# Recent seminars

## 19/07/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Sven Bachmann, University of British Columbia

Recent years have seen much progress in the mathematical understanding of quantum charge transport under slow driving, in the presence of strong interactions between the charge carriers. I will give an overview of recent results, starting with the adiabatic theorem in an interacting setting, and continuing to topological transport where quantization can be shown to be valid beyond the linear response setting.

Sven Bachmann slides.pdf

## 05/07/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Ákos Nagy, University of California, Santa Barbara
Concentrating Majorana fermions

I will begin by defining a canonical family of perturbations of the Dirac equation. These perturbations are complex anti-linear, thus ground states only form a real vector space. A special case of this theory is known as the Jackiw–Rossi theory, which models surface excitations on the surface of a topological insulator placed in proximity to an s-wave superconductor. While the physics of the theory is relatively well-understood, the mathematical side has not been studied, even on surfaces, not to mention its generalizations to higher dimensional and on nontrivial manifolds. I call these equations the generalized Jackiw–Rossi equations.

After the definitions and connections to physics, I will present my current work on the generalized Jackiw–Rossi equations. My main result is a concentration phenomenon which proves the physical expectation that such Majorana fermions concentrate around the vortices of the superconducting order parameter. Moreover, I provide approximate solutions that are exponentially sharp in the large coupling limit.

If time permits, then I will show how these Majorana fermions define a bundle of projective spaces over the simple part of vortex moduli spaces. The holonomies of such bundles give rise to projective representations of (surface) braid groups, and thus, speculatively, can be of interest to quantum information theorists.

https://akosnagy.com/talks/Majorana-GM3/talk.html

## 28/06/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Rubem Mondaini, Beijing Computational Science Research Center
Quantum Critical Points and the Sign Problem

The "sign problem" (SP) is the fundamental limitation to simulations of strongly correlated materials in condensed matter physics, solving quantum chromodynamics at finite baryon density, and computational studies of nuclear matter. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians, since the details of how it onsets, and its eventual occurrence, can be altered by the choice of algorithm or many-particle basis. Despite that, I plan to show in this talk that the SP in determinant quantum Monte Carlo (DQMC) is quantitatively linked to quantum critical behavior. This demonstration is done via simulations of a number of fundamental models of condensed matter physics, all of whose critical properties are relatively well understood.

## 14/06/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Clement Delcamp, Max-Planck-Institute of Quantum Optics
On tensor network representations of the $(3+1)d$ toric code

Tensor network states provide a comprehensive framework for the analytic and numerical study of strongly correlated many-body systems. In recent years, this framework has been successfully applied to topological phases of matter. In this talk, I will present two dual tensor network representations of the $(3+1)d$ toric code ground state subspace, which are obtained by initially imposing either family of stabilizer constraints. I will discuss topological properties of the model from the point of view of these virtual symmetries, demonstrate that one of these representations is stable to all local tensor perturbations — including those that do not map to local operators on the physical Hilbert space — and explain, both from a physical and category theoretical viewpoint, how the distinguishing properties of these representations are related to the phenomenon of bulk-boundary correspondence.

## 07/06/2021, Monday, 17:00–18:00 Europe/Lisbon — Online

Michael Fleischhauer, Dept. of Physics & research center OPTIMAS, Univ. of Kaiserslautern, Germany
Topology of mixed states

Topological states of matter have fascinated physicists since a long time. The notion of topology is however ususally associated with ground states of (many-body)-Hamiltonians, which are pure. So what is left of it at finite temperatures and can topological protection be extended to non-equilibrium steady states (NESS) of open systems? Can suitable observables be constructed that preserve the integrity of topological invariants for mixed states and what are measurable consequences of their existence? Can we classify the topology of finite temperature and NESS using generalized symmetries? Motivated by topological charge pumps, first introduced by Thouless, I will first discuss a topological invariant for systems that break time reversal symmetry based on the many-body polarization, called ensemble geometric phase (EGP) [1]. In contrast to charge transport, the EGP can be used to probe topology in one dimensional non-interacting [2] and interacting [3], closed and open systems alike. Furthermore different from other constructions, such as the Uhlmann phase, it can be extended to two dimensions [4]. I will then extend the definition to systems with time-reversal symmetry and finally talk about measurable consequences of mixed-states topological invariants.

1. C.E. Bardyn, L. Wawer, A. Altland, M. Fleischhauer, S.Diehl, (PRX 2018).
2. D. Linzner, L. Wawer, F. Grusdt, M. Fleischhauer, (PRB 2016).
3. R. Unanyan, M. Kiefer-Emmanouilidis, M. Fleischhauer, (PRL 2020).
4. L. Wawer, M. Fleischhauer, arxiv 2104.12115.