Related papers: Local interactions and non-Abelian quantum loop ga…

Condensation of quantum loops naturally leads to topological phases with Abelian excitations. Here, I propose that non-Abelian topological phases can arise from merging two (or several) identical Abelian quantum loop condensates. I define…

I define quantum loop models whose degrees of freedom are Ising spins on the square lattice as in the toric code, but where the excitations should have non-abelian statistics. The inner product is topological, allowing a direct…

It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply gaplessness. This is exemplified by the…

Topological systems, such as fractional quantum Hall liquids, promise to successfully combat environmental decoherence while performing quantum computation. These highly correlated systems can support non-Abelian anyonic quasiparticles that…

String-net condensation can give rise to non-Abelian anyons whereas loop condensation usually gives rise to Abelian anyons. It has been proposed that generalized quantum loop gases with non-orthogonal inner products can produce non-Abelian…

A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y superconductor or quasiholes in certain quantum Hall states - gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions…

We established a large class of exactly soluble spin liquids and chiral spin liquids on three dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous…

Internal degrees of freedoms of the quantum electron (spin and charge) introduced by Dirac lead to the non-Abelian field configuration of the electron in the complex projective Hilbert space $CP(3)$ of the unlocated quantum states (UQS).…

We show that non-abelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with non-abelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly…

We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian…

Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…

We elaborate on the principle that for gapped quantum spin systems with local interaction "local perturbations [in the Hamiltonian] perturb locally [the ground state]". This principle was established in [Bachmann et al. 2012], relying on…

Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological…

We analyze a model of quantum nets and show it has non-abelian topological order of doubled Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined…

Recent theoretical insights into the possibility of non-Abelian phases in $\nu=2/3$ fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body…

This work provides the first experimental elucidation of quantum topological effects in individual hopfions, establishing their potential as building blocks for three-dimensional topological quantum spintronics. The observed Non-Abelian…

The geometric aspects of quantum mechanics are underlined most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a closed path in Hilbert space. The geometric phase is determined only…

When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…

In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of…

Circuits can provide a platform to study novel physics and have been used, for example, to explore various topological phases. Gauge fields-particularly, non-Abelian gauge fields-can play a pivotal role in the design and modulation of novel…