09:00  09:45

Alexander Kruchkov
(Princeton University)
Dispersionless electrons, emergent phases, and quantum geometry
Advancements in newgeneration quantum materials have unveiled a plethora of emergent phases, from unconventional superconductors to Fractional Chern Insulators. Beyond their unique bandstructures, such materials, represented by twisted transition metal dichalcogenides and twisted multilayer graphene, exhibit nearly dispersionless quantum states ("flat bands") with distinctive quantum geometrical properties. A new paradigm, centered on the quantum geometry of flat bands, is gaining momentum in understanding the nature of these phases. Quantum geometry, which quantifies the proximity between adjacent quantum states in Hilbert space, has been instrumental in quantum information science, but had been largely overlooked in solidstate experiments. In this seminar, we will explore the quantum transport formalism through the lens of quantum geometry and demonstrate the construction of novel observables. As a practical application, we propose an innovative experimental approach to measure the ultranarrow topological band gap using quantum noise measurements. Time permitting, we discuss importance of quantum geometry for developing newgeneration Fractional Chern insulators, and the challenge of constructing Fractional Chern insulators supporting nonabelian anyons.

09:45  10:15

Ivan Amelio
(Université Libre de Bruxelles)
Lasing in nonHermitian flat bands: quantum geometry, coherence, and the fate of KardarParisiZhang physics
We show that lasing in flat band lattices can be stabilized by means of the geometrical properties of the Bloch states, in settings where the singleparticle dispersion is flat in both its real and imaginary parts.
We illustrate a general projection method and compute the collective excitations, which display a diffusive behavior ruled by quantum geometry through a peculiar coefficient involving gain, losses and interactions, and entailing resilience against modulational instabilities.
Then, we derive an equation of motion for the phase dynamics and identify a KardarParisiZhang term of geometric origin. This term is shown to exactly cancel whenever the real and imaginary parts of the laser nonlinearity are proportional to each other, or when the uniformpairing condition is satisfied.
We confirm our results through numerical studies of the $\pi$flux diamond chain. This work highlights the key role of Bloch geometric effects in nonlinear dissipative systems and KPZ physics, with direct implications for the design of laser arrays with enhanced coherence.

10:15  11:00

coffee break

11:00  11:30

discussion

11:30  12:00

RobertJan Slager
(University of Cambridge)
Quantum geometry beyond projective single bands
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semimetals. Although the metric tensor has been connected to many geometrical concepts for single bands, the exploration of these concepts to a multiband paradigm still promises a new field of interest. Formally, multiband systems, featuring in particular degeneracies, have been related to projective spaces, explaining also the success of relating quantum geometrical aspects of flat band systems, albeit usually in the single band picture. Here, we propose a different route involving Pl\"ucker embeddings to represent arbitrary classifying spaces, being the essential objects that encode $all$ the relevant topology.This paradigm allows for the quantification of geometrical quantities directly in readily manageable vector spaces that a priori do not involve projectors or the need of flat band conditions. As a result, our findings are shown to pave the way for identifying new geometrical objects and defining metrics in arbitrary multiband systems, especially beyond the single flatband limit, promising a versatile tool that can be applied in contexts that range from response theories to finding quantum volumes and bounds on superfluid densities as well as possible quantum computations."

12:00  12:30

Jan Behrends
(University of Cambridge)
Quantum geometry of nonHermitian systems
The Berry curvature can be understood as a consequence of the geometry of quantum states. It materializes, among other experimental consequences related to transport and topology, as an anomalous velocity of wave packets. In nonHermitian systems, these wave packet dynamics are enriched by additional terms that can be expressed by generalizations of the Berry connection to nonorthogonal eigenstates. Here, we contextualize these anomalous nonHermitian contributions by showing that they directly arise from the geometry of the underlying quantum states as a higherorder correction to the distance between left and perturbed right eigenstates. By calculating the electric susceptibility for a singleband wave packet and comparing it with the wave packet’s localization, we demonstrate that these terms can, in some circumstances, lead to a violation of fluctuationdissipation relations in nonHermitian systems.

12:30  13:30

lunch

13:30  14:00

discussion

14:00  14:45

Bogdan A. Bernevig
(Princeton University)
Quantum geometry in electron phonon coupling and a principle for strong superconductivity (virtual)

