TQM seminar #18 : January 26 2023, 2pm (LPTHE library, towers 13-14, 4th floor)

**Karim Noui** (ICJLab, Orsay)

*Topological Invariants and Quantum Gravity*. Very naively, quantum gravity would provide a “way” to integrate (using path integral) over all spacetime metrics. Hence, if we integrate on the metrics, finally, the only information that we could extract on the space-time would be its topological properties! This argument is very naive but it illustrates that topology and topological invariants could play a very important role in quantum gravity. This is indeed the case for quantum gravity in 3 (space-time) dimensions where there is, for example, a very beautiful and very deep link between knot invaiants and the physical observables, a link which has been shown by Witten at the end of the 1980s. Quantifying gravity in 4 dimensions is much more involved and to date we do not know a

solution to this problem. However, we can try to adapt the methods used in dimension 3 to advance in the problem, which is exactly what has been done in some approaches to quantum gravity (loop gravity and spin foam models). Here again, topological invariants play a crucial role… In this talk, I will try to show (through simple examples) the connection between topology and quantum gravity.

You will then see that the structures which appear are very similar to those that appear in the analysis of the topological phases in condensed matter.

TQM seminar #19 : February 2 2023, 2pm (INSP great hall, towers 22-23, 3rd floor, room 317)

**Anne Anthore** (C2N Palaiseau & Université Paris Cité)

*Noise signatures of Anyon statistics and Andreev scattering in the =1/3 fractional quantum Hall regime*With P. Glidic, O. Maillet, C. Piquard, A. Aassime, A. Cavanna, Y. Jin, U. Gennser, F. Pierre. Anyons are exotic quasiparticles which can carry a fractional charge of an electron and with an exchange statistic inbetween that of fermions and bosons. These properties were revealed using quantum point contacts (QPC) in the fractional quantum Hall regime [1,2].

In this talk, I will report further noise investigation of anyon physics. Sourcing e/3 anyons at a first QPC, noise measured on a downstream “analyzer” QPC reveals different mechanisms. Setting the analyser to allow e/3 tunneling charges, we reproduce the negative cross-correlations previously observed [2], indicative of a non-trivial anyon exchange phase [3]. When 1 e charges tunnel across the analyser, the braid phase is predicted to be trivial. Our observation of negative cross-correlations points on a scattering mechanism akin to Andreev reflection at Normal/Superconductor interfaces, as suggested in [4].

Remarkably, in both cases, electrical conduction through the analyser does not preserve the nature or number of quasiparticles, rendering the beam splitter analogy of a QPC invalid.

[1] L. Saminadayar et al., PRL 79, 2526 (1997)

[2] H. Bartolomei et al., Science 368, 173-177 (2020)

[3] B. Rosenow et al. PRL, 116, 156802 (2016)

[4] C. L. Kane and M. P. A. Fisher, PRB 67, 045307 (2003)

TQM seminar #17 : January 5 2023, 2pm (LPTHE library, towers 13-14, 4th floor)

**Kareljan Schoutens** (University of Amsterdam)

*Supersymmetric lattice models*

This seminar will introduce supersymmetry as a remarkable and potent symmetry in lattice models in condensed matter. Our original proposal (Fendley, Schoutens, de Boer 2003) specifies a N=2 supersymmetric Hamiltonian on a general graph. This so-called M_1 model, which features hopping terms and local interactions, exhibits remarkable properties. In 1D it turns out to be integrable and critical, and it connects to a supersymmetric version of Conformal Field Theory, first considered in the String Theory literature. On many 2D lattices, the M_1 model shows superfrustration: a proliferation of zero-energy supersymmetric ground states. Generalizations such as M_k models and models with staggered supercharges enrich the supersymmetric landscape. We end the seminar with a proposal for a quantum simulation of the 1D M_1 model using Rydberg atoms.

