相关论文: Interacting SPT phases are not Morita invariant
We investigate the stability of weak symmetry-protected topological phases (SPTs) in the presence of short-range interactions, focusing on the tenfold way classification. Using Atiyah's Real $\mathit{KR}$-theory and Anderson-dualized…
We provide a mathematically rigorous classification of symmetry-protected topological (SPT) phases of neutral free fermions. Our approach utilizes Karoubi triples with negative squares, thought of as polarizations. We prove that neutral…
The tenfold way is a classification scheme for the building blocks of free fermion systems. More precisely, it classifies the isomorphism classes of spaces of equivariant free Hamiltonians in irreducible fermion systems with symmetries.…
Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory.…
The tenfold way became important in physics around 2010: it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when C. T. C. Wall classified real super division algebras. These are…
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…
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this paper, we develop a characterization and classification of…
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)…
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…
After briefly recalling the quantum entanglement-based view of topological phases of matter in order to outline the general context, we give an overview of different approaches to the classification problem of topological insulators and…
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…
The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless…
It is demonstrated that fermionic/bosonic symmetry-protected topological (SPT) phases across different dimensions and symmetry classes can be organized using geometric constructions that increase dimensions and symmetry-forgetting maps that…
The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels.…
Symmetry-protected topological $\left(SPT\right)$ phases are gapped short-range entangled states with symmetry $G$, which can be systematically described by group cohomology theory. $SU(3)$ and $SU(2)\times{U(1)}$ are considered as the…
It has been proposed recently that interacting Symmetry Protected Topological (SPT) phases can be classified using cobordism theory. We test this proposal in the case of fermionic SPT phases with Z/2 symmetry, where Z/2 is either…
Correlations in topological states of matter provide a rich phenomenology, including a reduction in the topological classification of the interacting system compared to its non-interacting counterpart. This happens when two phases that are…
For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by…
Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the symmetry. It has been shown that a large…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…