Robustness and Universality of Quantum Many-Body Scars

• Applicant: Professor Dr. Michael Knap
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 425961213

Strong interactions and frustration can lead to constrained excitations of quantum matter. Examples include spin-ice compounds, frustrated quantum magnets, and fractional quantum Hall liquids. Such constrained quantum matter are often characterized by a Hilbert space that does not have a simple product space structure anymore. Recently a constrained quantum many-body system has also been realized experimentally with one-dimensional ultracold Rydberg atoms in the blockaded regime, which can be mapped onto a constrained hard core boson model. When initializing this system in a far-from equilibrium state, the ensuing quantum dynamics has been found to feature long-lived coherent oscillatory dynamics; an observation that is at odds with the general expectations for the quantum thermalization dynamics of highly excited states. An exceptional set of eigenstates, which are almost decoupled from the rest of the spectrum have been made responsible for these long-lived coherent dynamics. Therefore, these states were called quantum many-body scars. Thus far, it is largely unclear how robust and universal these exceptional eigenstates are. It is the goal of this project to investigate a set of many-body models, which possess projective constraints, to search for exceptional eigenstates in the many-body spectrum which dictate the quantum dynamics. In particular, we will focus on three different types of models: (1) Gauge theories, whose gauge degree of freedom can be converted to a constraint via Gauss’ law, (2) quantum many-body glasses, which possess volume excluding constraints, (3) and projective spin models, such as the AKLT model. By developing Krylov space based exact diagonalization techniques, which take into account the constraints and the symmetries of the problem exactly, and by developing effective descriptions for the quantum dynamics based on the time-dependent variational principle for matrix product states, we will obtain an understanding for the universality and robustness of quantum many-body scars in constrained quantum matter. Beyond their conceptual significance, understanding these questions will be important for interpreting and devising experiments with synthetic quantum matter, for which engineered strong interactions and geometrical frustration may realize controllable constrained quantum matter.

• DFG Programme: Research Grants