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Variational matrix product state approach to quantum impurity models

A. Weichselbaum·F. Verstraete·U. Schollwöck·J. I. Cirac·Jan von Delft
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Abstract

We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows improvements over Wilson's NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially \emph{linear} scaling of complexity for $n$-channel problems.

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A. Weichselbaum, F. Verstraete, U. Schollwöck, J. I. Cirac, Jan von Delft. 2008-05-14. Variational matrix product state approach to quantum impurity models. https://doi.org/10.1103/physrevb.80.165117

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