Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions

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 {\em et al.,} Phys. Rev. B {\bf 89}, 075118 (2014); Phys. Rev. B {\bf 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 {\em et al.}, Phys. Rev. Lett. {\bf 95}, 196801 (2005); Nghiem {\em et al.}, Phys. Rev. Lett. {\bf 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. {\bf 101}, 066804 (2008)].Comment: 15 pages and 10 figures; Additional figures and references added; typos fixed; references fixe

The nature of NGO microfinance in Vietnam and stakeholders� perceptions of effectiveness

The microfinance industry in Vietnam, particularly those sponsored by non-government organisations (NGOs), has experienced rapid expansion in recent years. While there have been anecdotal reports alluding to their contribution in alleviating poverty, a systematic analysis of this issue has been lacking. In a bid to help address this shortcoming, this paper reports on data that was obtained during a survey and interview process that incorporated various stakeholders including financial donors, NGO-sponsored microfinance institutions (NMPs), village leaders and NMP members and non-members. Firstly, the nature of NMPs is described - their objectives, target groups and the financial products they offer. Secondly, perceptions of NMPs effectiveness are discussed from the standpoint of various stakeholders. NMPs are found to be at a critical juncture. While their activities are widely perceived to contribute to poverty alleviation, their future viability is clouded by donor requirements that they become financially self-sufficient. At the same time, certain government policies make achieving this goal very difficult.