Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1509.03920

Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry

AtMa P. O. Chan·Jeffrey C. Y. Teo·Shinsei Ryu
View original source ↗Read source document ↗Export metadata ↓

Abstract

We discuss (2+1)D topological phases on non-orientable spatial surfaces, such as Möbius strip, real projective plane and Klein bottle, etc., which are obtained by twisting the parent topological phases by their underlying pairty symmetries through introducing parity defects. We construct the ground states on arbitrary non-orientable closed manifolds and calculate the ground state degeneracy. Such degeneracy is shown to be robust against continuous deformation of the underlying manifold. We also study the action of the mapping class group on the multiplet of ground states on the Klein bottle. The physical properties of the topological states on non-orientable surfaces are deeply related to the parity symmetric anyons which do not have a notion of orientation in their statistics. The number of ground states on the projective plane equals the root of the number of distinguishable parity symmetric anyons, while the ground state degeneracy on the Klein bottle equals the total number of parity symmetric anyons; In deforming the Klein bottle, the Dehn twist encodes the topological spins whereas the Y-homeomorphism tells the particle-hole relation of the parity symmetric anyons.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

AtMa P. O. Chan, Jeffrey C. Y. Teo, Shinsei Ryu. 2016-03-10. Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry. https://doi.org/10.1088/1367-2630%2F18%2F3%2F035005

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Competing Interlayer Loop Currents and Superconductivity in the Bilayer $t$-$J_\perp$-$V$ Model

The recent discovery of high-$T_c$ superconductivity in pressurized and thin-film bilayer nickelates, featuring a strong interlayer exchange coupling, and their potential similarities with cuprate superconductors, has made this a very active topic in condensed matter physics. In the present paper we study the strongly correlated one-orbital ($d_{x^2-y^2}$) bilayer $t$-$J_\perp$-$V$ model for nickelates, where $V$ denotes the Coulomb interactions, using a controlled large-$N$ expansion at and beyond the mean-field level. Focusing on the out-of-plane spin exchange interaction ($J_\perp$), we find that it triggers both out-of-plane $s$-wave superconductivity and an out-of-plane bond-order phase ($z$-BOP) instability. The $z$-BOP gives rise to a complex $z$-axis hopping dominated by its imaginary component, which drives out-of-plane currents and induces in-plane ones, spontaneously forming on the vertical plaquettes a loop-current state that breaks time-reversal symmetry. Competition between this loop-current phase and superconductivity yields a dome-shaped superconducting region, with optimal superconductivity occurring near the $z$-BOP quantum critical point. The resulting phase diagram features a pure loop-current region, a low-doping coexistence phase, a pure superconducting state at higher doping, and a correlated metallic state.

cond-mat.str-el↗
arXiv2026

Optically induced metallic state with persistent monoclinic symmetry in NdNiO$_3$

Understanding whether electronic and structural order remain coupled under nonequilibrium conditions is a central challenge in correlated materials. Here, we simultaneously track metallicity and symmetry across the photoinduced insulator-to-metal transition in NdNiO$_3$ using time-resolved optical reflectivity and symmetry-sensitive second-harmonic generation. We find that metallic reflectivity emerges at significantly lower excitation fluence than restoration of the orthorhombic high-temperature symmetry. As a result, optical excitation stabilizes a metastable state that combines the reflectivity of the metallic phase with the monoclinic symmetry of the insulating phase, revealing an optically induced monoclinic metal. Only at substantially higher fluences does the symmetry fully recover to that of the high-temperature phase. These results demonstrate a nonequilibrium decoupling of metallicity and structural symmetry and establish simultaneous multiprobe spectroscopy as a powerful approach for identifying emergent phases in correlated materials.

cond-mat.str-el↗
arXiv2026

Instabilities in self-consistent diagrammatic approaches and how to cure them

While self-consistent diagrammatic approaches are widely used to compute the physical properties of correlated quantum materials, their applicability may get severely hindered precisely in the parameter regions, where the most exciting physics is observed. One of the major issues, referred to as "misleading convergence", is the tendency of iterative schemes to converge to unphysical fixed points for intermediate-to-strong electronic interactions, regardless of numerical accuracy of the computation. Here, we explicitly verify that the origin of this problem in several established self-consistent many-electron approaches, defined in the general diagrammatic framework of the boson-exchange formalism, resides exclusively in the stability condition of the respective iteration schemes, and not in an intrinsic breakdown of their self-consistent diagrammatic description. This insight enables a simple and general remedy, as recently proposed in Phys. Rev. Lett. 137, 016502 (2026): The redefinition of the iterative procedure, by inverting the unstable eigendirections of the Jacobian associated to the fixed point of the self-consistent algorithm. We illustrate the successful outcome of this procedure by means of systematic calculations performed on testbed, exactly solvable, models. Our results demonstrate that the physical fixed point of the diagrammatic schemes we considered can be stabilized, de facto, across the entire parameter range, including the most challenging nonperturbative/strong-coupling regimes.

cond-mat.str-el↗