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Quantum Monte Carlo methods and strongly correlated electrons on honeycomb structures

Abstract

In this thesis we apply recently developed, as well as sophisticated quantum Monte Carlo methods to numerically investigate models of strongly correlated electron systems on honeycomb structures. The latter are of particular interest owing to their unique properties when simulating electrons on them, like the relativistic dispersion, strong quantum fluctuations and their resistance against instabilities. This work covers several projects including the advancement of the weak-coupling continuous time quantum Monte Carlo and its application to zero temperature and phonons, quantum phase transitions of valence bond solids in spin-1/2 Heisenberg systems using projector quantum Monte Carlo in the valence bond basis, and the magnetic field induced transition to a canted antiferromagnet of the Hubbard model on the honeycomb lattice. The emphasis lies on two projects investigating the phase diagram of the SU(2) and the SU(N)-symmetric Hubbard model on the hexagonal lattice. At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. Previously elusive in experimentally relevant microscopic two-dimensional models, we show by means of large-scale quantum Monte Carlo simulations of the SU(2) Hubbard model on the honeycomb lattice, that a quantum spin-liquid  More>>
Authors:
Publication Date:
Dec 16, 2010
Product Type:
Thesis/Dissertation
Resource Relation:
Other Information: Diss. (Dr.rer.nat.)
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ANTIFERROMAGNETIC MATERIALS; COMPUTERIZED SIMULATION; CORRECTIONS; ELECTRON CORRELATION; ELECTRONIC STRUCTURE; HEISENBERG MODEL; HEXAGONAL LATTICES; HUBBARD MODEL; MAGNETIC FIELDS; MONTE CARLO METHOD; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; PHONONS; PROJECTION OPERATORS; QUANTUM FLUIDS; QUANTUM MECHANICS; SU-2 GROUPS; TEMPERATURE ZERO K; TWO-DIMENSIONAL CALCULATIONS
OSTI ID:
22535832
Research Organizations:
Wuerzburg Univ. (Germany). Fakultaet fuer Physik und Astronomie
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
TRN: DE16F4401106811
Availability:
Available from: http://www.physik.uni-wuerzburg.de/~assaad/Diss/Diss_TCLang.pdf
Submitting Site:
DE
Size:
193 page(s)
Announcement Date:
Dec 03, 2016

Citation Formats

Lang, Thomas C. Quantum Monte Carlo methods and strongly correlated electrons on honeycomb structures. Germany: N. p., 2010. Web.
Lang, Thomas C. Quantum Monte Carlo methods and strongly correlated electrons on honeycomb structures. Germany.
Lang, Thomas C. 2010. "Quantum Monte Carlo methods and strongly correlated electrons on honeycomb structures." Germany.
@misc{etde_22535832,
title = {Quantum Monte Carlo methods and strongly correlated electrons on honeycomb structures}
author = {Lang, Thomas C.}
abstractNote = {In this thesis we apply recently developed, as well as sophisticated quantum Monte Carlo methods to numerically investigate models of strongly correlated electron systems on honeycomb structures. The latter are of particular interest owing to their unique properties when simulating electrons on them, like the relativistic dispersion, strong quantum fluctuations and their resistance against instabilities. This work covers several projects including the advancement of the weak-coupling continuous time quantum Monte Carlo and its application to zero temperature and phonons, quantum phase transitions of valence bond solids in spin-1/2 Heisenberg systems using projector quantum Monte Carlo in the valence bond basis, and the magnetic field induced transition to a canted antiferromagnet of the Hubbard model on the honeycomb lattice. The emphasis lies on two projects investigating the phase diagram of the SU(2) and the SU(N)-symmetric Hubbard model on the hexagonal lattice. At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. Previously elusive in experimentally relevant microscopic two-dimensional models, we show by means of large-scale quantum Monte Carlo simulations of the SU(2) Hubbard model on the honeycomb lattice, that a quantum spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. Inspired by the rich phase diagrams of SU(N) models we study the SU(N)-symmetric Hubbard Heisenberg quantum antiferromagnet on the honeycomb lattice to investigate the reliability of 1/N corrections to large-N results by means of numerically exact QMC simulations. We study the melting of phases as correlations increase with decreasing N and determine whether the quantum spin liquid found in the SU(2) Hubbard model at intermediate coupling is a specific feature, or also exists in the unconstrained t-J model and higher symmetries.}
place = {Germany}
year = {2010}
month = {Dec}
}