# Séminaire du LPTMS: duo Xiangyu Cao & Kirill Plekhanov

### « *Liouville field theory and log-correlated Random Energy Models* » by Xiangyu Cao (LPTMS, Université Paris-Sud)

An exact mapping is established between the c ≥ 25 Liouville field theory (LFT) and the

Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic

confining potential. The probability distribution of the position of the minimum of the energy

landscape is obtained exactly by combining the conformal bootstrap and one-step replica sym-

metry breaking methods. Operator product expansions in LFT allow to unveil novel universal

behaviours of the “log-correlated Random Energy Models” class. Applications will include multi-

fractality (inverse participation ratios and their corrections) and the overlap distribution in the

directed polymer on a Cayley tree model.

Ref.: Xiangyu Cao, Pierre Le Doussal, Alberto Rosso and Raoul Santachiara, preprint arXiv:1611.02193.

### « *Chiral spin state of the frustrated XY model on the honeycomb lattice* » by Kirill Plekhanov (LPTMS, Université Paris-Sud)

Abstract: Currently, it was suggested that the frustrated XY model for spin-1/2 on the honeycomb lattice can support a chiral spin liquid (CSL) phase, that is characterized by the spontaneous breaking of the time-reversal and parity symmetries. The ground state of the system in the CSL phase will be characterized by the gapped bulk and gapless chiral modes along the edges, if open boundary conditions are used. In this talk I will present analytical arguments that lead to this conclusion and a numerical verification of analytical results based on the calculations of local order parameters, structure factors and scalar spin chirality using the exact diagonalization technique. An experimental realization of the model in the context of ultra-cold atoms and circuit-QED systems, based on the application of time-dependent periodic (Floquet) modulations, will be discussed.

**Date/Time : ** 14/02/2017 - *11:00 - 12:00*

**Location : ** LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay

#### Upcoming seminars

- Physics-Biology interface seminar: Emmanuel de Langre - 4 Avr 2018 - 11:00
- Physics-Biology interface seminar: David Bensimon - 30 Mai 2018 - 11:00