Related papers: A relation between chiral central charge and groun…
Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not…
We introduce the concept of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary degeneracy provides richer information than the bulk degeneracy.…
The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I…
Chiral edge states of 2+1 dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and non-integer values of central charge, respectively. In this work we describe certain…
We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace,…
Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with…
We propose that, up to invertible topological orders, 2+1D fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry $G$ are classified by non-degenerate unitary braided fusion categories…
This thesis aims at concluding the classification results for topological phases with symmetry in 2+1 dimensions. The main result is that topological phases are classified by a triple of unitary braided fusion categories $\mathcal…
We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups $G_f$ and general values of the chiral central charge $c_-$. Here $G_f$ is a…
We demonstrate that spin-charge separation can occur in two dimensions and note its confluence with superconductivity, topology, gauge theory, and fault-tolerant quantum computation. We construct a microscopic Ising-like model and, at a…
Fully gapped two-dimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order. In this work, we develop a unified low-energy description for spin-singlet paired states by deriving topological…
The classification of topological phases of matter in the presence of interactions is an area of intense interest. One possible means of classification is via studying the partition function under modular transforms, as the presence of an…
The chiral central charge $c_-$ is a key topological invariant of the edge characterizing the bulk two-dimensional chiral topological order, but its direct evaluation in microscopic spin models has long been a challenge, especially for…
There are indications from the large-N analysis that multi-channel Kondo lattices have topological order. We use the coupled-wire construction to study the channel paramagnetic regime of a two-channel Kondo lattice model of spin-1/2 SU(2)…
"Topological ordered" phases such as gapped quantum spin-liquids and fractional quantum Hall states possess ground state degeneracy on a torus. We show that the topological nature of this degeneracy has interesting consequences for the…
Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the…
The hallmark of two-dimensional chiral topological phases is the existence of anomalous gapless modes at the spatial boundary. Yet, the manifestation of this edge anomaly within the bulk ground-state wavefunction itself remains only…
Spinor bosons offer conceptually simple picture of macroscopic quantum behavior of topological order-by-disorder: Paramagnetic state of two-component dipolar bosons in orbitally degenerate zig-zag lattice is unstable against infinitezimal…
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not…
In 1T-TaS2, the nearly-commensurate charge density wave (NC-CDW) exhibits emergent chirality, a property of interest for technological applications such as memory. We study the relationship between chirality and topological defects using…