While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. By including interactions in the topologically nontrivial Haldane model, we show that a quarter-filled state emerges with a nonzero Chern number provided the interactions are sufficiently large. We first motivate this result on physical grounds and then by two methods: Analytically by solving exactly a model in which interactions are local in momentum space and then numerically through the corresponding Hubbard model. All methods yield the same result: For sufficiently large interaction strengths, the quarter-filled Haldane model is a ferromagnetic topological Mott insulator with a Chern number of unity. Possible experimental realizations in cold-atom and solid-state systems are discussed.
We investigate the effects of electronic correlations on the Bernevig-Hughes-Zhang model using the real-space density matrix renormalization group (DMRG) algorithm. We introduce a method to probe topological phase transitions in systems with strong correlations using DMRG, substantiated by an unsupervised machine learning methodology that analyzes the orbital structure of the real-space edges. Including the full multi-orbital Hubbard interaction term, we construct a phase diagram as a function of a gap parameter (
m) and the Hubbard interaction strength (
U) via exact DMRG simulations on $N\ifmmode\times\else\texttimes\fi{}4$ cylinders. Our analysis confirms that the topological phase persists in the presence of interactions, consistent with previous studies, but it also reveals an intriguing phase transition from a paramagnetic to a stripey antiferromagnetic topological insulator. The combination of the magnetic structure factor, strength of magnetic moments, and the orbitally resolved density, provides real-space information on both topology and magnetism in a strongly correlated system.
We study interaction-induced topological phase transition in Bernevig-Hughes-Zhang model. The topological nature of the phase transition is revealed by directly calculating the Z 2 index of the interacting system from the single-particle Green's function. The interacting Z 2 index is also consistently checked through the edge spectra. Combined with ab initio methods, the present approach is a useful tool for searching for correlated topological insulating materials from the first-principle point of view.
Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number C=2 and the band insulator with C=0 present already in the noninteracting model, the system also exhibits a C=0 Mott insulating phase, and a C=1 quantum Hall phase. We explain the latter phase by a spontaneous symmetry breaking where one of the spin components is in the Hall state and the other in the band insulating state.
We explore the ground-state properties of a one-dimensional model with two orbitals per site, where, in addition to atomic energies $\ifmmode\pm\else\textpm\fi{}M$ and intra- and interorbital hoppings, the intraorbital Hubbard
(U) and nearest-neighbor density-density
(V) repulsions are included. Our results are primarily based on a Jastrow-Slater wave function and variational Monte Carlo methods but also corroborated by density-matrix renormalization group calculations. In the noninteracting limit, when varying
M>0, a gapless point separates a trivial phase from a topological one. The inclusion of a finite Hubbard-
U repulsion does not give rise to any phase transition within the topological region, inducing a smooth crossover into a Haldane (spin gapped) insulator; notably, the string-order parameter, which characterizes the latter phase, is already finite in the noninteracting limit. Most importantly, at finite values of
U, the transition between the trivial and topological states is not direct, since an emergent insulator, which shows evidence of sustaining gapless spin excitations, intrudes between them. A small-
V interaction further stabilizes the intermediate insulator, while a sufficiently large value of this nearest-neighbor repulsion gives rise to two different charge-density wave insulators, one fully gapped and another still supporting gapless spin excitations. Our results demonstrate the richness of multiorbital Hubbard models, in the presence of a topologically nontrivial band structure, and serve as a basis for future investigations on similar two-dimensional models.
A rich variety of phases can exist in quantum systems. For example, the fractional quantum Hall states have persistent topological characteristics that derive from strong interaction. This thesis uses the exact diagonalization method to investigate quantum lattice models with strong interaction. Our research topics revolve around quantum phase transitions between novel phases. The goal is to find the best schemes for realizing these novel phases in experiments. We studied the fractional Chern insulator and its transition to uni-directional stripes of particles. In addition, we studied topological Mott insulators with spontaneous time-reversal symmetry breaking induced by interaction. We also studied emergent kinetics in one-dimensional lattices with spin-orbital coupling. The exact diagonalization method and its implementation for studying these systems can easily be applied to study other strongly correlated systems.