstates of many-body quantum Hamiltonians describing pairing force interactions (Cooper pairs) or systems of interacting spins (Gaudin magnets). During my talk I will review a connection proposed by Sierra between 2d CFT and the exact solution, and integrability of the so-called Richardson model (reduced BCS model) as well as Gaudin spin models. Then I will present our new observations which relate Sierra’s results concerning the Richardson model and spectra of Gaudin Hamiltonians to a classical limit of Virasoro conformal blocks.

The talk is based on a common work with R.G. Nazmitdinov, A. Puente, A.R. Pietrykowski.