TQM seminar #16 : December 8, 2pm (INSP great hall, towers 22-23, 3rd floor, room 317)

**Nicolas Dupuis** (LPTMC, CNRS & Sorbonne Université, Paris)

*One-dimensional disordered Bose fluid: from Bose glass to Mott glass*

In a one-dimensional Bose fluid, disorder can induce a quantum phase transition between a superfluid phase (Luttinger liquid) and a localized phase (Bose glass). Using bosonization, the replica method and a nonperturbative functional renormalization-group approach, we find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form. This reveals the glassy properties (pinning, “shocks” and “avalanches”) due to the existence of metastable states, as well as the crucial role of quantum tunneling between different metastable configurations. We also show that long-range interactions can stabilize a Mott glass, i.e. a state intermediate between a Mott insulator and a Bose glass, and characterized by a vanishing compressibility and a gapless optical conductivity.

TQM seminar #15 : November 24, 2pm (INSP great hall, towers 22-23, 3rd floor, room 317)

**Massimo Capone** (SISSA, Trieste)

*Competing Correlated Insulators in multi-orbital systems coupled to phonons*

It is nowadays established that multi-orbital correlated materials display a number of distinctive phenomena which can be captured in terms of Hubbard models featuring the interplay between Hubbard repulsion U and the Hund’s exchange J. In this talk I will address how an electron-phonon coupling affects this picture. I will show that a Jahn-Teller coupling coexists with the Mott localization driven by the Hubbard repulsion U, but it competes with the Hund’s coupling J. This interplay leads to two spectacularly different Mott insulators, a standard high-spin Mott insulator with frozen phonons which is stable when the Hund’s coupling prevails, and a low-spin Mott-bipolaronic insulator favoured by phonons, where the characteristic features of Mott insulators and bipolarons coexist. The two phases are separated by a sharp boundary along which an intriguing intermediate solution emerges as a kind of compromise between the two solutions. I will finally address the stability of this scenario when doping is included.

TQM seminar #14 : October 27, 2pm (INSP great hall, towers 22-23, 3rd floor, room 317)

**Adam Rançon** (Université Lille 1)

*Tan’s contact of a planar Bose gas: theory vs experiment*

In a dilute gas, Tan’s contact relate the thermodynamics to the short distance properties of quantum many-body systems. Recently, the contact of a Bose gas confined in a plane has been measured in a broad temperature range, from the normal to the superfluid phase, and across the Berezinskii-Kosterlitz-Thouless transition. We show that the contact of this quasi-2D system can be obtained from the universal equation of state of a two-dimensional Bose gas. We compute the contact using the functional renormalisation group, and find a remarkable agreement with experiment.

TQM seminar #13 : September 22, 2pm (INSP great hall, towers 22-23, 3rd floor, room 317)

**Alice Sinatra** (LKB, Ecole Normale Supérieure, Paris)

*Amortissement Landau-Khalatnikov des phonons dans un superfluide*

Nous avons revisité les interactions entre les excitations de basse énergie d’un superfluide en marchant dans les pas de l’école russe de Landau et Khalatnikov. En particulier nous avons étudié l’amortissement des phonons à basse température dans un gaz de fermions appariés en interaction forte. Après avoir généralisé et corrigé le calcul original de Landau et Khalatnikov de 1949 nous donnons la prédiction du taux d’amortissement à l’ordre le plus bas en température. Notre résultat théorique, allié aux progrès expérimentaux dans les gaz de fermions froids, ouvre la voie à la première observation de l’amortissement Landau-Khalatnikov.

[1] Landau-Khalatnikov phonon damping in strongly interacting Fermi gases, H. Kurkjian, Y. Castin, A. Sinatra , Europhysics Lett. 116 , 40002 (2016).

[2] Three-phonon and four-phonon interaction processes in a pair-condensed Fermi gas, H. Kurkjian, Y. Castin, A. Sinatra, Annalen des Physik 529 , Issue 9, (2017).

[3] Landau Phonon-Roton Theory Revisited for Superfluid 4He and Fermi gases, Y. Castin, A. Sinatra, H. Kurkjian, Phys. Rev. Lett. 119, 260402 (2017).

