A new class of (2 + 1)-dimensional topological superconductors with $\mathbb {Z}_8$ topological classificationA new class of (2 + 1)-dimensional topological superconductors with $\mathbb {Z}_8$ topological classification

Xiao-Liang Qi

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors, the topological classification is obtained systematically and non-trivial topological insulators are classified by either integer or Z 2 . The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in (2 + 1) dimensions which has time-reversal symmetry and a spin conservation symmetry. We demonstrate that the superconductors in this class are classified by when electron interaction is considered, while the classification is without interaction.The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors, the topological classification is obtained systematically and non-trivial topological insulators are classified by either integer or Z 2 . The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in (2 + 1) dimensions which has time-reversal symmetry and a spin conservation symmetry. We demonstrate that the superconductors in this class are classified by when electron interaction is considered, while the classification is without interaction.

arXiv:1202.3983New Journal of PhysicsJun 3, 2013137 citations

Topological spin liquids

Antônio Sérgio Teixeira Pires

Institute of Physics eBooksApr 1, 20210 citations

Time-reversal invariant U(1) spin liquids in three dimensions

Chong Wang, T. Senthil

Bulletin of the American Physical SocietyMar 3, 20140 citations

Unwinding of a one-dimensional topological superconductor

Achim Rosch

We show that a topological superconductor made of four chains of superconducting spinless fermions characterized by four Majorana edge states can adiabatically be deformed into a trivial band insulator. To unwind this time-reversal invariant topological superconductor, interactions to spinful fermions are switched on along an adiabatic path. Thereby, we couple modes which belong to two different representations of the time-reversal symmetry operator $\mathcal{T}$ with ${\mathcal{T}}^{2}=1$ and ${\mathcal{T}}^{2}=\ensuremath{-}1$, respectively. This observation can be understood by investigating how the relevant symmetries act on the entanglement spectrum giving rise to four instead of eight different topological phases with Majorana edge modes. We also show that a simple level crossing of doubly and singly degenerate states occurs in the entanglement spectrum on deforming the quantum state.We show that a topological superconductor made of four chains of superconducting spinless fermions characterized by four Majorana edge states can adiabatically be deformed into a trivial band insulator. To unwind this time-reversal invariant topological superconductor, interactions to spinful fermions are switched on along an adiabatic path. Thereby, we couple modes which belong to two different representations of the time-reversal symmetry operator $\mathcal{T}$ with ${\mathcal{T}}^{2}=1$ and ${\mathcal{T}}^{2}=\ensuremath{-}1$, respectively. This observation can be understood by investigating how the relevant symmetries act on the entanglement spectrum giving rise to four instead of eight different topological phases with Majorana edge modes. We also show that a simple level crossing of doubly and singly degenerate states occurs in the entanglement spectrum on deforming the quantum state.

arXiv:1203.5541Physical Review BSep 14, 20124 citations

Non-Abelian bosonization of topological insulators and superconductors

Yen-Ta Huang, D. H. Lee

Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic free fermions, we derive the (non-Abelian) bosonized theory for free fermion topological insulators and superconductors that have, in addition to the U(1) charge, time reversal and charge conjugation symmetries and flavor symmetries. For the case we consider, the flavor symmetries render the topological classification $\mathbb{Z}$ . The results are nonlinear $\ensuremath{\sigma}$ models with the topological $\ensuremath{\theta}$ term. In addition, we present the theory of a class of bosonic symmetry-protected topological states, whose boundaries are critical spin liquids.Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic free fermions, we derive the (non-Abelian) bosonized theory for free fermion topological insulators and superconductors that have, in addition to the U(1) charge, time reversal and charge conjugation symmetries and flavor symmetries. For the case we consider, the flavor symmetries render the topological classification $\mathbb{Z}$. The results are nonlinear $\ensuremath{\sigma}$ models with the topological $\ensuremath{\theta}$ term. In addition, we present the theory of a class of bosonic symmetry-protected topological states, whose boundaries are critical spin liquids.

Physical review. B./Physical review. BDec 19, 20220 citations

A new class of (2 + 1)-dimensional topological superconductors with

\mathbb {Z}_8

topological classification

\mathcal{T}

with

{\mathcal{T}}^{2}=1

and ${\mathcal{T}}^{2}=\ensuremath{-}1$, respectively. This observation can be understood by investigating how the relevant symmetries act on the entanglement spectrum giving rise to four instead of eight different topological phases with Majorana edge modes. We also show that a simple level crossing of doubly and singly degenerate states occurs in the entanglement spectrum on deforming the quantum state.

\mathbb{Z}

. The results are nonlinear $\ensuremath{\sigma}$ models with the topological $\ensuremath{\theta}$ term. In addition, we present the theory of a class of bosonic symmetry-protected topological states, whose boundaries are critical spin liquids.