Holzner, Andreas Michael (2012): DMRG studies of Chebyshevexpanded spectral functions and quantum impurity models. Dissertation, LMU München: Faculty of Physics 

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Abstract
This thesis is concerned with two main topics: first, the advancement of the density matrix renormalization group (DMRG) and, second, its applications. In the first project of this thesis we exploit the common mathematical structure of the numerical renormalization group and the DMRG, namely, matrix product states (MPS), to implement an efficient numerical treatment of a twolead, multilevel Anderson impurity model. By adopting a starlike geometry, where each species (spin and lead) of conduction electrons is described by its own socalled Wilson chain, instead of a single Wilson chain we achieve a very significant reduction in the numerical resources required to obtain reliable results. Moreover, we show that it is possible to find an "optimal" chain basis, in which chain degrees of freedom of different Wilson chains become effectively decoupled from each other further out on the Wilson chains. This basis turns out to also diagonalize the model's chaintochain scattering matrix. In the second project we show that Chebychev expansions offer numerically efficient representations for calculating spectral functions of onedimensional lattice models using MPS methods. The main features of this Chebychev matrix product state (CheMPS) approach are: (i) it achieves uniform resolution over the spectral function's entire spectral width; (ii) it offers a wellcontrolled broadening scheme; (iii) it is based on using MPS tools to recursively calculate a succession of Chebychev vectors, (iv) whose entanglement entropies were found to remain bounded with increasing recursion order for all cases analyzed here. We present CheMPS results for the structure factor of spin1/2 antiferromagnetic Heisenberg chains and perform a detailed finitesize analysis. Making comparisons to benchmark methods, we find that CheMPS yields results comparable in quality to those of correction vector DMRG, at dramatically reduced numerical cost and agrees well with Bethe Ansatz results for an infinite system, within the limitations expected for numerics on finite systems. Following these technologically focused projects we study the socalled Kondo cloud by means of the DMRG in the third project. The Kondo cloud describes the effect of spatially extended spinspin correlations of a magnetic moment and the conduction electrons which screen the magnetic moment through the Kondo effect at low temperatures. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spinspin correlations. We investigate how perturbations which destroy the Kondo effect, like an applied gate potential or a magnetic field, affect the formation of the screening cloud. In a forth project we address the impact of Quantum (anti)Zeno physics resulting from repeated singlesite resolved observations on the manybody dynamics. We use timedependent DMRG to obtain the time evolution of the full manybody wave function that is then periodically projected in order to simulate realizations of stroboscopic measurements. For the example of a 1D lattice of spinpolarized fermions with nearestneighbor interactions, we find regimes for which manyparticle configurations are stabilized and destabilized depending on the interaction strength and the time between observations.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  DMRG, Numerik, Chebyshev, quantum physics, Kondo 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  27. January 2012 
1. Referee:  Delft, Jan von 
Persistent Identifier (URN):  urn:nbn:de:bvb:19139333 
MD5 Checksum of the PDFfile:  ae3e72060fa119e0f3436b4fa124c82e 
Signature of the printed copy:  0001/UMC 20034 
ID Code:  13933 
Deposited On:  03. Feb 2012 08:00 
Last Modified:  16. Oct 2012 08:58 