Search results for "topological [model]"
showing 10 items of 88 documents
Compact Topological Quantum Groups
1995
Using vector spaces topologies we unify the different models of quantum groups. Duality and reflexivity are built in. The Drinfeld deformation can be extended to the distributions on a simple compact Lie group and dually to the infinitely differentiable functions. The topological quantum double is similarly defined and a uniqueness result is obtained.
Simulating long-distance entanglement in quantum spin chains by superconducting flux qubits
2014
We investigate the performance of superconducting flux qubits for the adiabatic quantum simulation of long distance entanglement (LDE), namely a finite ground-state entanglement between the end spins of a quantum spin chain with open boundary conditions. As such, LDE can be considered an elementary precursor of edge modes and topological order. We discuss two possible implementations which simulate open chains with uniform bulk and weak end bonds, either with Ising or with XX nearest-neighbor interactions. In both cases we discuss a suitable protocol for the adiabatic preparation of the ground state in the physical regimes featuring LDE. In the first case the adiabatic manipulation and the …
Topological Phases in Planar Electrodynamics
2001
This section is meant to be an extension of Chap. 31 on the quantal Berry phases. In particular, we are interested in studying the electromagnetic interaction of particles with a nonzero magnetic moment in \(D = 2 + 1\) dimensions and of translational invariant configurations of \((D = 3 + 1)\)-dimensional charged strings with a nonzero magnetic moment per unit length. The whole discussion is based on our article in Physical Review D44, 1132 (1991).
Topological Defects in Nanostructures—Chiral Domain Walls and Skyrmions
2016
In this chapter, spin structures with particular topologies in confined geometries are presented. Domain walls in nanowires exhibit a spin structure that depends on the material and geometry while in discs Skyrmions can be stabilized by different competing interactions. The topologies of these spin structures can be characterized by a Skyrmion or Winding number that governs the dynamics and stability.
Analysis method for detecting topological defect dark matter with a global magnetometer network
2019
Abstract The Global Network of Optical Magnetometers for Exotic physics searches (GNOME) is a network of time-synchronized, geographically separated, optically pumped atomic magnetometers that is being used to search for correlated transient signals heralding exotic physics. GNOME is sensitive to exotic couplings of atomic spins to certain classes of dark matter candidates, such as axions. This work presents a data analysis procedure to search for axion dark matter in the form of topological defects: specifically, walls separating domains of discrete degenerate vacua in the axion field. An axion domain wall crossing the Earth creates a distinctive signal pattern in the network that can be d…
Two topologically distinct Dirac-line semimetal phases and topological phase transitions in rhombohedrally stacked honeycomb lattices
2018
Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by…
Comments on "Neutron-proton mass difference in the chiral solitonic bag model"
1990
It is pointed out that the topological soliton bag is incompletely quantized in the papers of Durgut, Pak, and Yilmaz and of Wittman and Woloshyn, leading to results on the neutron-proton mass difference and other phenomena that are not implied by the model. The purpose of this paper is to clarify how and where their scheme goes wrong and to propose an alternative consistent scheme of quantization.
Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model
2008
The spectral properties of Kitaev's honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the $2^n$-fold ground state degeneracy in the presence of $2n$ well separated vortices and the lifting of the degeneracy due to t…
Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
2014
Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on Projected Entangled Pair States to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation…
Noncompact Topological Quantum Groups
1995
A star-product construction of quantum semisimple real Lie groups is performed for the noncompact case.