Transport Dark States and Quantum Phase Transitions

• Applicant: Professor Dr. Andreas Knorr, since 4/2017
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2010 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 177864488

• Final Report Year: 2020

Final Report Abstract

Within this project, we have investigated the effects of dissipation and nonequilibrium conditions on quantum phase transitions and topology. Regarding quantum critical systems, we have developed a method based on a combination of reaction coordinate mapping and polaron transformation to describe open system undergoing quantum phase transitions. Here, we have showed that our approach allows to access transport properties to probe quantum criticality. Furthermore, we demonstrated that the power output can be increased in a quantum Otto engine, when considering the Lipkin-Meshkov-Glick model as working fluid. In the field of topological band structures, we have investigated fermionic transport along a dimer chain by considering an open version of the Su-Schrieffer-Heeger model. By employing a nonequilibrium Greens function approach, we were able to solve the system without the need of perturbative methods and could show that it may be used as thermoelectric converter at very high efficiency. These results have triggered further investigations of the influence of dissipation on topological systems. Based on our previous results on the electron shuttle, we considered a trimer chain of shuttles to analyze the interplay of synchronization and topology. Here, we have found that topological band-structures may enhance the robustness of synchronized motion at the boundaries of the chain against local perturbations. The methods developed within this project are particularly relevant for quantum critical systems like quantum Ising chains and spinor Bose-Einstein condensates and systems undergoing topological phase transitions. However, our approach may be extended to generic open systems with small or vanishing energy gaps and opens the avenue for very interesting physics to be investigated.

Publications

• Thermoelectric performance of topological boundary modes, Physical Review B 98, 035132 (2018)
  S. Bohling, G. Engelhardt, G. Platero, and G. Schaller
  
• Collective performance of a finite-time quantum Otto cycle, Physical Review E 100, 042126 (2019)
  M. Kloc, P. Cejnar, and G. Schaller
  
• Polaron-transformed dissipative Lipkin-Meshkov-Glick model, Phyical Review A 100, 063815 (2019)
  W. Kopylov and G. Schaller
  
• Proposal of a Realistic Stochastic Rotor Engine Based on Electron Shuttling, Physical Review Applied 12, 024001 (2019)
  C. W. Wächtler, P. Strasberg, and G. Schaller
  
• Dissipative nonequilibrium synchronization of topological edge states via self-oscillation, Physical Review B 102, 014309 (2020)
  C. W. Wächtler, V. M. Bastidas, G. Schaller, and W. J. Munro
  
• Transport through a quantum critical system: A thermodynamically consistent approach, Physical Review Research 2, 023178 (2020)
  C. W. Wächtler and G. Schaller