# Seminars at the Landau Institute scientific council

## Superconductivity that breaks time-reversal symmetry and its experimental manifestations

28 September in 11:30

Victor Yakovenko (University of Maryland)

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 [1]. 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 [2]. 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.

[1] X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Science Advances 3, e1602579 (2017), arXiv:1609.08538

[2] P. M. R. Brydon, D. S. L. Abergel, D. F. Agterberg, and V. M. Yakovenko, arXiv:1802.02280

[1] X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Science Advances 3, e1602579 (2017), arXiv:1609.08538

[2] P. M. R. Brydon, D. S. L. Abergel, D. F. Agterberg, and V. M. Yakovenko, arXiv:1802.02280

## Irreversible Markov chains: From the TASEP to all-atom Coulomb computations

28 September in 15:00

Werner Krauth, Ecole normale supérieure, Paris (France)

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.

References:

S. C. Kapfer, W. Krauth, Physical Review Letters 119, 240603 (2017)

Z. Lei, W. Krauth, arXiv:1806.06786 (2018)

M. F. Faulkner, L. Qin, A. C. Maggs, W. Krauth, arXiv:1804.05795 (2018)

References:

S. C. Kapfer, W. Krauth, Physical Review Letters 119, 240603 (2017)

Z. Lei, W. Krauth, arXiv:1806.06786 (2018)

M. F. Faulkner, L. Qin, A. C. Maggs, W. Krauth, arXiv:1804.05795 (2018)

## Colloquium: Quantum electrodynamics of heavy ions and atoms

5 October in 11:30

Vladimir Shabaev (St. Petersburg State University)

The present status of the QED theory of heavy ions and atoms
is reviewed. The theoretical predictions for the Lamb shifts, the
hyperfine splittings, and the bound-electron g factors of highly charged
few-electron ions are compared with available experimental data. Special attention is paid to tests of QED at strong-coupling regime and determination of
fundamental constants. The current status of studying the parity
nonconservation effects with heavy atoms is also reported. Recent
results on the charge-transfer and pair-creation probabilities in low-energy
heavy-ion collisions are presented. Prospects for tests of QED at
supercritical fields are discussed.

## The free field representation for the GL(1|1) WZW model revisited

12 October in 11:30

M. Lashkevich

The Wess—Zumino—Witten theory related to the GL(1|1) supergroup possesses some interesting features. On one hand, its structure is rather simple, but, on the other hand, it is an example of a so called logarithmic theory, i.e. a conformal field theory that contains fields whose correlation functions depend on distances logarithmically. The spectrum of conformal dimensions in this theory is continuous, and logarithmic operators appear at some degenerate points, including those of zero dimension. The free field representation is an effective tool to study models of the conformal field theory, and that of the GL(1|1) theory seems to be rather simple and well-studied in previous works. Nevertheless, on my opinion, not all advantages of this representation were used. In the present work, beside a more detailed calculation of the structure constants, the fusion and braiding matrices were studied. It was shown that in the vicinity of degenerate points it is possible to chose a basis of conformal blocks, which resolves degeneration. I show how this basis is related to the logarithmic operators of the theory.

## TBA (kollokvium)

16 November in 11:30

Konstantin Postnov (GAISh MGU)

Seminars are held on Fridays in the conference hall of Landau Institute for Theoretical Physics in Chernogolovka, beginning at 11:30.

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