%0 Journal Article
%A Nghiem, H. T. M.
%A Costi, Theodoulos
%T Time-dependent numerical renormalization group method for multiple quenches: Towards exact results for the long-time limit of thermodynamic observables and spectral functions
%J Physical review / B
%V 98
%N 15
%@ 2469-9950
%C Woodbury, NY
%I Inst.
%M FZJ-2018-05700
%P 155107
%D 2018
%X We develop an alternative time-dependent numerical renormalization group (TDNRG) formalism for multiple quenches and implement it to study the response of a quantum impurity system to a general pulse. Within this approach, we reduce the contribution of the NRG approximation to numerical errors in the time evolution of observables by a formulation that avoids the use of the generalized overlap matrix elements in our previous multiple-quench TDNRG formalism [Nghiem et al., Phys. Rev. B 89, 075118 (2014); Phys. Rev. B 90, 035129 (2014)]. We demonstrate that the formalism yields a smaller cumulative error in the trace of the projected density matrix as a function of time and a smaller discontinuity of local observables between quenches than in our previous approach. Moreover, by increasing the switch-on time, the time between the first and last quench of the discretized pulse, the long-time limit of observables systematically converges to its expected value in the final state, i.e., the more adiabatic the switching, the more accurately is the long-time limit recovered. The present formalism can be straightforwardly extended to infinite switch-on times. We show that this yields highly accurate results for the long-time limit of both thermodynamic observables and spectral functions, and overcomes the significant errors within the single quench formalism [Anders et al., Phys. Rev. Lett. 95, 196801 (2005); Nghiem et al., Phys. Rev. Lett. 119, 156601 (2017)]. This improvement provides a first step towards an accurate description of nonequilibrium steady states of quantum impurity systems, e.g., within the scattering states NRG approach [Anders, Phys. Rev. Lett. 101, 066804 (2008)].
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000446296600003
%R 10.1103/PhysRevB.98.155107
%U https://juser.fz-juelich.de/record/852913