TQM Seminar #12

July 7, 2pm (LPTMC, towers 12-13, 5th floor, room 5-23)

**Gregory Fiete** (Northeastern university, Boston)

*Manipulation of magnetic order and band topology through selective phonon excitation*

Quantum materials driven out-of-equilibrium by a laser pump offer new opportunities for exploring intriguing quantum phenomena, including electron-correlation behaviors and topological properties of excitations. After reviewing some recent motivating pump-probe experiments, I will turn to our theoretical studies of driven many-body quantum systems. I will place particular emphasis on the situation where the laser frequency is chosen to selectively excite particular phonon modes and describe the impact of the non-equilibrium lattice on the electron properties, such as magnetism and band topology. The layered van der Waals materials CrI3 and MnBi2Te4 serve as excellent examples of the broader phenomena one might expect. I will also describe how hybrid phonon-magnon excitations in insulating antiferromagnets can exhibit highly tunable topological transitions in the presence of an externally applied magnetic field. The talk will conclude with an outlook for the prospects of achieving other interesting many-body phenomena in driven materials.

TQM Seminar #11

Jun 9, 2pm (INSP great hall, towers 22-23, 3rd floor, room 317)

**Julia Meyer** (Univ. Grenoble Alpes)

*Topological properties of multi-terminal Josephson junctions* Topological phases of matter have been a subject of intense studies in recent years. In many instances, topological properties are encoded in the band structure and one has to find the right material or combination of materials in order to realize them. More recently, an alternative approach to finding and exploring topological states of matter has emerged: namely, one can “imitate” necessary physical ingredients by using other degrees of freedom. Multi-terminal Josephson junctions are of interest both as probes of the topological properties of the superconducting leads and as synthetic topological matter. Using the superconducting phases of the terminals in n-terminal Josephson junctions as variables, one may realize topological band structures in d=n-1 dimensions. In particular, we show that a 4-terminal junction may realize the analog of a 3-dimensional Weyl semimetal, whereas a 3-terminal junction may realize the analog of a 2-dimensional Chern insulator. Extending the analogy to more terminals opens the possibility of realizing topological phases in dimensions d>3, not accessible in real materials.

TQM Seminar #10 (May 19, 2pm, LPTHE library)

**Laura Messio** (LPTMC, Sorbonne Université, Paris)

*Overview of the possibilities of high temperature series expansions*

In the search for exotic properties of spin lattices, many numerical methods focus on the ground state and on the low-energy excitations of a model. Here, we use the opposite approach, with high temperature series expansions. The coefficients of the free energy, the specific heat or the magnetic susceptibility series are obtained up to beta^20 (depending on the model complexity). But the convergence radius limits the range of temperature where information can been obtained by simple summation. Thus, alternative methods are required. One of them is the entropy method, that uses some hypothesis on the nature of the ground state to reconstruct thermodynamic quantities over the whole temperature range. This method has been used on several compounds to propose exchange parameter values. When a finite temperature phase transition occurs, a singularity forbids to use the entropy method, but then, informations on the critical exponents and on the critical temperature can be extracted. A review of these methods and their limitations, together with some applications, will be presented.

TQM Seminar #9 (Mar 24, 2pm, LPTHE library)

**Andrea de Luca** (LPTM Cergy)

*Thermalisation and chaos in many-body quantum systems*

I will present a brief overview about the general principles controlling the out-of-equilibrium dynamics of closed quantum systems with a large number of degrees of systems. I will discuss the main mechanisms which allow an isolated system undergoing fully unitary dynamics to be well described by a thermal ensemble. I will stress the important role played by conservation laws, ergodicity and chaos as it manifests itself in the correlation of energy levels and their repulsion. Quantum chaos is an evasive concept which, at the level of single particles, is historically understood by comparing spectral features with those of an ensemble of random matrices. I will then introduce random unitary circuits for which several dynamical properties are computable explicitly at least in the limit of large local Hilbert space dimensions. In particular, I will employ them to derive the general features of the spectral correlations in many body systems: Only at times larger than the Thouless time, the random matrix behavior is recovered. Beyond the well-known universality of random matrices, I will derive scaling functions which characterize a universal transient regime towards the random matrix prediction.

