Dynamics of correlated quantum systems out of equilibrium

• Applicant: Dr. André Erpenbeck
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2021 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 453644843

• Final Report Year: 2023

Final Report Abstract

In strongly correlated quantum systems, the cooperative behavior of multiple quantum particles leads to the emergence of unusual phenomena like superconductivity, metal-insulator transitions, and exotic quantum phases, which are of significant importance in modern condensed matter physics. However, understanding and theoretically describing these effects is challenging, as it requires to accurately capture the deeply interwoven motion of numerous quantum particles. Furthermore, correlations arise when various driving forces in the system, such as the kinetic energy of the quantum particles and their interaction strength, intricately balance each other, which requires a highly accurate description of the system. This is especially true under nonequilibrium conditions, where bias voltages, magnetic fields, or laser pulses can create or disrupt such energy balances. The goal of this project was to enhance the understanding of nonequilibrium quantum systems in the strongly correlated regime, as well as quantum materials whose characteristics are governed by correlations and quantum effects. To this end, an accurate description based on Quantum Monte Carlo methods was to be developed and applied to model systems of increasing complexity. One main accomplishment of thus project was the development of an inchworm quantum Monte Carlo scheme that can directly characterize system properties in the steady-state. Since strongly correlated systems exhibit dynamics spanning vast timescales, this method allows to distinguish a system’s short-term response to an external stimulus from its long-term physical properties, effectively surpassing the “death valley” separating short and long timescales in strongly correlated systems. This development enabled the investigation of nonequilibrium correlation effects in nanoscale systems, such as quantum dots, with unprecedented precision. Additionally, it provided insight into the strongly correlated regime of nonequilibrium quantum materials. Furthermore, this methodology inspired the proposal of a quantum device that utilizes correlation effects to control currents on macroscopic scales and facilitated the accurate description of stable states in strongly correlated materials that are optically excited. Beyond these applications, a significant enhancement of Quantum Monte Carlo methods was achieved using tensor-based approaches. Tensor methods are utilized to efficiently structure, approximate, and compress large multi-dimensional problems, reducing the computational complexity for simulating quantum systems. Within this project, it was shown that tensor schemes can make Quantum Monte Carlo methods orders of magnitude more efficient and precise. As such, the results of this project have significantly advanced our ability to describe strongly correlated systems under nonequilibrium conditions and have provided valuable insights into representative systems.

Publications

• Nonadiabatic vibronic effects in single-molecule junctions: A theoretical study using the hierarchical equationsof motion approach. Physical Review B, 105(19).
  Kaspar, C.; Erpenbeck, A.; Bätge, J.; Schinabeck, C. & Thoss, M.
  
• Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach. The Journal of Chemical Physics, 157(3).
  Ke, Yaling; Kaspar, Christoph; Erpenbeck, André; Peskin, Uri & Thoss, Michael
  
• Steady state formulation of Inchworm Monte Carlo. APS March Meeting (2022)
  A. Erpenbeck; E. Gull & G. Cohen
  
• Steady state formulation of Inchworm Quantum Monte Carlo. Frontiers of Quantum and Mesoscopic Thermodynamics (2022)
  A. Erpenbeck; E. Gull & G. Cohen
  
• Steady state formulation of Inchworm Quantum Monte Carlo. Recent Developments in Computer Simulation Studies in Condensed Matter Physics (2022).
  A. Erpenbeck; E. Gull & G. Cohen
  
• How an electrical current can stabilize a molecular nanojunction. Nanoscale, 15(40), 16333-16343.
  Erpenbeck, André; Ke, Yaling; Peskin, Uri & Thoss, Michael
  
• Leaky-Integrate-and-Fire Neuron-Like Long-Short-Term-Memory Units as Model System in Computational Biology. 2023 International Joint Conference on Neural Networks (IJCNN), 1-9. IEEE.
  Gerum, Richard; Erpenbeck, André; Krauss, Patrick & Schilling, Achim
  
• Quantum Monte Carlo for multi-orbital systems at steady-state. APS March Meeting.
  A. Erpenbeck; T. Blommel; W.-T. Lin; L. Zhang; E. Gull & G. Cohen
  
• Quantum MonteCarlo Method in the Steady State. Physical Review Letters, 130(18).
  Erpenbeck, A.; Gull, E. & Cohen, G.
  
• Shaping Electronic Flows with Strongly Correlated Physics. Nano Letters, 23(22), 10480-10489.
  Erpenbeck, Andre; Gull, Emanuel & Cohen, Guy
  
• Tensor train continuous time solver for quantum impurity models. Physical Review B, 107(24).
  Erpenbeck, A.; Lin, W.-T.; Blommel, T.; Zhang, L.; Iskakov, S.; Bernheimer, L.; Núñez-Fernández, Y.; Cohen, G.; Parcollet, O.; Waintal, X. & Gull, E.
  
• Numerically Exact Simulation of Photodoped Mott Insulators. Physical Review Letters, 132(17).
  Künzel, Fabian; Erpenbeck, André; Werner, Daniel; Arrigoni, Enrico; Gull, Emanuel; Cohen, Guy & Eckstein, Martin
  
• Stark Many-Body Localization in Interacting Infinite Dimensional Systems. Physical Review Letters, 132(16).
  Atanasova, Hristiana; Erpenbeck, André; Gull, Emanuel; Lev, Yevgeny Bar & Cohen, Guy