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Electronic spins can form long-range entangled phases of condensed matter named quantum spin liquids. Their existence is conceptualized in models of two- or three-dimensional frustrated magnets that evade symmetry-breaking order down to…
We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units,…
Quantum spin Hall insulators (QSHIs) and excitonic insulators (EIs) are prototypical topological and correlated states of matter, respectively. The topological phase transition between the two has attracted much theoretical interest but…
The integral and fractional quantum Hall effects are among the most important discoveries in condensed matter physics in 1980s. The main results can be summarized in the conductance matrix. When the filling factor is an integer or some…
Fractionally charged elementary excitations, the quasi-electron and quasi-hole, are one of the hallmarks of the fractional Chern insulator (FCI). In this work, we observe that spontaneous spin polarization in twisted MoTe$_2$ leads to…
Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on…
Recent discoveries, as well as open questions, in experimentally realized correlated electron materials are reviewed. In particular, high temperature superconductivity in the cuprates and in the recently discovered iron pnictides, possible…
Motivated by the recently discovered incompressible insulating phase in the bilayer graphene exciton experiment [arXiv:2306.16995], we study using bosonization two Coulomb-coupled spinless quantum wires and examine the possibility of…
Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems like the B-phase of superfluid helium He$_3$, where vortices are associated with low energy excitations in…
We study novel itinerant phases that can be accessed by doping a fractional quantum anomalous Hall (FQAH) insulator, with a focus on the experimentally observed Jain states at lattice filling $\nu = p/(2p+1)$. Unlike in the lowest Landau…
The realization of fractional Chern insulators opens up the possibility of exploring fractionally charged excitations and anyonic statistics in the absence of a magnetic field. One of the central questions is whether lattice-based systems…
To probe the nature of the even-fraction quantum Hall system, we have investigated the low-lying excitation spectrum by means of exact diagonalization for finite systems. We have found (i) a striking one-to-one correspondence (i.e., a shell…
The new Kondo material YbIr$_3$Si$_7$, similar to other Kondo insulators, has been reported to exhibit charge-neutral fermionic excitations through measurements of specific heat and thermal conductivity at low temperatures. We performed…
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged…
Quantum spin liquid (QSL) has become an exciting topic in interacting spin systems that do not order magnetically down to the lowest experimentally accessible temperature; however, conclusive experimental evidence remains lacking. Motivated…
The search of new topological insulators that demonstrate the quantum anomalous Hall effect (QAHE) is a cutting-edge research topic in condensed matter physics and materials science. So far, the QAHE has been observed only in Cr-doped…
Correlated electrons often crystalize to the Mott insulator usually with some magnetic orders, whereas the "quantum spin liquid" has been a long-sought issue. We report numerical evidences that a nonmagnetic insulating (NMI) phase gets…
The interplay between interactions and topology in quantum materials is of extensive current interest. Strong correlations are known to be important for insulating topological states, as exemplified by the fractional quantum Hall effect.…
By explicit microscopic construction involving a mapping to a quantum vertex model subject to the `ice rule,' we show that an electronically `trivial' band insulator with suitable vibrational (phonon) degrees of freedom can host a…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…