Density matrix renormalization group study of a quantum impurity model with Landau-Zener time-dependent Hamiltonian

TL;DR

This paper employs the adaptive time-dependent density matrix renormalization group method to analyze the nonequilibrium dynamics of a quantum impurity system with a time-dependent Hamiltonian, providing insights into Landau-Zener transitions.

Contribution

It introduces a t-DMRG approach to study a Landau-Zener driven quantum impurity model, mapping it onto a Wilson chain for accurate time-dependent analysis.

Findings

t-DMRG results agree well with exact solutions at zero temperature

The method provides a physical interpretation of the impurity dynamics

The approach effectively captures nonequilibrium behavior in quantum impurity systems

Abstract

We use the adaptive time-dependent density matrix renormalization group method (t-DMRG) to study the nonequilibrium dynamics of a benchmark quantum impurity system which has a time-dependent Hamiltonian. This model is a resonant-level model, obtained by a mapping from a certain Ohmic spin-boson model describing the dissipative Landau-Zener transition. We map the resonant-level model onto a Wilson chain, then calculate the time-dependent occupation $n_d(t)$ of the resonant level. We compare t-DMRG results with exact results at zero temperature and find very good agreement. We also give a physical interpretation of the numerical results.