Research project is (co) funded by the Slovenian Research Agency.
UL Member: Faculty of Mathematics and Physics
Code: N1-0243
Project: Symmetries and Transport in Interacting Many-Body Systems
Period: 1. 10. 2022 - 30. 9. 2024
Range per year: 0,7 FTE, category: C
Head: Enej Ilievski
Research activity: Natural sciences and mathematics
Research Organisations, Researchers and Citations for bibliographic records
Project description:
In the spirit of the original ERC Starting Grant proposal, the adapted research proposal aims at surveying various foundational aspects of interacting many-body quantum systems confined to one spatial dimension. The general and overarching objective is to advance our current understanding of transport properties and noneqilibrium phenomena in such systems at the level of the underlying microscopic models for interacting degrees of freedom. This is currently an active field of theoretical research fuelled by a steady stream of experimental advancements. In particular, optical lattice technologies have now finally progressed to the point to enable the manufacturing of tunable and versatile cold-atom simulators, allowing to perform direct measurements on strongly-interacting quantum matter and to probe their relaxation with a high degree of accuracy. Another, even more concrete, motivation for actively pursuing this research direction stems from the recent surprising discovery of superdiffusive magnetization transport in the ferromagnetic quantum Heisenberg spin chain in the universality class of the celebrated Kardar-Parisi-Zhang equation. Apart from generating a huge amount interest in the theoretical community, there have already been two independent successful experimental demonstrations for the breakdown of normal diffusion, one performed in a cold-atom simulator and the other independently with methods of neutron scattering. This importantly corroborates the theoretical picture that I with co-authors had established a few years earlier and thereby places it on firm grounds. The observed anomalous behavior can be traced back to long-lived solitonic quasiparticle excitations and, more importantly, crucially relies on the presence of unbroken rotational symmetry of local interactions.
With all this insightful information at hand, it is natural to raise the question whether there may exist other, possibly more sophisticated, types of symmetry restrictions that could give birth to yet undisclosed anomalous emergent macroscopic laws of physics. The goal of the adapted proposal is to examine a number of promising candidates. I thereby propose to systematically study a variety of analytically tractable models, as detailed out in the original proposal. There I have compiled a list of interacting quantum many-body systems subjected to various forms of symmetries and elaborated why they can plausibly accommodate for unconventional physical properties (such as, for example, lack of thermalization, anomalous transport laws or anomalous fluctuations of macroscopic quantities), or perhaps even entirely new features.
Specifically, there are three distinct profound algebraic notions that lie at the heart of this proposal: (i) supersymmetry, (ii) Yangian symmetry and (iii) conformal symmetry in two space-time dimensions. These are fairly well-known paradigms in theoretical physics, all of which have drawn a substantial amount of interest in the past, despite largely confined to the high-energy communities. There is nevertheless currently merely a handful of applications in the realm of condensed matter systems at best, while virtually nothing is known about their behavior out of equilibrium. For instance, physical implications of supersymmetry exhibited by certain fermionic systems on a one-dimensional lattice have not been yet systematically explored. Likewise, integrable models that exhibit long-range interactions and give birth to quasiparticles carrying fractionalized charges that obey semionic statistics have mostly been studied only at a formal level, without any notable physics applications. Besides partially filling this gap, one of the central objectives of this adapted research proposal is to advance our present empirical and analytical understanding of non-ergodic strongly-correlated quantum dynamical systems from the microscopic viewpoint. This will be achieved by employing a combination of powerful exact and approximate analytical techniques and rigorous tools of integrability theory. As an independent and complementary approach, the plan is also to devise and implement efficient tools for performing numerical simulations based on suitable lattice discretizations.
