Recent seminars

12/04/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

David J. Luitz, Max Planck Institute for the Physics of Complex Systems, Dresden
Hierarchy of Relaxation Timescales in Local Random Liouvillians

To characterize the generic behavior of open quantum many-body systems, we consider random, purely dissipative Liouvillians with a notion of locality. We find that the positivity of the map implies a sharp separation of the relaxation timescales according to the locality of observables. Specifically, we analyze a spin-$1/2$ system of size $\ell$ with up to n-body Lindblad operators, which are n local in the complexity-theory sense. Without locality ($n=l$), the complex Liouvillian spectrum densely covers a “lemon”-shaped support, in agreement with recent findings [S. Denisov et al., Phys. Rev. Lett. 123, 140403 (2019), L. Sa et al., JPA 53, 305303].However, for local Liouvillians ($n < l$), we find that the spectrum is composed of several dense clusters with random matrix spacing statistics, each featuring a lemon-shaped support wherein all eigenvectors correspond to $n$-body decay modes. This implies a hierarchy of relaxation timescales of n-body observables, which we verify to be robust in the thermodynamic limit. Our findings for n locality generalize immediately to the case of spatial locality, introducing further splitting of timescales due to the additional structure.

To test our theoretical prediction, we perform experiments on the IBM quantum computing platform, designing different "waiting circuits" to inject two body dissipative interactions by two qubit entangling gates. We find excellent agreement with our theory and observe the predicted hierarchy of timescales.

[1] K. Wang, F. Piazza, D. J. Luitz ” Hierarchy of relaxation timescales in local random Liouvillians “ Phys. Rev. Lett. 124, 100604 (2020)

[2] O. E. Sommer, F. Piazza, and D. J. Luitz “Many-body Hierarchy of Dissipative Timescales in a Quantum Computer” arXiv:2011.08853

Video

David Luitz slides.pdf

29/03/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Alexander Altland, University of Cologne
Spectral density of weakly disordered Weyl semimetals

Weyl semimetals contain an even number of singular points in their Brillouin zone around which the dispersion is linear and the density of states (DoS) vanishes. How does the density of states change in the (inevitable) presence of impurities? This question has been the subject of an intensive and partially controversial discussion in the recent literature. In particular, it has been suggested that below a critical disorder strength the DoS remains zero, and that the system supports a phase transition separating an intrinsically clean from a disordered phase. In this talk, I discuss this problem on the basis of several effective models. All these support the integrity of the Weyl node and hence are compatible with the above scenario. I will also comment on the (tricky) comparison to numerics and point out a puzzle whose solution invites mathematical research.

22/03/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Markus Heyl, Max-Planck Institute for the Physics of Complex Systems, Dresden
Quantum many-body dynamics in two dimensions with artificial neural networks

In the last two decades the field of nonequilibrium quantum many-body physics has seen a rapid development driven, in particular, by the remarkable progress in quantum simulators, which today provide access to dynamics in quantum matter with an unprecedented control. However, the efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter still remains a key challenge for current computational methods especially beyond one spatial dimension. In this talk I will present a versatile and efficient machine learning inspired approach. I will first introduce the general idea of encoding quantum many-body wave functions into artificial neural networks. I will then identify and resolve key challenges for the simulation of real-time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, I will consider the dynamics of the paradigmatic two-dimensional transverse field Ising model, where we observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached time scales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.

Video

Markus Heyl slides.pdf

15/03/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

In this talk I will discuss how one can detect quantum chaos in generic interacting models using adiabatic transformations, specifically the fidelity susceptibility. In particular, I will show that it exhibits a very sharp crossover behavior from the algebraic to the exponential scaling form with the system size in the presence of a small integrability breaking parameter. This sensitivity allows one to identify tiny integrability breaking perturbations, not detectable by conventional methods. I will also discuss that generically integrable and chaotic regimes are separated by a universal regime of “maximal chaos” where the fidelity susceptibility saturates its upper bound and the system exhibits exponentially slow, glassy dynamics. I will illustrate how this probe works using several examples of both clean and disordered systems and, in particular, will argue that numerical results indicate absence of a continuous many-body localization transition in the thermodynamic limit.

Video

Anatoli Polkovnikov slides.pdf

08/03/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Hannah Price, University of Birmingham
Exploring 4D topological physics in the laboratory

Spatial dimensionality plays a key role in our understanding of topological physics, with different topological invariants needed to characterise systems with different numbers of spatial dimensions. In a 2D quantum Hall system, for example, a robust quantisation of the Hall response is related to the first Chern number: a 2D topological invariant of the electronic energy bands. Generalising to more spatial dimensions, it was shown that a new type of quantum Hall effect could emerge in four dimensions, but where the quantised response was related to a four-dimensional topological invariant, namely the second Chern number. While systems with four spatial dimensions may seem abstract, recent developments in ultracold atoms and photonics have opened the door to exploring such higher-dimensional topological physics experimentally. In this talk, I will introduce the theory of 4D topological phases of matter, before discussing recent experiments in cold atoms, photonics and electrical circuits that have begun to probe aspects of this physics in the laboratory.