FOR 5522 PhD School on Nonergodic Quantum Dynamics

23 Sept 2024, 08:45 → 27 Sept 2024, 14:00 Europe/Berlin

HS 2 (Max Born Hörsaal) (Faculty of Physics)

Fabian Heidrich-Meisner (Georg-August-Universität Göttingen), Markus Heyl (University Augsburg, Germany), Roderich Moessner (MPIPKS Dresden), Frank Pollmann (TUM)

FOR 5522 PhD School on Nonergodic Quantum Dynamics

You can now find the lecture notes in the sidebar under "Lecture notes". If you do not yet have access to it, please get in touch with Silas Hardt (silas.hardt@stud.uni-goettingen.de).

Topics

• Thermalization in Closed Quantum Systems
• Eigenstate Thermalization Hypothesis and Quantum Chaos
• Many-body localization
• Constrained dynamics: Lattice gauge theories
• Constrained dynamics: Hilbert space fragmentation
• Quantum Scars
• Anomalous transport and hydrodynamics
• Beyond Standard ETH
• Experiments with quantum gases
• Computational methods

Lectures

• Monika Aidelsburger, MPQ Garching & LMU Munich , Germany
• Immanuel Bloch, LMU Munich & MPQ Garching, Germany
• Sarang Gopalakrishnan, Princeton University, U.S.A.
• Markus Heyl, Universität Augsburg, Germany
• Sanjay Moudgalya, TUM, Garching, Germany
• Anne Nielsen, Aarhus University, Denmark
• Silvia Pappalardi, Universität zu Köln, Germany
• Anatoli Polkovnikov, Boston University, U.S.A.
• Frank Pollmann, TUM, Garching, Germany
• Alan Tennant, University of Tennessee, Knoxville, U.S.A

Organizers

• Fabian Heidrich-Meisner, Universität Göttingen
• Markus Heyl, Universität Augsburg
• Roderich Moessner, MPIPKS Dresden
• Frank Pollmann, TUM

 

This PhD school is sponsored by the DFG Research Unit FOR 5522.

Monday, 23 September

FOR 5522: Welcome

1 Welcome: For FOR 5522 members and interested school Attendees

FOR 5522: RDM in FOR 5522

2 RDM in FOR 5522 (open to all interested school attendees)

Speaker: Timo Henne (eResearch Alliance)

10:30 Coffee break - Discussion between lecturers and participants

FOR 5522: Equal opportunity

3 Equal Opportunity, Gender equality, Diversity: Open Discussion (open to all interested school attendees)

12:30 Lunch break

MPS, Lunchbox

4 Welcome - Opening School

Lecture

5 Lecture 1 - Transport and hydrodynamics in one-dimensional systems

Speaker: Sarang Gopalakrishnan (Princeton University, U.S.A.)

15:45 Coffee break - Discussion between lecturers and participants

Catering

Lecture

6 Lecture 2 - Dynamics of complex systems through the prism of adiabatic transformations.

Speaker: Anatoli Polkovnikov (Boston University, U.S.A.)

Tuesday, 24 September

Lecture

7 Lecture 3 - Dynamics of complex systems through the prism of adiabatic transformations.

Speaker: Anatoli Polkovnikov (Boston University, U.S.A.)

10:30 Coffee break - Discussion between lecturers and participants

Catering

Lecture

8 Lecture 4 - Numerical simulations of quantum many-body systems out of equilibrium

Speaker: Frank Pollmann (TU Munich, Germany)

12:30 Lunch break

Lecture

9 Lecture 5 - Full Eigenstate Thermalization hypothesis: correlations and beyond

The universality of chaotic many-body dynamics has long been identified by random matrix theory, leading to the Eigenstate Thermalization Hypothesis (ETH).
In this lecture, I will present the full version of ETH, which encompasses correlations among matrix elements needed to describe dynamical correlations of different times. Then, I will show how this ansatz can be highly simplified by the use of Free Probability theory, an extension of probability for non-commuting random variables.

References:
- L. Foini and J. Kurchan, Eigenstate thermalization hypothesis and out of time order correlators, Phys. Rev. E 99, 042139 (2019); - S. Pappalardi, L. Foini and J. Kurchan, Eigenstate thermalization hypothesis and free probability, Phys. Rev. Lett. 129, 170603 (2022); - Lecture notes "Free Probability Approaches to (chaotic) Quantum Dynamics" by S. Pappalardi

Speaker: Silvia Pappalardi (Universität zu Köln, Germany)

15:45 Coffee break - Discussion between lecturers and participants

Poster Session

Catering (Drinks and Snacks)

Wednesday, 25 September

Lecture

10 Lecture 6 - Tutorial

Speaker: Frank Pollmann (TU Munich, Germany)

10:30 Coffee break - Discussion between lecturers and participants

Catering

Lecture

11 Lecture 7 - Introduction to nonergodic quantum matter

Quantum many-body systems are genuinely characterized by ergodic behavior
according to the principles of statistical mechanics. In this set of lectures,
I will discuss how such ergodic behavior can be broken by different kinds of
mechanisms including integrability, many-body localization, gauge symmetries
and local constraints.

