Related papers: A degeneracy bound for homogeneous topological ord…
Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech.,…
A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the…
In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…
Systems hosting flat bands offer a powerful platform for exploring strong correlation physics. Theoretically topological degeneracy rising in systems with non-trivial topological orders on periodic manifolds of non-zero genus can generate…
Often noisy point clouds are given as an approximation of a particular compact set of interest. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the…
It is commonly believed that models defined on a closed one-dimensional manifold cannot give rise to topological order. Here we construct frustration-free Hamiltonians which possess both symmetry protected topological order (SPT) on the…
Nondegeneracy conditions need to be imposed in K.A.M. theorems to insure that the set of diophantine tori has a large measure. Although they are usually expressed in action coordinates, it is possible to give a geometrical formulation using…
We address the problem of stability of one-dimensional non-periodic ground-state configurations with respect to finite-range perturbations of interactions in classical lattice-gas models. We show that a relevant property of non-periodic…
Topological entanglement entropy is a topological invariant which can detect topological order of quantum many-body ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of $d-1$ dimensional surfaces in a $d$ dimensional ambient space. We construct a local Hamiltonian which is a sum of…
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)…
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…
Let $D$ be a closed unit $2$-disk on the plane centered at the origin $O$, and $F$ be a smooth vector field such that $O$ is a unique singular point of $F$ and all other orbits of $F$ are simple closed curves wrapping once around $O$. Thus…
This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces…
We begin with an introduction to topological order using Wegner's quantum $Z_2$ gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying $Z_2$ magnetic flux. The interplay between…
We consider quantum phases of tightly-confined spin-2 bosons in an external field under the presence of rotationally-invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model.…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…
We study the robustness of quantum information stored in the degenerate ground space of a local, frustration-free Hamiltonian with commuting terms on a 2D spin lattice. On one hand, a macroscopic energy barrier separating the distinct…
Consider the configuration spaces of manifolds. An influential theorem of McDuff, Segal and Church shows that the (co)homology of the unordered configuration space is independent of number of points in a range of degree called the stable…