59 citations · 106 across the 16 of their papers we have counts for
18 papers · 1 filter
Localization Dichotomy for Hall Insulators on the Lattice
Alex Bols
We prove the localization dichotomy conjecture for non-periodic Hall insulators on the lattice. That is, we show that the Fermi projector of a gapped exponentially local Hamilt…
A complete classification of 2d symmetry protected states with symmetric entanglers
Alex Bols, Wojciech De Roeck, Michiel De Wilde +1
We consider symmetry protected topological states of 2d quantum spin systems, with a finite symmetry group . It has been conjectured that such states are classified by the cohom…
Sector Theory of Levin-Wen Models II : Fusion and Braiding
Alex Bols, Boris Kjær
This is the continuation of our study of the Levin-Wen model based on an arbitrary unitary fusion category on the infinite plane. The ground state of the Levin-Wen mo…
Sector Theory of Levin-Wen Models I : Classification of Anyon Sectors
Alex Bols, Boris Kjær
We classify the irreducible anyon sectors of Levin-Wen models over an arbitrary unitary fusion category , showing that they are in one-to-one correspondence with equiv…
The category of anyon sectors for non-abelian quantum double models
Alex Bols, Mahdie Hamdan, Pieter Naaijkens +1
We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations…
Many-body Fu-Kane-Mele index
Sven Bachmann, Alex Bols, Mahsa Rahnama
We define a -valued index for stably short-range entangled states of two-dimensional fermionic lattice systems with charge conservation and time reversal symmetry. Th…
Classification of the anyon sectors of Kitaev's quantum double model
Alex Bols, Siddharth Vadnerkar
We give a complete classification of the anyon sectors of Kitaev's quantum double model on the infinite triangular lattice and for finite gauge group , including the non-abelian…
The double semion state in infinite volume
Alex Bols, Boris Kjaer, Alvin Moon
We describe in a simple setting how to extract a unitary braided fusion category from a collection of superselection sectors of a two-dimensional quantum spin system, corresponding…
Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
Alex Bols, Christopher Cedzich
We show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. The proof employs a time-revers…
Fredholm Homotopies for Strongly-Disordered 2D Insulators
Alex Bols, Jeffrey Schenker, Jacob Shapiro
We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to int…
Classification of equivariant quasi-local automorphisms on quantum chains
Alex Bols
We classify automorphisms on quantum chains, allowing both spin and fermionic degrees of freedom, that are moreover equivariant with respect to a local symmetry action of a finite…
Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice
Alex Bols, Albert H. Werner
The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support balli…
Rational indices for quantum ground state sectors
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We consider charge transport for interacting many-body systems with a gapped ground state subspace which is finitely degenerate and topologically ordered. To any locality-preservin…
A many-body Fredholm index for ground state spaces and Abelian anyons
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We propose a many-body index that extends Fredholm index theory to many-body systems. The index is defined for any charge-conserving system with a topologically ordered -dimensi…
Note on linear response for interacting Hall insulators
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We relate explicitly the adiabatic curvature -- in flux space -- of an interacting Hall insulator with nondegenerate ground state to various linear response coefficients, in partic…
A many-body index for quantum charge transport
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We propose an index for pairs of a unitary map and a clustering state on many-body quantum systems. We require the map to conserve an integer-valued charge and to leave the state,…
Quantization of conductance in gapped interacting systems
Sven Bachmann, Alex Bols, Wojciech De Roeck +1
We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen…
Asymptotic Localization in the Bose-Hubbard Model
Alex Bols, Wojciech De Roeck
We consider the Bose-Hubbard model. Our focus is on many-body localization, which was described by many authors in such models, even in the absence of disorder. Since our work is r…