69 citations · 328 across the 12 of their papers we have counts for
12 papers
Crossing with the circle in Dijkgraaf-Witten theory and applications to topological phases of matter
Alex Bullivant, Clement Delcamp
Given a fully extended topological quantum field theory, the 'crossing with the circle' conditions establish that the dimension, or categorification thereof, of the quantum invaria…
Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
Alex Bullivant, Clement Delcamp
We study lattice Hamiltonian realisations of (3+1)d Dijkgraaf-Witten theory with gapped boundaries. In addition to the bulk loop-like excitations, the Hamiltonian yields bulk dyoni…
Excitations in strict 2-group higher gauge models of topological phases
Alex Bullivant, Clement Delcamp
We consider an exactly solvable model for topological phases in (3+1)d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a…
Tube algebras, excitations statistics and compactification in gauge models of topological phases
Alex Bullivant, Clement Delcamp
We consider lattice Hamiltonian realizations of (+1)-dimensional Dijkgraaf-Witten theory. In (2+1)d, it is well-known that the Hamiltonian yields point-like excitations classifi…
Representations of the Necklace Braid Group: Topological and Combinatorial Approaches
Alex Bullivant, Andrew Kimball, Paul Martin +1
The necklace braid group is the motion group of the component necklace link in Euclidean . Here consists of …
Representations of the Loop Braid Group and Aharonov-Bohm like effects in discrete (3+1)-dimensional higher gauge theory
Alex Bullivant, João Faria Martins, Paul Martin
We show that representations of the loop braid group arise from Aharonov-Bohm like effects in finite 2-group (3+1)-dimensional topological higher gauge theory. For this we introduc…
Twisted Quantum Double Model of Topological Orders with Boundaries
Alex Bullivant, Yuting Hu, Yidun Wan
We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given t…
Higher lattices, discrete two-dimensional holonomy and topological phases in (3+1) D with higher gauge symmetry
Alex Bullivant, Marcos Calcada, Zoltán Kádár +2
Higher gauge theory is a higher order version of gauge theory that makes possible the definition of 2-dimensional holonomy along surfaces embedded in a manifold where a gauge 2-con…
Topological phases from higher gauge symmetry in 3+1D
Alex Bullivant, Marcos Calçada, Zoltán Kádár +2
We propose an exactly solvable Hamiltonian for topological phases in dimensions utilising ideas from higher lattice gauge theory, where the gauge symmetry is given by a finit…
Entropic Topological Invariants in Three Dimensions
Alex Bullivant, Jiannis K. Pachos
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to th…
Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers
James de Lisle, Suvabrata De, Emilio Alba +4
Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species o…
Nonreversal and nonrepeating quantum walks
T. J. Proctor, K. E. Barr, B. Hanson +4
We introduce a variation of the discrete time quantum walk, the nonreversal quantum walk, which does not step back onto a position which it has just occupied. This allows us to sim…