Nonequilibrium quantum impurity problems via matrixproduct states in the temporal domain
Abstract
Describing a quantum impurity coupled to one or more noninteracting fermionic reservoirs is a paradigmatic problem in quantum manybody physics. While historically the focus has been on the equilibrium properties of the impurityreservoir system, recent experiments with mesoscopic and coldatomic systems enabled studies of highly nonequilibrium impurity models, which require novel theoretical techniques. We propose an approach to analyze impurity dynamics based on the matrixproduct state (MPS) representation of the FeynmanVernon influence functional (IF). The efficiency of such a MPS representation rests on the moderate value of the temporal entanglement (TE) entropy of the IF, viewed as a fictitious "wave function" in the time domain. We obtain explicit expressions of this wave function for a family of onedimensional reservoirs, and analyze the scaling of TE with the evolution time for different reservoir's initial states. While for initial states with shortrange correlations we find temporal arealaw scaling, Fermiseatype initial states yield logarithmic scaling with time, closely related to the realspace entanglement scaling in critical 1d systems. Furthermore, we describe an efficient algorithm for converting the explicit form of the reservoirs' IF to MPS form. Once the IF is encoded by a MPS, arbitrary temporal correlation functions of the interacting impurity can be efficiently computed, irrespective of its internal structure. The approach introduced here can be applied to a number of experimental setups, including highly nonequilibrium transport via quantum dots and realtime formation of impurityreservoir correlations.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.04995
 Bibcode:
 2022arXiv220504995T
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Quantum Gases;
 Quantum Physics