Related papers: Topological Phases for Extended Objects: Semiclass…

When two non-identical quasi-particles in the Hall fluid encircle each other, relative AB type phase developes.As the quasi-particles advance towards the edge in a similar circular way, the developed current should have connection with this…

The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector…

Strong coupling between matter and quantized electromagnetic fields in a cavity has emerged as a possible route toward controlling the phase of matter in the absence of an external drive. We develop a faithful and efficient theoretical…

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases…

We introduce the concept of Berry's phase in Josephson junctions and consider how this geometric phase arises due to applied oscillating electric fields. The electromagnetic field excites topological quasi-particles from the junction vacuum…

Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…

We investigate the build-up of quasi-long-range order in the XX chain with transverse magnetic field at finite size. As the field is varied, the ground state of the system displays multiple level crossings producing a sequence of…

For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…

Spurred by recent development of fracton topological phases, unusual topological phases possessing fractionalized quasi-particles with mobility constraints, the concept of symmetries has been renewed. In particular, in accordance with the…

We introduce topological skyrmion semimetal phases of matter, characterized by bulk electronic structures with topological defects in ground state observable textures over the Brillouin zone (BZ), rather than topological degeneracies in…

Identifying and understanding interacting systems that can host non-Abelian topological phases with fractionalized quasiparticles have attracted intense attentions in the past twenty years. Theoretically, it is possible to realize a rich…

While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…

Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…

We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read--Rezayi state whose effective theory is the SU(2)_K Chern--Simons theory. As a generalization of…

Topology describes properties of physical systems that remain constant under continuous deformations. For infinite vector waves, global topological invariants in position space are typically associated with periodic patterns. We demonstrate…

We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the…

We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground…

We consider a topologically non-trivial flat band structure in one spatial dimension in the presence of nearest and next nearest neighbor Hubbard interaction. The non-interacting band structure is characterized by a symmetry protected…

We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can…

Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi-Hubbard model. We show how the topological…