Hügel, Dario Frank (2018): Selfconsistent methods for interacting lattice bosons with U(1)symmetrybreaking. Dissertation, LMU München: Faculty of Physics 

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Abstract
This thesis is dedicated to the derivation and benchmarking of selfconsistent numerical methods that can be applied to interacting bosonic lattice models. The central goal is to derive methods with low numerical complexity but high accuracy, to be applied to complex systems which are outof reach for established methods such as path integral quantum Monte Carlo (QMC) or the density matrix renormalization group. In the first part we derive the selfenergy functional theory (SFT) for bosons. Building upon previous works on lattice systems without U(1)symmetrybreaking, we systematically extend SFT to the possibility of a broken U(1)symmetry and the presence of disorder. SFT incorporates bosonic dynamical meanfield theory as a certain limit, and represents a general nonperturbative framework, enabling the construction of diagrammatically sound approximations in the thermodynamical limit that are controlled in the number of optimization parameters. Using just three variational parameters, we are able to study the BoseHubbard model both in its clean version and in the presence of local disorder, showing excellent agreement with numerically exact QMC results. We systematically analyze the corresponding spectral functions, which cannot be fully captured by QMC. In particular, we find that in the presence of disorder the phase transition from the Bose glass to the superfluid phase at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites, leading to a small condensate fraction over a stronglylocalized background. The second part is dedicated to the derivation of reciprocal cluster meanfield theory (RCMF) and its application to the stronglyinteracting HarperHofstadterMott model (HHMm). In RCMF the full lattice in the thermodynamical limit is projected onto finitesize clusters, which are decoupled in reciprocal space through a meanfield decoupling approximation, crucially preserving the symmetries of the noninteracting dispersion. The resulting groundstate phase diagram of the HHMm exhibits band insulating, striped superfluid, and supersolid phases. Furthermore, we observe gapless uncondensed liquid phases at integer fillings, and a metastable competing fractional quantum Hall (fQH) phase. The fQH phase, predicted as the groundstate by other methods, is most likely underestimated by RCMF. We then show how a quasionedimensional geometry stabilizes gapped topologically nontrivial groundstates in the HHMm. We observe quasionedimensional analogues of fQH phases at fillings 1/2 and 3/2, and unconventional gapped nondegenerate groundstates at integer filling with quantized Hall responses. By systematically comparing results computed with RCMF and exact diagonalization (ED), we are able to give conclusive quantitative answers on the phase boundaries of the system, as the two methods approach the thermodynamical limit from opposite sides, since RCMF favours gapless and ED gapped phases.
Item Type:  Theses (Dissertation, LMU Munich) 

Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  26. February 2018 
1. Referee:  Pollet, Lode 
MD5 Checksum of the PDFfile:  c4265401725ab394897681e2878bdc12 
Signature of the printed copy:  0001/UMC 25360 
ID Code:  21897 
Deposited On:  16. Mar 2018 14:30 
Last Modified:  23. Oct 2020 17:49 