Jacopo de Nardis (Université de Gand, Belgique)
Diffusion and super-diffusion in quantum and classical chains

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Topological phases of quantum walks and how they can be detected

Janos Asboth (Wigner Research Centre for Physics & Budapest University, Hungary)

Quantum walks are versatile toy models for periodically driven systems in the nonperturbative regime of low-frequency and high-intensity drive. In this regime, systems can have "hidden" topological invariants: they can host topologically protected edge states even if their effective Hamiltonian is topologically trivial. I will discuss schemes we developed [1,2] to measure the bulk topological invariants, including the "hidden" ones, directly, which also work in the case with spatial disorder, and which have recently been measured in quantum walk experiments[3,4].

[1]: T Rakovszky, JK Asbóth, A Alberti: Detecting topological invariants in chiral symmetric insulators via losses, Phys Rev B 95 (20), 201407

[2]: B Tarasinski, JK Asbóth, JP Dahlhaus: Scattering theory of topological phases in discrete-time quantum walks, Phys Rev A 89 (4), 042327

[3]: Zhan, X., Xiao, L., Bian, Z., Wang, K., Qiu, X., Sanders, B.C., Yi, W. and Xue, P.: Detecting topological invariants in nonunitary discrete-time quantum walks. Phys Rev Lett, 119(13), 130501

[4]: S Barkhofen, T Nitsche, F Elster, L Lorz, A Gábris, I Jex, C Silberhorn: Measuring topological invariants in disordered discrete-time quantum walks, Phys Rev A 96 (3), 033846

Quantum Spin Liquids in Dipolar-Octupolar Pyrochlores

Owen Benton (MPIPKS Dresden)

Over many years, there has been a concerted research effort to identify systems realizing Quantum Spin Liquid (QSL) ground states. Realization of QSL states is of great interest due to their association with large-scale quantum entanglement, fractional excitations and emergent gauge fields. A particularly interesting subset of QSLs is those that realise emergent electromagnetism, with gapless photons and gapped, fractional charges as excitations.

In this regard the “dipolar-octupolar” pyrochlore oxides R2M2O7 (R=Ce, Sm, Nd) represent an important opportunity. The effective S=1/2 exchange Hamiltonian which governs their low energy physics has an alluringly simple “XYZ” form and is known to be conducive to forming a U(1) QSL ground state, at least in certain limits. Meanwhile, recent experiments on these materials strongly suggest QSL physics.

Motivated by this, we present here a complete analysis of the ground state phase diagram of dipolar-octupolar pyrochlores. Combining perturbation theory, variational arguments and exact diagonalization we discover multiple U(1) QSL phases which together occupy a large fraction of the parameter space. By comparing numerical calculations to published thermodynamic data we can also locate the materials Ce2Zr2O7 and Ce2Sn2O7 on the phase diagram, finding strong support for a QSL ground state.

Statistical properties of energy barriers and activated dynamics in mean-field models of glasses

Valentina Ros (IPhT CEA Saclay)

Understanding the geometrical properties of high-dimensional, random energy landscapes is an important problem in the physics of glassy systems, with plenty of interdisciplinary applications. Among these properties, an important role is played by the statistics of stationary points, which is relevant in determining the evolution of local dynamics within the landscape. In this talk I will focus on the energy landscape of a simple model for glasses (the so-called spherical *p*-spin model) and I will present a framework to compute the statistical properties of the saddle points surrounding local minima of the landscape. I will discuss how this computation allows to extract information on the distribution of energy barriers surrounding the minimum, as well as on its connectivity in configuration space. I will comment on the dynamical implications on these results, especially for the activated regime of the dynamics, relevant when the dimension of configuration space is large but finite.