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## Topological phases in condensed matter and cold atom systems

#### CECAM-FR-GSO

#### Organisers

The theoretical prediction of (non-abelian) Majorana particles in topological insulators and closely related

systems [1] has recently boosted the quest for the discovery of emergent non-abelian particles [2] beyond

the realm of the quantum Hall effect [3].

In parallel to the developments in condensed matter physics, tremendous progress has been made in the

field of cold atomic systems [4]. Such systems are extremely versatile, because of their tunability, and there

are several proposals to use exploit the properties cold atomic gasses offer. Amongst these are the

realization of interesting model lattice systems, which are known to exhibit interesting topological phases,

such as Kitaev's honeycomb model [5], to name an interesting example. In addition, there are several

proposals, to use atomic gasses, to emulate non-abelian gauge-potentials [6]. Success in this direction, in

particular in combination with `traditional' condensed matter physics, would open up a whole new realm of

interesting topological phases of matter.

During the recent years, the field of topological phases has been boosted by the possible application to

quantum computing [7]. Topological quantum computation solves by construction, the problem of local

decoherence. Implementing topological quantum computation [8] in realistic experimental systems is one

of the grail of the community.

Numerical simulations with theoretical guidance have provided enormous insights on these complex

many-body systems - quantum Monte Carlo simulations of cold atoms [9], density matrix renormalisation

group [10] and tensor network studies [11] of topological spin liquids or exact diagonalizations of

non-Abelian strongly interacting anyons [12] to cite only a few. Using these techniques, the properties of

non-abelian particles can now be studied in detail [13].

Progress has been made recently on constructing interesting topological phases in strongly interacting

systems. In [14], phases exhibiting non-abelian anyons that generalize Majorana's alluded to above. Though

works along these lines are very promising, the feasibility of these proposals have to be improved, so that

real experiments come within reach.

From the above, it should be clear that the field of topological phases in condensed matter physics is an

active field, where theoretical (both analytic approaches and simulations) and experimental progress go

hand in hand. It is therefor important to have a regular platform, where physicist with different backgrounds

- numerical, theoretical or experimental - but with the common interest of topological phases of matter, can

report and discuss the recent developments in the field.

. machine learning: to what extent can recent developments be harnessed to identify, classify and describe topological phases. how are these related to current developments in tensor network algorithms.

. new types of phases: recent additions to the zoo of topological phenomena include fracton phases; jammed spin liquids; spin liquids with pinch-line singularities and more. how do these fit into our present worldview, and to what extent do they force us to extend it

. many-body quantum dynamics, chaos and beyond: much interest has of late been devoted to studying real-time dynamics, under the headings of scrambling, holography, OTOCs etc. In this rapidly advancing field, we would like to understand what the status and signatures of topological properties (such as topological invariants, entanglement entropy, and superselection sectors) are

. topology and disorder: with the proposal of topological quantum order, and the discovery of discrete time crystals -- including a Z_3 parafermion variant -- the question of how disorder and topology can interact to provide genuinely new phenomena has come back into focus. This is on top of the perennial question regarding the robustness of topological phases and their applications in settings such as topological quantum computing. The latter point is, however, also particularly salient, given the present explosive increase in industrial funding for the field, with view of generating an actual working quantum computer exhibiting 'quantum supremacy'.

. topological spin liquids: there has been much excitement regarding the possibility of realising topological spin liquids in quantum materials such as alpha-RuCl_3. This has generated many questions which are being actively discussed, such as concrete signatures of Majorana fermions in magnetic insulators; their fate upon a low-temperature ordering instability ('proximate spin liquid physics'); and the possibility of field-tuning to non-Abelian spin liquid phases. These ideas go along with impressive progress on the methodological front, such as MPS-based dynamics codes for 2d lattice models, and finite-temperature analyses of spin liquid properties based on a combination of quantum Monte Carlo, exact solutions and the development of more established techniques such as finite-temperature Lanczos.

**Location of workshop**

Institut d'Etudes Scientifique de. Cargèse, Corsica, France

http://www.iesc.univ-corse.fr/

**Application and registration **

https://www.azur-colloque.fr/DR14/inscription/info/108

Contact and organization : Malika Bentour, topo2018@irsamc.ups-tlse.fr Deadline Application : 31/08/2018

Registration Fees (includes lodging, lunches, breakfasts and coffee breaks) : 750 euros (free for invited speakers and CNRS PhD/post-docs)

## References

**France**

Didier Poilblanc ( CNRS - University Toulouse III) - Organiser

Nicolas Regnault (CNRS, ENS -Paris) - Organiser

**Germany**

Roderich Moessner (Max Planck Institute Dresden) - Organiser