Speaker: Markus Heyl (University Augsburg, Germany)

12:30 Lunch break

Excursions: Forum Wissen

Excursions: Hike to Castle Plesse

Excursions: Dinner (Burg Plesse)

Thursday, 26 September

Lecture

12 Lecture 8 - Introduction to nonergodic quantum matter

Quantum many-body systems are genuinely characterized by ergodic behavior
according to the principles of statistical mechanics. In this set of lectures,
I will discuss how such ergodic behavior can be broken by different kinds of
mechanisms including integrability, many-body localization, gauge symmetries
and local constraints.

Speaker: Markus Heyl (University Augsburg, Germany)

10:30 Coffee break - Discussion between lecturers and participants

Lecture

13 Lecture 9 - Engineering local constraints and gauge symmetries in optical lattices

Recently, there has been remarkable progress in realizing constrained models and lattice gauge theories in a number of experimental platforms, ranging from trapped ions to cold-atoms in optical lattices, Rydberg atoms arrays and superconducting qubits. In this lecture I will introduce the basic ingredients needed to engineer local constraints and gauge symmetries and will review experimental protocols that have led to successful implementations and first studies of phase transitions and out-of-equilibrium dynamics. While most of the results have been obtained in 1D models with Abelian symmetry, there are first promising routes towards simulations in higher dimensions, as well as more complex gauge theories, which I will discuss as an outlook.

Speaker: Monika Aidelsburger (LMU Munich, Germany)

12:30 Lunch break

Lecture

14 Lecture 10 - Hilbert-space fragmentation

Speaker: Sanjay Moudgalya (TU Munich, Germany)

15:45 Coffee break - Discussion between lecturers and participants

Catering

Lecture

15 Lecture 11 - Quantum many-body scars

Highly-excited states of quantum many-body systems are typically described well by the eigenstate thermalization hypothesis and show volume law entanglement entropy. In models with quantum many-body scars, however, a few states at high energies behave differently. These scar states typically have area law entanglement entropy and form a tower of states with equidistant energies. The scar states thus violate the eigenstate thermalization hypothesis, and they can give rise to revival dynamics. One can also see quantum many-body scars as a way to have several ground-state-like energy eigenstates in a single system, which opens new opportunities for quantum engineering. Here, we discuss to what extent scar states are like ground states. In particular, we show that scar states can undergo phase transitions like ground states and that adiabatic time evolution is possible for scar states. We also propose and construct inverted quantum many-body scars. These are systems, in which most of the states in the spectrum are localized and have area law entanglement entropy, while a few, highly-excited states have much higher entanglement entropy.

Speaker: Anne Nielsen (Aarhus University, Denmark)

Friday, 27 September

Lecture

16 Lecture 12 - Experimental access to non-ergodic behavior in quantum magnets with neutron scattering

Experiments involving the behavior of quantum magnetic systems in the non-ergodic regime have been difficult to access due to a lack of clearly defined theoretical targets. The situation is changing with the realization that experiments can access the signatures of non-ergodic behavior both in the dynamical correlations in the weakly out-of-equilibrium scattering regime as well as under transient conditions. In the lecture I will cover experiments on one dimensional magnets that show Kardar-Parisi-Zhang like out-of-equilibrium universality, laser pumping in magnon systems, as well as the ways that glass formation and signatures of many-body localization can be accessed.

Speaker: Alan Tennant (University of Tennessee, Knoxville, U.S.A)

10:30 Coffee break - Discussion between lecturers and participants

Catering

Lecture

17 Lecture 13 - Probing Quantum Dynamics using Ultracold Atoms in Optical Lattices

Ultracold atoms and molecules offer intriguing opportunities for probing the quantum dynamics of quantum many-body systems. Initial states, lattice geometries and interactions can be fully tuned to explore novel regimes of quantum transport. Atoms can be counted one-by-one using quantum gas microscopy, giving access to the full counting statistics and non-local correlations. In this lecture, I will introduce the basic physics and detection techniques of these systems and discuss a few key experiments on quantum dynamics with ultracold atoms. These include the observation of Lieb-Robinson bounds in the speed of correlation spreading, anamalous spin transport in Heisenberg magnets, the measurement of full counting statistics in these systems as well as the realization of Hilbert space fragmentation in these systems. Open questions in this research will also be delineated that offer opportunities for further research.

Speaker: Immanuel Bloch (LMU Munich & MPQ Garching, Germany)

18 Final comments