14:45  15:15

Clara Wanjura
(Max Planck Institute for the Science of Light)
NonHermitian topology and directional amplification
A remarkable phenomenon associated with Hermitian topology is the quantum Hall effect – the quantisation of the Hall resistance in terms of a topological invariant. So far, such a clear observable signature of nonHermitian topology had been lacking. In this talk, I will show that nontrivial, nonHermitian topology is in onetoone correspondence with the phenomenon of directional amplification [13] in onedimensional bosonic systems, e.g., cavity arrays. Directional amplification allows to selectively amplify signals depending on their propagation direction and has attracted much attention as key resource for applications, such as quantum information processing. Remarkably, in nontrivial topological phases, the endtoend gain grows exponentially with the number of sites [1]. Furthermore, we show this effect to be robust against disorder [2] with the amount of tolerated disorder given by the separation between the complex spectrum and the origin. Beyond that, it is possible to restore the bulkboundary correspondence with the help of the singular value decomposition which has a clear link to directional amplification [3].
In collaboration with the group of Ewold Verhagen at AMOLF, Amsterdam, we experimentally demonstrated the connection between nonHermitian topology and directional amplification in a cavity optomechanical system [4] by realising a bosonic version of the KitaevMajorana chain proposed in [5] which relies on a different notion of nonreciprocity [6]. Furthermore, we show in the experiment that a similar system proposed in [7] can be utilised as a sensor with a sensitivity that grows exponentially with system size [4].
Our work opens up new routes for the design of both phasepreserving and phasesensitive multimode robust directional amplifiers and sensors based on nonHermitian topology that can be integrated in scalable platforms such as superconducting circuits, optomechanical systems and nanocavity arrays.
[1] Wanjura, Brunelli, Nunnenkamp. Nat Commun 11, 3149 (2020).
[2] Wanjura, Brunelli, Nunnenkamp. Phys. Rev. Lett. 127, 213601 (2021)
[3] Brunelli, Wanjura, Nunnenkamp. SciPost Phys 15, 173 (2023).
[4] Slim, Wanjura, Brunelli, del Pino, Nunnenkamp, Verhagen. arXiv:2309.05825 (2023); Nature, in press.
[5] McDonald, PeregBarnea, Clerk. Phys Rev X 8, 041031 (2018).
[6] Wanjura, Slim, del Pino, Brunelli, Verhagen, Nunnenkamp. Nat Phys 19, 1429–1436 (2023).
[7] McDonald, Clerk. Nat Commun 11, 5382 (2020).

15:15  16:00

coffee break

16:00  16:45

Bruno Mera
(Instituto Superio Técnico  University of Lisbon)
Geometry of Generalized Landau Levels: holomorphic curves and Cartan moving frames
This talk aims to provide an introduction to the notion of Generalized Landau Levels (GLLs) from a geometric point of view. GLLs are Bloch bands that generalize the standard notion of Landau levels of a charged particle in a uniform magnetic field. Beginning with a foundational introduction to quantum geometrythe differential geometry of families of quantum stateswe delve into the specific case of Bloch bands, unraveling the inequalities that emerge relating the quantum metric and the Berry curvature, the saturation of which implies holomorphicity and gives rise to the concept of Kähler band. A Kähler band can then be understood as a regular holomorphic curve in complex projective space. The geometry of holomorphic curves shares many properties with that of real curves in Euclidean space. In particular, there is a distinguished moving frame along the curve, the FrenetSerret frame (unique up to a global phase), whose elements are the GLLs. The frame satisfies the socalled FrenetSerret equations which, together with the MaurerCartan structure equation, allow us not only to derive the quantum geometry of each GLL but also to establish geometric recursion relations among them. The content of these recursion relations is a manifestation of Calabi's rigidity theorem for Kähler immersions into projective space that, in this language, not only establishes the uniqueness, up to a momentumindependent unitary transformation, of a Kähler band with a given Berry curvature profile, but also completely determines the quantum geometry of the GLLs. As a natural consequence, the quantum volume of the quantum metric of the $n$th GLL is exactly quantized to $2n+1$. The discussion finds direct applications to moiré materials, where the $0$th GLL, the Kähler band, and the $1$st GLL are bands which can stabilize fractional Abelian and nonAbelian, respectively, fractional Chern insulating phases.

16:45  17:15

Jie Wang
(Temple University)
Generalized Higher Landau Levels and Implications to nonAbelian Fractionalization in Moire Materials
Quantum geometry is a fundamental concept to quantum states. Recent works pointed out saturating certain quantum geometric bounds allows for a topological Chern band to share many essential features with the lowest Landau level. In this talk, we discuss the generalization of this line to arbitrary higher Landau levels. We derive geometric properties of individual and multiple generalized Landau levels from Landau level analogs. Moreover, we use generalized Landau levels to construct a toy model which captures a large portion of the singleparticle Hilbert space of a generic Chern band analogous to the first Landau level. Using this model, we employ largescale exact diagonalization to identify a singleparticle geometric criterion allowing for the nonAbelian MooreRead phase. We discuss implications of our findings to nonAbelian fractionalization in small angle twisted MoTe2 material.

17:15  17:45

Armin Rahmani
(Western Washington University)
Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
Intermediatescale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their presentday limitations. In solidstate materials, fractional quantum Hall (FQH) phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the nonperturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasionedimensional model that captures the geometric properties and graviton dynamics of FQH states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimallycompiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimalcontrolbased variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.

18:00  19:00

dinner

19:00  21:30

poster session  focus on odd poster numbers
