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arXiv:1205.1708

New implementation of hybridization expansion quantum impurity solver based on Newton-Leja interpolation polynomial

Huang, Li, Xi Dai

Published May 8, 2012• 0 citations
arXivHTMLPDF

Abstract

We introduce a new implementation of hybridization expansion continuous time quantum impurity solver which is relevant to dynamical mean-field theory. It employs Newton interpolation at a sequence of real Leja points to compute the time evolution of the local Hamiltonian efficiently. Since the new algorithm avoids not only computationally expansive matrix-matrix multiplications in conventional implementations but also huge memory consumptions required by Lanczos/Arnoldi iterations in recently developed Krylov subspace approach, it becomes advantageous over the previous algorithms for quantum impurity models with five or more bands. In order to illustrate the great superiority and usefulness of our algorithm, we present realistic dynamical mean-field results for the electronic structures of representative correlated metal SrVO$_{3}$.

DOI
10.48550/arxiv.1205.1708

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We introduce a new implementation of hybridization expansion continuous time quantum impurity solver which is relevant to dynamical mean-field theory. It employs Newton interpolation at a sequence of real Leja points to compute the time evolution of the local Hamiltonian efficiently. Since the new algorithm avoids not only computationally expansive matrix-matrix multiplications in conventional implementations but also huge memory consumptions required by Lanczos/Arnoldi iterations in recently developed Krylov subspace approach, it becomes advantageous over the previous algorithms for quantum impurity models with five or more bands. In order to illustrate the great superiority and usefulness of our algorithm, we present realistic dynamical mean-field results for the electronic structures of representative correlated metal SrVO3_{3}3​.
We present an implementation of the hybridization expansion impurity solver which employs sparse-matrix exact-diagonalization techniques to compute the time evolution of the local Hamiltonian. This method avoids computationally expensive matrix-matrix multiplications and becomes advantageous over the conventional implementation for models with five or more orbitals. In particular, this method will allow the systematic investigation of 7-orbital systems (lanthanide and actinide compounds) within single-site dynamical mean-field theory. We illustrate the power and usefulness of our approach with dynamical mean-field results for a 5-orbital model which captures some aspects of the physics of the iron-based superconductors.
We develop a fast impurity solver which is based on the combination of Hubbard-I approximation and hybridization expansion continuous-time quantum Monte Carlo algorithm. This solver inherits the advantages of both algorithms. In order to demonstrate the power and usefulness of this solver, we use it to study the magnetic phase transitions of single-band and two-band Hubbard models in the framework of single-site dynamical mean-field theory. The calculated results agree well with those obtained by hybridization expansion quantum impurity solver. It is suggested that this solver is very suitable to solve the multi-orbital quantum impurity models efficiently and can be used to study more realistic systems with magnetic long-range order in the future.
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We present a new continuous-time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons with Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.
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Impurity solvers play an essential role in the numerical investigation of strongly correlated electrons systems within the ``dynamical mean field'' approximation. Recently, a new class of continuous-time solvers has been developed based on a diagrammatic expansion of the partition function in either the interactions or the impurity-bath hybridization. We investigate the performance of these two complementary approaches and compare them to the well-established Hirsch-Fye method. The results show that the continuous-time methods, and, in particular, the version which expands in the hybridization, provide substantial gains in computational efficiency.