Related papers: Topological order in higher composites
Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of…
We report the discovery of several classes of novel topological insulators (TIs) with hybrid-order boundary states generated from the first-order TIs with additional crystalline symmetries. Unlike the current studies on hybrid-order TIs…
The bottom-up design of strongly interacting quantum materials with prescribed ground state properties is a highly nontrivial task, especially if only simple constituents with realistic two-body interactions are available on the microscopic…
While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…
We show that binary mixtures of Bose-condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a…
The order from quantum disorder (OFQD) phenomenon was first discovered in quantum spin systems in geometric frustrated lattice. Similar phenomenon was also discovered in interacting bosonic systems or quantum spin systems with spin-orbit…
In this short note, I review some recent results about gapped ground state phases of quantum spin systems and discuss the notion of topological order.
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
Photonic modes exhibiting a polarization winding akin to a vortex possess an integer topological charge. Lasing with topological charge 1 or 2 can be realized in periodic lattices of up to six-fold rotational symmetry. Higher order charges…
Exploring novel topological matters with exotic quantum states has always been a core issue in the field of condensed matter physics, which can update the understanding of topological phases and broaden the classification of topological…
We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…
In condensed matter systems, the atoms, electrons or spins can sometimes arrange themselves in ways that result in unexpected properties but that cannot be detected by conventional experimental probes. Several historical and contemporary…
We study the bulk-boundary correspondence for topological crystalline phases, where the crystalline symmetry is an order-two (anti)symmetry, unitary or antiunitary. We obtain a formulation of the bulk-boundary correspondence in terms of a…
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…
Topological quantum materials hold great promise for future technological applications. Their unique electronic properties, such as protected surface states and exotic quasiparticles, offer opportunities for designing novel electronic…
We propose to combine Bose-Einstein condensation in higher Bloch bands and a driven-dissipative cavity-BEC system into a hybrid light-matter platform. Specifically, the condensate is trapped in a bipartite $s$-$p_x$-$p_y$-lattice, with a…
Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework, which has…
We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory 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…