Scientific Council of the Landau Institute, Friday, September 28, 2018, Landau Institute, 11:30 am|
Victor Yakovenko (University of Maryland)
Superconductivity that breaks time-reversal symmetry and its experimental manifestations
Since 2006, it has been found experimentally that superconductivity spontaneously breaks time-reversal symmetry (TRS) in certain materials, such as Sr2RuO4, UPt3, URu2Si2, and Bi/Ni bilayers. In the latter case, we argue that the superconducting order parameter has the winding number of +-2 around the Fermi surface, thus making Bi/Ni bilayers a rare example of intrinsic 2D topological superconductivity . The experimental evidence for TRS breaking comes from the polar Kerr effect, which is rotation of polarization of normally incident light upon reflection from the sample. Theoretical studies indicate that this effect is possible only if a superconductor has more than one band. To clarify these conditions, we study a model of chiral TRS-breaking superconductivity on the honeycomb lattice . We consider superconducting pairing on the neighboring sites belonging to different sublattices. The matrix of this superconducting pairing is non-unitary and does not commute with the normal-state Hamiltonian. We find that the latter condition is necessary for experimental manifestations of the TRS breaking. We show that such superconducting pairing generates persistent loop currents around each lattice site and opens a topological mass gap at the Dirac points with the corresponding chiral edge states, as in Haldane's model of the quantum anomalous Hall effect. We calculate the intrinsic ac Hall conductivity in the absence of an external magnetic field, which determines the polar Kerr effect, and show that it is proportional to the loop-current order parameter.
Scientific Council of the Landau Institute, Friday, September 28, 2018, Landau Institute, 3:00 pm|
Werner Krauth, Ecole normale supérieure, Paris (France)
Irreversible Markov chains: From the TASEP to all-atom Coulomb computations
The Markov chain Monte Carlo method traditionally consists in exploring large configuration spaces using a reversible random walk where moves are accepted or rejected based on an energy criterion. In this talk, I will present recent progress on irreversible Markov chains that challenge this picture. In one-dimensional particle systems, the new algorithms are related to the TASEP (totally asymmetric simple exclusion model). We can rigorously prove that they mix on much shorter time scales than the reversible Metropolis algorithms.
I will then show how these algorithms sample the Boltzmann distribution (and thus explore configuration space) without computing the energy. In long-range interacting systems, where the computation of the energy is time-consuming, this provides a key advantage for the new method. For locally charge-neutral systems in three dimensions, we obtain a highly efficient algorithm, of N log N complexity in the number N of particles. I discuss the main paradox of this method: How is it possible to sample the Boltzmann distribution without computing the energy, and then review some recent successes as well as prospects and challenges for irreversible Markov chains in statistical physics.
Laboratory building, room 122
Moscow Institute of Physics and Technology
contact e-mail address: firstname.lastname@example.org (head M.V.Feigel'man, deputy head I.V.Zagorodnev)Research topics
Theory seminar, Thursday, September 13, 2018, Kapitza Institute, 11:30 am|
Alexey Kitaev (Caltech)
Statistical mechanics of a two-dimensional black hole
Rassmatrivaemaya zadacha voznikla pri izuchenii modeli SYK, kotoraya sostoit iz bol'shogo chisla vzaimodeistvuyushchikh fermionov (vzaimodeistvie «vse so vsemi», t.e. effektivnaya razmernost' sistemy — 0+1). Pri nizkoi temperature vazhnuyu rol' igraet myagkaya moda s deistviem, vyrazhayushchimsya cherez shvartsian. Eto deistvie ekvivalento dvumernoi gravitatsii s dilatonom v opredelennom predele. Pervaya chast' doklada posvyashchena obzoru upomyanutykh rezul'tatov. Zatem shvartsiannaya moda (ili dvumernaya gravitatsiya) budet rassmotrena kak otdel'naya kvantovaya sistema. Statsumma v etoi modeli imeet neobychnoe vyrazhenie: Z = tr(e-βHP), gde P — opredelennyi operator, kommutiruyushchii s gamil'tonianom.