TQM Seminar #8 (Mar 10, 2pm, INSP great hall)

**Benoît Douçot** (LPTHE, Sorbonne Université, Paris)

*Topological Electrostatics*

Two-dimensional electron gases under a strong magnetic field have tremendously expanded our understanding of many-body physics, with the discovery of integer and fractional quantum Hall effects, together with chiral edge states, fractional excitations, anyons. Another striking effect is the strong coupling between charge and spin and valley degrees of freedom, which takes place near integer filling *M* of the magnetic Landau levels. More precisely, because of the large energy gap associated to cyclotron motion, any slow spatial variation of the spin background induces a variation of the electronic density proportional to the topological density of the spin background. Minimizing Coulomb energy leads to an exotic class of two-dimensional crystals, which exhibit a periodic non-collinear spin texture called a Skyrmion lattice. Magnon propagation through such lattice has been recently investigated experimentally in a graphene layer.

I will focus on the limit where we neglect coupling anisotropies in the *N*-dimensional spin and valley internal space, so that a perfect SU(*N*) symmetry is assumed to hold. In this case, minimal energy Skyrmion lattices may be described in terms of holomorphic maps from a torus (unit cell) to the Grassmannian manifold Gr(*M,N*)*, *such that the associated topological charge density is as uniform as possible. The case of an undoped graphene layer corresponds to *N *= 4 and *M *= 2. The main outcome of this analysis is the existence of two regimes depending on whether the topological charge on the unit cell is smaller (unfrustrated case) or larger (frustrated case) than the number of internal states *N* accessible to electrons. I will show that we can, to a large extent, identify minimal energy Skyrmion lattices by combining the solution of the *M* = 1 case with Atiyah’s explicit description of rank *M* vector bundles on a torus.

TQM Seminar #7 (Feb 10, 2pm, INSP great hall)

**Rebeca Ribeiro** (C2N Palaiseau)

*Tunable valley currents in aligned bilayer graphene/BN*

The relative angular alignment between 2D layers of a van der Waals (vdW) heterostructure can dramatically alter its fundamental properties[1]. A striking example is the recent observation of strongly correlated states and intrinsic superconductivity in twisted bilayer graphene[2]. Another remarkable effect of angular layer alignment, predicted for certain vdW heterostructures, is the emergence of phases of matter with non-trivial topological properties, where charge carriers flow without dissipation, being protected against perturbations. In graphene aligned with boron nitride (BN), such a phase has been predicted, with topological protection linked not to the spin, as commonly observed, but rather to the valley degree of freedom. The experimental observations of these topological valley currents [3] has been largely put in question by theorist, results of numerical simulation [4] and recent scanning SQUID results[5]. In these, the observed non-local signal have been attributed mostly to localized states on the edge of graphene. In this talk, we will show how these two pictures are not incompatible and can be reconciliated if we take the angular layer alignment into account.

[1] Ribeiro-Palau et al., Science 361 (2018), 690

[2] Cao et al., Nature 556 (2018) 43.

[3] Gorbachev et al., Science 436 (2014), 448; Komatsu et al., Science Advances 4 (2018)

[4] J M Marmolejo-Tejada et al., J. Phys. Mater. 1 (2018) 015006

[5] A. Aharon-Steinberg et al., Nature 593 (2021), 528

TQM Seminar #6 (Jan 27, 2pm, online)

**Félix Werner** (LKB Paris)

*Higher-order diagrammatic expansion around BCS Hamiltonians: polarized superfluid phase of the attractive Hubbard model*

