Hall effect is one of the most central measures in condensed matter systems. In the most naïve semi-classical theories, it gives access to the number of carriers. We know however that this vision is way too simple and for non-interacting systems the Hall effect has been beautifully connected to the curvature of the Fermi surface and to topological invariants. However, and despite severe efforts, understanding the Hall effect for interacting systems remain an ongoing challenge.
I will show in this talk how one can compute the Hall effect for coupled 1D structures such as ladders, and how using numerical approaches one can predict at large tunnelling between the legs of the latter or large interactions a universal behavior of the Hall coefficient for an interacting ladder [1]. This prediction will be successfully compared with recent experiments in systems with synthetic gauge fields and synthetic dimensions [2].
I will also discuss how in the opposite limit of small tunnelling, field theory methods such as bosonisation allow to compute the Hall coefficient and related it to the charge stiffness of the system in the absence of a magnetic field [3].
[1] S. Greschner, M. Filippone, T. Giamarchi, Phys. Rev. Lett. 122, 083402 (2019).
[2] T.-W. Zhou, G. Cappellini, D. Tusi, L. Franchi, J. Parravicini, C. Repellin, S. Greschner, M. Inguscio, T. Giamarchi, M. Filippone, J. Catani, L. Fallani, Science 381, 427 (2023).
[3] R. Citro, T. Giamarchi, E. Orignac, arXiv:2404.16973 (2024).
As the frontiers of artificial intelligence advance more rapidly than ever before, generative language models like GPT are already causing significant economic and social transformation. In addition to their remarkable performance on typical language tasks - such as generating text from a prompt - language models are being rapidly adopted as powerful ansatze states for quantum many-body systems. In this talk, I will discuss the use of language models for learning states realized in today's experimental quantum simulators. By combining variational optimization with data-driven learning using qubit projective measurements, I will show how language models are poised to become one of the most powerful computational tools in our arsenal for the design and characterization of quantum simulators and fault-tolerant computers.
Kontakt:
Prof. Dr. Heidrich-Meisner
Do
07.11.2024
Institute for Theoretical Physics/SR 3 A03.101
Theoretische Physik
14:15
Seminar Statistical Physics
Rick Bebon
MPINAT
Path-based statistical mechanics from the perspective of measure concentration
Integrable unitary circuits can be seen as a Trotter formulation of certain integrable continuous-time Hamiltonians. Their importance lies in the potential to use analytical methods to compute physical observables, such as correlation functions and mean particle current. In this talk, I will explain the different terms in the title and explore their connections.
I will begin with an introduction to integrability, which is the property of a physical system having an infinite number of commuting conserved charges. Then, I will discuss the discrete dynamical evolution of a quantum system and explain how a quantum circuit can be integrable. Using this construction, I will build different quantum circuits with open boundary conditions and address the question of under which conditions the structure of the boundary gate factorizes. In continuous-time evolution, this question corresponds to understanding when we can interpret the boundary terms as a Lindbladian: the effective action of a Markovian environment on the system. I will show how, for specific parameter choices, these solutions correspond to Lindbladians that inject or remove particles at the boundaries of the spin chain.
Based on arXiv:2406.12695 with T. Prosen.
Ultracold atoms in optical lattices are one of the major platforms for quantum simulations and many-body physics. Their versatile nature and high controllability enable the realization of novel quantum phases, the study of phase transitions, and the observation of non-equilibrium dynamics. In the past, most experiments studied these phenomena in the simplest lattice geometries, namely the primitive 1D lattice, the square lattice, and the cubic lattice.
In this talk, we look at many-body physics in 2D in different lattice geometries. These range from the triangular lattice, where geometric frustration can give rise to chiral superfluids, over the Kagome lattice, where it gives rise to a flat band, to optical quasicrystals, where the notion of band-structure is not even directly applicable. In all cases I will present experimental results and highlight open questions.
Parity-time-(PT-)symmetric, non-Hermitian quantum many-body systems are realized as open quantum systems with PT symmetry and compatible couplings to the environment. I review the methodology to theoretically investigate such systems. Taking a mathematical physics perspective, the corresponding Hamiltonians are studied on one hand using the formalisms of PT-symmetric and biorthogonal quantum mechanics, both of which are strongly related. In these frameworks, the notion of observables is altered compared to the standard formalism of Hermitian quantum mechanics. Furthermore, the inner product is modified by including a metric operator. On the other hand, the formalism of Hermitian quantum mechanics is employed. Considering several models ranging from a toy model to one exhibiting quantum critical behavior, I show that the standard formalism always leads to reasonable results while PT-symmetric and biorthogonal quantum mechanics produces results that cannot be reconciled with our physical intuition. The ancilla approach provides a justification for using the standard formalism independent of any specific models. I discuss that within the standard formalism useful methods of quantum many-body theory such as linear response theory and functional integrals cannot easily be extended to non-Hermitian systems. Ironically, this is straightforward within PT-symmetric and biorthogonal quantum mechanics.
