Topology in Nonequilibrium Quantum Many-Body Dynamics

• Applicant: Professor Dr. Jan Budich
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 419241108

• Final Report Year: 2024

Final Report Abstract

This project has contributed to revealing the role of topology in dynamical and dissipative quantum many-body systems. To this end a broad toolbox combining analytical methods such as perturbation theory and computational methods including exact diagonalization, matrix product state simulations, and non-equilibrium Green’s function techniques have been used and adapted. The results range from fundamental insights regarding the generalization of topologically robust spectral properties to dynamical and dissipative systems to concrete protocols for the dynamical preparation of topological states. In particular, it has been demonstrated how both inter-particle- and potentialscattering lead to the (dynamical) formation of exceptional degeneracies, i.e. complex level crossings unique to dissipative systems. Fingerprints of such topologically protected nodal structures may be observed in basic physical observables such as conductances and spectral functions. Since real experiments are always performed finite temperature or, in a non-equilibrium scenario, lead to finite entropy in local subsystems due to thermalization, the results of this project are of quite generic practical relevance. Remarkably, the topological stability of such dissipation induced (or non-Hermitian) properties has in many cases, including protected nodal structures, been found to be more robust than its coherent counterpart found in clean systems. Furthermore, regarding the dynamical preparation of topological states – a key challenge in the field of quantum simulation – twofold progress for the particularly obstinate case of fractional quantum Hall (FQH) states has been reported within this project. First, we have demonstrated how certain FQH model states may be prepared as steady states of dissipative quantum dynamics with comparably simple (two-particle) dissipative processes. Second, we have studied how tuning a spatial anisotropy in the kinetic energy that is directly accessible in state of the art atomic quantum simulators allows for the coherent preparation of FQH states in adiabatic quantum dynamics.

Publications

• Dissipative preparation of fractional Chern insulators. Physical Review Research, 3(4).
  Liu, Zhao; Bergholtz, Emil J. & Budich, Jan Carl
  
• Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals. Physical Review Letters, 127(10).
  Lehmann, Carl; Schüler, Michael & Budich, Jan Carl
  
• Exceptional non-Hermitian phases in disordered quantum wires. Physical Review B, 104(3).
  Michen, Benjamin; Micallo, Tommaso & Budich, Jan Carl
  
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit. Physical Review Research, 5(2).
  Michen, Benjamin; Repellin, Cécile & Budich, Jan Carl
  
• Correlation-induced sensitivity and non-Hermitian skin effect of quasiparticles. Physical Review Research, 5(4).
  Micallo, Tommaso; Lehmann, Carl & Budich, Jan Carl
  
• Topology in the space-time scaling limit of quantum dynamics. Physical Review B, 107(24).
  Rossi, Lorenzo; Budich, Jan Carl & Dolcini, Fabrizio