In contrast to conventional QMC methods, expansions of intensive quantities in series of connected Feynman diagrams can be formulated directly in the thermodynamic limit. Over the last decade, diagrammatic Monte Carlo algorithms made it possible to reach large expansion orders and to obtain state-of-the-art results for various models of interacting fermions in 2 and 3 dimensions, mostly in the normal phase. We obtained first results inside a superconducting phase, for the 3D attractive Hubbard model [1]. Spontaneous symmetry breaking is implemented by expanding around a BCS Hamiltonian. All diagrams up to 12 loops are summed thanks to the connected determinant algorithm [2] with anomalous propagators. Working on the BCS side of the strongly correlated regime, we observe convergence of the expansion, and benchmark the results against determinant diagrammatic Monte Carlo [3]. In presence of a polarizing Zeeman field (where unbiased benchmarks are unavailable due to the fermion sign problem) we observe a first-order superconducting-to-normal phase transition, and a thermally activated polarization of the superconducting phase well captured by a quasiparticle description. We also discuss the large-order behavior of the expansion and its relation to Goldstone and instanton singularities.

[1] G. Spada, R. Rossi, F. Simkovic, R. Garioud, M. Ferrero, K. Van Houcke, F. Werner, arXiv:2103.12038

[2] R. Rossi, PRL 119, 045701 (2017)

[3] E. Burovski, N. Prokof’ev, B. Svistunov, M. Troyer, PRL 96, 160402 (2006)

TQM Seminar #5 (Jan 13, 2pm, INSP great hall)

**Alex Chin** (INSP, Sorbonne Université, Paris)

*Excitons in 1D organic topological semiconductors*

Organic pi-conjugated polymers have been studied for many years in the context of optoelectronic applications such as solar cells, LEDs and sensors, and remain a highly promising class of materials for cheap, non-toxic and flexible light-matter coupling devices. Recently, on-surface synthesis techniques have allowed novel quasi-1D molecular polymers to be fabricated whose electronic and optical properties can be controlled via the connectivity and composition of the monomer units. For polymers based on acene units, Cirera et al. have shown that varying the size of the acene unit causes the polymer band gap to close and reopen, as the system passes from a trivial to a topologically non-trivial electronic phase [1]. In this talk, I will present our recent exploration of the behaviour of the strongly bound excitonic excitations of acene polymers as they pass through this transition. Using self-consistent GW and Bethe Salt-Peter techniques, we show that the presence of the topological transition and the related band flattening and inversion lead to a range of rich, measureable and functionally exploitable properties of singlet and triplet excitons, including negative dispersions and the possibility of spontaneous fission of singlets into entangled triplet pairs.

[1] Cirera et al., Nature Nanotechnology, 15, 437–443 (2020)

TQM Seminar #4 (Dec 16, 2021, 2pm, INSP great hall)

**Gwendal Fève** (LPENS Paris)

*Fractional statistics of anyons in a mesoscopic collider*

In three-dimensional space, elementary particles are divided between fermions and bosons according to the properties of symmetry of the wave function describing the state of the system when two particles are exchanged. When exchanging two fermions, the wave function acquires a phase, phi=pi. On the other hand, in the case of bosons, this phase is zero, phi=0. This difference leads to deeply distinct collective behaviors between fermions, which tend to exclude themselves, and bosons which tend to bunch together. The situation is different in two-dimensional systems which can host exotic quasiparticles, called anyons, which obey intermediate quantum statistics characterized by a phase phi varying between 0 and pi [1,2].

For example in the fractional quantum Hall regime, obtained by applying a strong magnetic field perpendicular to a two-dimensional electron gas, elementary excitations carry a fractional charge [3,4] and have been predicted to obey fractional statistics [1,2] with an exchange phase phi=pi/m (where m is an odd integer) for Laughlin states corresponding to a fractional filling nu=1/m of the first Landau level. I will present how fractional statistics of anyons can be demonstrated in this system by implementing and studying anyon collisions at a beam-splitter [5,6]. The collisions are first studied in the low magnetic field regime, where the elementary excitations are electrons which obey the usual fermionic statistics. It leads to the observation of an antibunching effect in an electron collision: electrons systematically exit in two different arms of the beam-splitter. The observed result is completely different in the fractional quantum Hall regime at filling factor nu=1/3. Fractional statistics lead to a suppression of the antibunching effect and quasiparticles tend to bunch together in larger packets of charge in a single output of the splitter. This effect leads to the observation of negative correlations of the current fluctuations [6] in perfect agreement with recent theoretical predictions [5].

