Quantum Monte Carlo study of the phase diagram of strongly correlated two-dimensional electron systems

Kenneth L. Graham

Thomas C. Lang

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.

Elke Berger, P. Valášek, Wolfgang von der Linden

The interplay of electron-phonon coupling and strong electronic correlations is studied in the frame of the two-dimensional Hubbard-Holstein model. Static and dynamic properties are determined by quantum Monte Carlo simulations and by Migdal-Eliashberg theory. The comparison allows us to assess the diagrammatic approach. The competition between the phonon-mediated electron-electron attraction and the local Coulomb repulsion leads to a rich phase diagram, which we study in detail for a wide range of parameters. We address the question, to which extent the systems can be described by an effective negative-U Hubbard model.

Zhongbing Huang

Kristel F. L. Michielsen

An overview of lattice models for strongly correlated electrons is given. A detailed study is presented of a model recently introduced by Montorsi and Rasetti. Analytical, exact diagonalization and Quantum Monte Carlo techniques are employed to investigate the static and dynamic properties of this model. The complete ground state phase diagram of the one-, two- and three-dimensional model is given. The Montorsi-Rasetti model is shown to exhibit a metal-insulator transition of the Mott type, independent of the dimensionality of the lattice, and has a ferromagnetic phase. Results for the two-dimensional Montorsi-Rasetti model strongly suggest the occurrence of a phase transition at finite temperatures.

Thomas C. Lang, Martin Bercx, David J. Luitz +3 more