Related papers: Topological and nontopological degeneracies in gen…
We show that, in certain circumstances, exact excitation energies appear as locally site-independent (or flat) modes if one records the excitation spectrum of the effective Hamiltonian while sweeping through the lattice in the variational…
In a model that supports both Abelian (Abrikosov-Nielsen-Olesen) and non-Abelian strings we analyze the parameter space to find examples in which these strings not only coexist but are degenerate in tension. We prove that both solutions are…
We proposed a framework for the topological classification of non-Hermitian systems. Different from previous $K$-theoretical approaches, our approach is a homotopy classification, which enables us to see more topological invariants.…
We develop a systematically general theory of one-dimensional (1D) non-Hermitian systems, elaborating on the energy bands, the band degeneracy, and the defectiveness of eigenstates under open boundary conditions. We analyze the band…
We construct 2+1-dimensional lattice models of symmetry-protected topological (SPT) phases with non-invertible symmetries and investigate their properties using tensor networks. These models, which we refer to as generalized cluster models,…
We investigate the multifusion generalization of string-net ground states and lattice Hamiltonians, delving into its associated weak Hopf symmetry. For the multifusion string-net, the gauge symmetry manifests as a general weak Hopf algebra,…
A degenerate variant of mean field perturbation theory for the on-site Bose-Hubbard Hamiltonian is presented. We split the perturbation into two terms and perform exact diagonalization in the two-dimensional subspace corresponding to the…
We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wavefunction for the $\nu$ = 5/2 fractional quantum Hall state…
Systems with topologically protected ground-state degeneracies are currently of great interest due to their potential applications in quantum computing. In practise this degeneracy is never exact, and the magnitude of the ground-state…
Line excitations in topological phases are a subject of particular interest because their mutual linking structures encode robust topological information of matter. It has been recently shown that the linking and winding of complex…
The existence of degenerate or gapless edge states is a characteristic feature of topological insulators, but is difficult to detect in the presence of interactons. We propose a new method to obtain the degeneracy of the edge states from…
We relate the ground state degeneracy (GSD) of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase to a trivial phase. Specifically, we propose that gapped boundary…
We report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically…
Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…
The structure of string-net lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor…
There have been recent advances in the analysis and visualization of 3D symmetric tensor fields, with a focus on the robust extraction of tensor field topology. However, topological features such as degenerate curves and neutral surfaces do…
We present a generalization of the Sutherland's multicomponent model. Our extension includes both the ferromagnetic and the antiferromagnetic t-J model for any value of the exchange coupling J and the hopping parameter t. We prove…
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…
Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well-defined and can be computed using methods of Topological Quantum Field Theory. We derive a general…
We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the…