[1] B. I. Halperin, Phys. Rev. Lett. **52**, 1583–1586 (1984).

[2] D. Arovas, J. R. Schrieffer, F. Wilczek, Phys. Rev. Lett. **53**, 722–723 (1984).

[3] R. de Picciotto et al., Nature **389**, 162–164 (1997).

[4] L. Saminadayar, D. C. Glattli, Y. Jin, B. Etienne, Phys. Rev. Lett. **79**, 2526–2529 (1997)

[5] B. Rosenow, I. P. Levkivskyi, B. I. Halperin, Phys. Rev. Lett. **116**, 156802 (2016).

[6] H. Bartolomei, M. Kumar et al. Science **368**, 173-177 (2020).

TQM Seminar #3 (Dec 9, 2021, 2pm, INSP great hall)

**Fabien Alet** (LPT Toulouse)

*Probing for Many-Body Localization in 2d disordered constrained systems*

Many-body localization (MBL) is a unique physical phenomenon driven by interactions and disorder for which a quantum system can evade thermalization. While the existence of a many-body localized phase in one-dimensional systems,is now (relatively well) established, its fate in higher dimension is an open question. In this talk, after a rapid overview of MBL, I will present a numerical study of the possibility of a MBL transition in disordered quantum dimer models on two-dimensional lattices. I will critically review our numerical results using state-of-the-art exact diagonalization and time evolution methods, probing both eigenstates and dynamical properties. We conclude for the existence of a localization transition, on the available time and length scales.

Work done in collaboration with H. Théveniaut. G. Meyer, Z. Lan and F. Pietracaprina.

TQM Seminar #2 (Nov 18, 2021, 2pm, INSP great hall)

**Benjamin Lenz** (IMPMC, Sorbonne Université, Paris)

*Investigation of a strongly correlated material by quantum cluster techniques: Electronic, magnetic and spectral properties of Sr2IrO4*

5d iridium oxides are of high interest due to the potential for new quantum states driven by strong spin- orbit coupling. In Sr_2IrO_4, the low-energy physics of the material is well described by a so-called j_eff=1/2 state, which consists of a quantum superposition of the three Ir t_2g orbitals. Moreover, the interplay of electron-electron interactions and spin-orbit coupling leads to an unconventional Mott insulating state, whose spectral properties strongly resemble those of isostructural cuprates. Despite not being superconducting upon doping down to lowest temperatures, the analogy with cuprates is corroborated by Fermi surface and pseudogap properties of doped Sr_2IrO_4, which suggests an effective minimal one-band model in terms of the j_{eff}=1/2 state. However, the k-dependent orbital composition of this state and recent measurements of its magnetization density distribution cast the validity of a *local* j_eff=1/2 picture into doubt. In this talk, I will use two complementary quantum cluster techniques to study selected electronic, magnetic and spectral properties of this strongly correlated material. The results of our simulations will be compared to different experimental probes and the validity and limitations of an established one-band model of Sr_2IrO_4 will be discussed.

TQM Seminar #1 (October 14, 2021, 2pm, LPTHE library)

**Clément Tauber** (IRMA, Strasbourg)

*Topological indices for shallow-water waves*

In this talk, I will apply tools from topological insulators to a fluid dynamics problem: the rotating shallow-water wave model with odd viscosity. The bulk-edge correspondence explains the presence of remarquable stable waves propagating towards the east along the equator and observed in some Earth oceanic layers. The odd viscous term is a small-scale regularization that provides a well defined Chern number for this continuous model where momentum space is unbounded. Equatorial waves then appear as interface modes between two hemispheres with a different topology. However, in presence of a sharp boundary there is a surprising mismatch in the bulk-edge correspondence: the number of edge modes depends on the boundary condition. I will explain the origin of such a mismatch using scattering theory and Levinson’s theorem. This talk is based on a series of joint works with Pierre Delplace, Antoine Venaille, Gian Michele Graf and Hansueli Jud.