SciPost Thesis Link
Title:  w2dynamics: continuous time quantum Monte Carlo calculations of one and twoparticle propagators  
Author:  Markus Wallerberger  
As Contributor:  Markus Wallerberger  
Type:  Ph.D.  
Field:  Physics  
Specialties: 


Approaches:  Theoretical, Computational  
URL:  http://repositum.tuwien.ac.at/urn:nbn:at:atubtuw:13537  
Degree granting institution:  TU Wien  Vienna University of Technology  
Supervisor(s):  Karsten Held  
Defense date:  20160601 
Abstract:
The singleimpurity Anderson model (SIAM), comprised of a single impurity with a local Hubbard interaction immersed in a bath of noninteracting electrons, is a fundamental model of electronic correlation. It has been used to study the Kondo effect and transport through quantum junctions. The SIAM in its multiorbital generalisation also lies at the computational core of dynamical mean field theory (DMFT) and its combination with density functional theory (DFT). DMFT improves on the rough treatment of correlations in DFT by including all local correlations in a nonperturbative manner, corresponding to the assumption of a local selfenergy, and was successfully used to study systems with partially filled 3d and 4f shells (Georges et al., 1996). While for the study of the SIAM and also in DMFT one typically focuses on the oneparticle impurity propagators, recently the local twoparticle irreducible vertex Gamma has come into focus. From a physical point of view, Gamma enters as vertex corrections into the charge and magnetic susceptibilities. Moreover, it was recently discovered that a set of divergencies of Gamma surround the Mott transition, marking a bifurcation of the selfenergy that proves problematic for methods relying on an expansion in Gamma (SchÃ¤fer et al., 2013). Finally, the impurity vertex is the central ingredient for postDMFT methods like the dynamical vertex approximation (DGA). DGA augments DMFT with a diagrammatic treatment of nonlocal correlations on all length scales, which in turn are dominant for lowdimensional systems or systems close to a secondorder phase transition (Toschi et al., 2007). A stateoftheart method for solving the SIAM at finite temperatures is continuous time quantum Monte Carlo in the hybridisation expansion (CTHYB). CTHYB expands the partition function Z with respect to the hybridisation with the bath and stochastically sums up the resulting series of strongcoupling Feynman diagrams. CTHYB can treat continuous baths, multiple orbitals, different types of local interaction and is free of systematic bias and thus numerically exact (Gull et al., 2011). The manybody propagators are usually obtained as a 'byproduct' of partition function sampling, as this allows for an easy implementation. The multiorbital vertex however is a large object, which is challenge for CTHYB from a computational and memory point of view. I will show how by using decompositions and nonequidistant fast Fourier transforms, one can overcome the problem. I will also analyse the symmetries, conserved quantities and asymptotics of the vertex. Furthermore, I will show that the estimator for Gamma has severe ergodicity problems for strong insulators and fails to yield spinflip and pairhopping terms of the vertex in highsymmetry cases. Worm sampling avoids above complications by directly sampling the manybody propagators. I will show that its use in CTHYB significantly improves the quality and statistical uncertainties of the propagators. I will also demonstrate how by using worm sampling for the impurity vertex, one can calculate frequency boxes of arbitrary sizes. I will then focus on the application of DMFT to models and real systems. I will study the oxide heterostructure formed by a thin layer of SrVO3 grown on a SrTiO3 substrate. I will show that local correlation is responsible for pushing the system close to a metalinsulator transition by enhancing the crystal field splitting. Thus, a small perturbation of a system by an electric field or a compressive strain may be used to form a 'Mott transistor'. I will show that this effect is stable with respect to choosing a donly or dp basis. CTHYB also allows us to study the divergency lines of Gamma at lower temperatures than other methods. I will show that at low temperatures, the divergencies start to bend away from the Mott transition and towards the noninteracting limit.