Project Details
Projekt
Coherent propagation and decay of excitations
Subject Area
Theoretical Condensed Matter Physics
Term
since 2021
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 449872909
We will develop real-frequency, real-time quantum impurity solvers with capabilities well beyond the current state of the art, and apply them to predict the dynamics and response functions including finite temperature transport of several key materials and models studied within Quast. Quantum impurity solvers are key ingredients of dynamical mean-field theory (DMFT) and its extensions, used in several Quast projects. DMFT treats the interplay between a given lattice site or cluster of sites (the ``impurity'') and the rest of the lattice (the ``bath'') as a quantum impurity model with a self-consistently determined bath. Many popular quantum impurity solvers employ imaginary times or frequencies. However, obtaining real-time or -frequency response functions, as observed in experiment, then requires analytic continuation of numerical data. This is a mathematically ill-posed problem, so that achieving very high real-frequency resolution is challenging. In project P7, we therefore focus on impurity solvers employing real frequencies or real times from the outset. We will employ three types of solvers: (1) The Quanty package developed by Maurits W. Haverkort, which can handle open d or f valence shells with arbitrary interactions hybridizing with a few hundred non-interacting bath sites. (2) The MuNRG package developed by current and former members (including Fabian Kugler) of Jan von Delft's group in Munich, based on the numerical renormalization group (NRG), which achieves unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures, but is currently limited to models with at most 4 (spinful) bands. (3) A new tangent-space Krylov solver, tanKS, developed in Jan von Delft's group, which achieves high resolution at both low and high energies and holds promise for handling models with more than 4 (spinful) bands. Our long-term goal, reaching beyond the next funding period, is to extend the capabilities of these impurity solvers such that they can calculate n-particle correlation functions in the time and frequency domain for open d or f shell elements with arbitrary material-realistic interactions, a Rydberg bandwidth, and 0.1 meV (1K) resolution. This will enable us to solve numerous important problems. Within the next funding period, we will take significant steps towards achieving this ambitious goal. We will develop methodological improvements of our three methods, benchmark them against each other, and, where possible, combine their strengths to boost performance. Within Quast, these methods will be applied, for example, to Ce Heavy fermion problems with flat bands, magnetic interactions, and possible Kondo ground states (P1), electronic transport in moiré systems (P5), and electron dynamics studied with pump-probe spectroscopy (P6).
DFG Programme
Research Units
