Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNatural orbital impurity solver for real-frequency properties at finite temperature
84
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We extend the natural orbital impurity solver [PRB 90, 085102 (2014)] to finite temperatures within the dynamical mean field theory and apply it to calculate transport properties of correlated electrons. First, we benchmark our method against the exact diagonalization result for small clusters, finding that the natural orbital scheme works well not only for zero temperature but for low finite temperatures. The method yields smooth and sufficiently accurate spectra, which agree well with the results of the numerical renormalization group. Using the smooth spectra, we calculate the electric conductivity and Seebeck coefficient for the two-dimensional Hubbard model at low temperatures which are in the scope of many experiments and practical applications. These results demonstrate the usefulness of the natural orbital framework for obtaining the real frequency information within the dynamical mean field theory.
rate research
Read More
We extend a previously proposed rotation and truncation scheme to optimize quantum Anderson impurity calculations with exact diagonalization [PRB 90, 085102 (2014)] to density-matrix renormalization group (DMRG) calculations. The method reduces the solution of a full impurity problem with virtually unlimited bath sites to that of a small subsystem based on a natural impurity orbital basis set. The later is solved by DMRG in combination with a restricted-active-space truncation scheme. The method allows one to compute Greens functions directly on the real frequency or time axis. We critically test the convergence of the truncation scheme using a one-band Hubbard model solved in the dynamical mean-field theory. The projection is exact in the limit of both infinitely large and small Coulomb interactions. For all parameter ranges the accuracy of the projected solution converges exponentially to the exact solution with increasing subsystem size.
Building on previous developments, we show that the Diagrammatic Monte Carlo technique allows to compute finite temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the systems action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon line-width in a homogeneous electron gas (jellium).
Diagrammatic expansions are a central tool for treating correlated electron systems. At thermal equilibrium, they are most naturally defined within the Matsubara formalism. However, extracting any dynamic response function from a Matsubara calculation ultimately requires the ill-defined analytical continuation from the imaginary- to the real-frequency domain. It was recently proposed [Phys. Rev. B 99, 035120 (2019)] that the internal Matsubara summations of any interaction-expansion diagram can be performed analytically by using symbolic algebra algorithms. The result of the summations is then an analytical function of the complex frequency rather than Matsubara frequency. Here we apply this principle and develop a diagrammatic Monte Carlo technique which yields results directly on the real-frequency axis. We present results for the self-energy $Sigma(omega)$ of the doped 32x32 cyclic square-lattice Hubbard model in a non-trivial parameter regime, where signatures of the pseudogap appear close to the antinode. We discuss the behavior of the perturbation series on the real-frequency axis and in particular show that one must be very careful when using the maximum entropy method on truncated perturbation series. Our approach holds great promise for future application in cases when analytical continuation is difficult and moderate-order perturbation theory may be sufficient to converge the result.
We present a very efficient solver for the general Anderson impurity problem. It is based on the perturbation around a solution obtained from exact diagonalization using a small number of bath sites. We formulate a perturbation theory which is valid for both weak and strong coupling and interpolates between these limits. Good agreement with numerically exact quantum Monte-Carlo results is found for a single bath site over a wide range of parameters. In particular, the Kondo resonance in the intermediate coupling regime is well reproduced for a single bath site and the lowest order correction. The method is particularly suited for low temperatures and alleviates analytical continuation of imaginary time data due to the absence of statistical noise compared to quantum Monte-Carlo impurity solvers.
We present a tensor network especially suited for multi-orbital Anderson impurity models and as an impurity solver for multi-orbital dynamical mean-field theory (DMFT). The solver works directly on the real-frequency axis and yields very high spectral resolution at all frequencies. We use a large number $left(mathcal{O}(100)right)$ of bath sites, and therefore achieve an accurate representation of the bath. The solver can treat full rotationally invariant interactions with reasonable numerical effort. We show the efficiency and accuracy of the method by a benchmark for the testbed material SrVO$_3$. There we observe multiplet structures in the high-energy spectrum which are almost impossible to resolve by other multi-orbital methods. The resulting structure of the Hubbard bands can be described as a broadened atomic spectrum with rescaled interaction parameters. Additional features emerge when $U$ is increased. The impurity solver offers a new route to the calculation of precise real-frequency spectral functions of correlated materials.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
