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Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
We consider a class of {\em quantum Hall topological insulators}: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counter-propagating edge states are protected by a symmetry (spatial or spin)…
The quadrupole insulator, a high-order topological insulator, with on-site Hubbard interaction is numerically studied by large-scale projector quantum Monte Carlo (PQMC) simulations. The Green's function formalism is successfully used to…
Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on…
We consider a system of two-dimensional electrons strongly localized by disorder. Interactions create a gap in the average tunneling density of states $\nu(E)$ at energies, E, close to the Fermi level. We derive a system of self-consistent…
In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, Z_1, Z_2, or Z. For example non-interacting 1D fermionic superconducting phases with…
The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful…
Topological crystalline insulators are phases of matter where the crystalline symmetries solely protect the topology. In this work, we explore the effect of many-body interactions in a subclass of topological crystalline insulators, namely…
Symmetry Protected Topological (SPT) phases are a minimal generalization of the concept of topological insulators to interacting systems. In this paper we describe the classification and properties of such phases for three dimensional(3D)…
We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multi-valley Dirac fermion surface states. We find that…
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
Certain band insulators allow for the adiabatic pumping of quantized charge or spin for special time-dependences of the Hamiltonian. These "topological pumps" are closely related to two dimensional topological insulating phases of matter…
The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of topological band…
Multi-orbital electronic models hosting a non-trivial band-topology in the regime of strong electronic interactions are an ideal playground for exploring a host of complex phenomenology. We consider here a sign-problem-free and…
We investigate the ground-state phase diagram of the spinless Haldane-Hubbard model in the presence of quenched disorder, contrasting results obtained from both exact diagonalization as well as density matrix renormalization group, applied…
Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
The interplay between electronic correlations and band topology is a central theme in modern condensed matter physics. In this work, we investigate the effects of on-site Hubbard interactions on the topological, magnetic, and quantum…
Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…
Exploring new topological phenomena and functionalities induced by strong electron correlation has been a central issue in modern condensed-matter physics. One example is a topological insulator (TI) state and its functionality driven by…