This thesis involves excitonic physics in bilayers of strongly correlated electron materials. The fermionic bilayer extended Hubbard model is studied by means of mean field theory and Determinant Quantum Monte Carlo simulations. A bosonic low-energy effective theory is developed, called the exciton t-J model. The phase diagram and the elementary excitations of this model are investigated. Surprisingly, the excitons are predicted to exhibit Ising confinement physics in the antiferromagnetic phase. In the exciton superfluid phase the magnetic triplon modes borrow kinetic energy from the excitons.
This thesis involves excitonic physics in bilayers of strongly correlated electron materials. The fermionic bilayer extended Hubbard model is studied by means of mean field theory and Determinant Quantum Monte Carlo simulations. A bosonic low-energy effective theory is developed, called the exciton t-J model. The phase diagram and the elementary excitations of this model are investigated. Surprisingly, the excitons are predicted to exhibit Ising confinement physics in the antiferromagnetic phase. In the exciton superfluid phase the magnetic triplon modes borrow kinetic energy from the excitons.
We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems, an exciton is the bound state of a double occupied and empty site. In the strong coupling limit, the exciton acts as a hard-core boson. Its physics is captured by the exciton t-J model, containing an effective XXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean-field theory, we constructed the ground-state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal, and the exciton superfluid. For most model parameters, however, we predict macroscopic phase separation between these phases. The exciton superfluid exists only for large exciton hopping energy. Additionally, we studied the collective modes and susceptibilities of the three phases. In the superfluid phase, we find the striking feature that the bandwidth of the spin-triplet excitations, potentially detectable by resonant inelastic x-ray scattering (RIXS), is proportional to the superfluid density. The superfluid phase mode is visible in the charge susceptibility, measurable by RIXS or electron energy loss spectroscopy (EELS).
We studied the possibility of exciton condensation in a strongly correlated bilayer extended Hubbard model using determinant quantum Monte Carlo. To model both the on-site repulsion U and the interlayer interaction V we introduced an update scheme extending the standard Sherman-Morrison update. We observe that the sign problem increases dramatically with the inclusion of the interlayer interaction V, which prohibits at this stage an unequivocal conclusion regarding the presence of exciton condensation. However, enhancement of the interlayer tunneling results suggest that the strongest exciton condensation tendency lies around 10−−20p/n doping. Magnetic properties and conductivity turn out to be relatively independent of the interlayer interaction.
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.
Three models of strongly correlated electron systems have been studied in this thesis: the Shastry-Sutherland quantum antiferromagnet, the quantum spin liquid emerging out of correlated Dirac fermions on the honeycomb lattice, and the edge-state magnetism in the graphene nanoribbons. The methods applied are quantum Monte Carlo simulations, namely, stochastic series expansion quantum Monte Carlo for bosonic (spin) systems and projector auxiliary field quantum Monte Carlo for fermionic systems. The stochastic series expansion quantum Monte Carlo method is applied to study the ground state properties as well as the magnetization process of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice. The quantum phase transitions between a N\'eel state, a dimer triplet state and a ferromagnetic XY phase have been characterized by finite size scaling analysis. The crystalline structures of the triplon magnetic excitations in the magnetic plateaus have been identified. The projector auxiliary field quantum Monte Carlo is applied to explore the ground state phase diagram of the SU(2) Hubbard model on the honeycomb lattice. The interplay between the relativistic Dirac dispersion, the vanishing density of states at half-filling and the strong quantum fluctuations, drives the system from a semimetal at weak coupling to an antiferromagnetic Mott insulator in the strong coupling regime. In between these phases there emerges an unexpected quantum spin liquid with no symmetry breaking in any channel. After careful finite size scaling analysis of various correlation functions, the quantum spin liquid phase is characterized as a short-range resonating valence bond state with a finite spin gap to all magnetic excitations. The study of edge-state magnetism in graphene nanoribbons is more experimentally motivated. The projector auxiliary field quantum Monte Carlo method is used to measure the static spin-spin correlation function, the single-particle spectral function, as well as the dynamic spin structure factor along the zigzag edge of graphene nanoribbons. A dominant low energy peak generated by the Coulomb interaction in the single-particle spectral function is identified as the dynamical signature of edge-state magnetism. The magnetic excitations along the zigzag edge show a linear dispersion at low energies due to the effective antiferromagnetic coupling of the edges across the ribbon. The magnetic excitations are damped by scattering processes into the particle-hole continuum at high energies.
The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and interlayer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave state. We extract the Berezinskii-Kosterlitz-Thouless transition temperature from superfluid density and a finite-size scaling analysis of the correlation functions and explain our results in terms of an effective biexcitonic hard-core boson model.
Strongly correlated electron systems are one of the most fascinating problems in current physics. The strong electron-electron interaction in these materials leads to the emergence of nontrivial elementary excitations (quasiparticles, QPs) above the ground state ranging from fractional spins in quasi-one-dimensional materials to magnetic monopole in the pyrochlore lattice. The condensation of these quasiparticles upon changing some external parameters may stabilize new exotic states of matter. Experimental measurements such as inelastic neutron scattering provide us with valuable information about the excitation spectrum of such systems which require microscopic models to be described. This thesis is devoted to a detailed analysis of the excitation spectrum and of the quantum phase transitions in the one-dimensional (1D) ionic Hubbard model (IHM). The IHM consists of a nearest-neighbor (n.n.) hopping, onsite Hubbard interaction, and an ionic (staggered) potential separating the odd and even sites energetically. The model exhibits two continuous phase transitions on increasing the Hubbard interaction identified by a low-energy effective field theory and confirmed by a rigorous density matrix renormalization group (DMRG) analysis after several attempts. The first transition occurs from band insulator (BI) phase to the 2-fold degenerate spontaneously dimerized insulator (SDI) phase. The transition is in the Ising universality class as is plausible from symmetry considerations. The SDI phase becomes unstable towards a quasi-long-range order Mott insulator (MI) phase at a second transition point resembling the Kosterlitz-Thouless (KT) transition in the frustrated Heisenberg chain. We employ continuous unitary transformations (CUT) to systematically map the IHM to effective Hamiltonians (almost) conserving the number of QPs in the system. Using an analysis in the BI regime where electrons and holes define QPs, the low-energy excitation spectrum of the model is quantitatively determined in the BI phase almost up to the first transition point. The transition from the BI to the SDI phase is signaled by the vanishing of an S=0 exciton mode at the total momentum K=\pi. The condensation of these excitons beyond the first transition point is described by a BCS-type-theory showing the stabilization of the SDI phase. The mean-field solution indicates no second phase transition to the quasi-long-range order MI phase. This is interpreted as the effect of strong quantum fluctuations in one dimension. We consider the IHM in the dimer limit where the uniform chain is separated into independent dimers. The different phases of the IHM are studied by increasing the interdimer hopping and reaching the uniform limit. This dimer limit satisfactorily produces the excitation spectrum of the BI phase confirming the vanishing of an S=0 exciton mode at the first transition point. It is found that the SDI-to-MI transition takes place by softening of a magnetic S=1 excitation, i.e., a triplon. We report rigorous results for the gapless triplon dispersion in the MI phase and discuss the binding effects in the 2-triplon sector.