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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 discuss different properties and the ability of several topological invariants based on position operators to identify phase transitions, and compare with more accurate methods, like crossing of excited energy levels and jumps in Berry…
Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. The detection of edge states remains an open question in ultracold atom setups. We propose a configuration to…
The vast majority of symmetry-protected topological (SPT) states are difficult to detect, which often leads to their misidentification as ordinary or topologically trivial phases. In this work, we propose a general framework for detecting…
Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that…
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2…
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e. with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs…
Topological properties of antiferromagnetic phases are studied for a correlated topological band insulator by applying the dynamical mean field theory to an extended Bernevig-Hughes-Zhang model including the Hubbard interaction. The…
We study the topological properties of the one-dimensional generalized quasiperiodic modulated Su-Schrieffer-Heeger model. The results reveal that topological re-entrant phase transition emerges. Through the analysis of a real-space winding…
The interacting SSH model provides an ideal ground to study the interplay between topologically insulating phases and electron-electron interactions. We study the polarization density as a topological invariant and provide an analytic…
Characterizing topological phases for strongly interacting fermions in the mixed-state regime remains a major challenge. Here we introduce a general and numerically efficient framework to diagnose mixed-state topological phases in strongly…
We study one-dimensional, interacting, gapped fermionic systems described by variants of the Peierls-Hubbard model and characterize their phases via a topological invariant constructed out of their Green's functions. We demonstrate that the…
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is…
Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however…
Topological band insulators which are dynamically generated by electron-electron interactions have been the- oretically proposed in two and three dimensional lattice models. We present evidence that the two-dimensional version can be…
Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the…
In this report we have analyzed a simple effective model for a description of magnetically ordered insulators. The Hamiltonian considered consists of the effective on-site interaction (U) and the intersite Ising-like magnetic exchange…
Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions.…
We construct an observable mixed state topological order parameter for symmetry-protected free fermion matter. It resolves the entire table of topological insulators and superconductors, relying exclusively on the symmetry class, but not on…
Constant energy contour (CEC) of the surface bands in topological insulators varies not only with materials but also at different energies. The quasiparticle interference caused by scattering-off from defects on the surface of topological…