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Bulletin of the American Physical Society

Improving the efficiency of the Finite Temperature Density Matrix Renormalization Group method

Alberto Nocera, Gonzalo Álvarez

Published Mar 17, 2016• 0 citations
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The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces and using canonical approaches. We furthermore explore its applicability beyond spins systems to $t\text{\ensuremath{-}}J$ and Hubbard models.
We implement and apply time-dependent density matrix renormalization group (TD-DMRG) algorithms at zero and finite temperature to compute the linear absorption and fluorescence spectra of molecular aggregates. Our implementation is within a matrix product state/operator framework with an explicit treatment of the excitonic and vibrational degrees of freedom, and it uses the locality of the Hamiltonian in the zero-exciton space to improve the efficiency and accuracy of the calculations. We demonstrate the power of the method by calculations on several molecular aggregate models, comparing our results against those from multilayer multiconfiguration time-dependent Hartree and n-particle approximations. We find that TD-DMRG provides an accurate and efficient route to calculate the spectrum of molecular aggregates.
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 linear scaling of complexity for nnn-channel problems.