Fenner Harper
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View article: Universal localization-delocalization transition in chiral-symmetric Floquet drives
Universal localization-delocalization transition in chiral-symmetric Floquet drives Open
Periodically driven systems often exhibit behavior distinct from static systems. In single-particle, static systems, any amount of disorder generically localizes all eigenstates in one dimension. In contrast, we show that in topologically …
View article: Localization renormalization and quantum Hall systems
Localization renormalization and quantum Hall systems Open
The obstruction to constructing localized degrees of freedom is a signature of several interesting condensed matter phases. We introduce a localization renormalization procedure that harnesses this property, and apply our method to disting…
View article: Classification of unitary operators by local generatability
Classification of unitary operators by local generatability Open
Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distincti…
View article: Fractional Chern insulators with a non-Landau level continuum limit
Fractional Chern insulators with a non-Landau level continuum limit Open
Recent developments in fractional quantum Hall (FQH) physics highlight the\nimportance of studying FQH phases of particles partially occupying energy bands\nthat are not Landau levels. FQH phases in the regime of strong lattice effects,\nc…
View article: Compactly supported Wannier functions and strictly local projectors
Compactly supported Wannier functions and strictly local projectors Open
Wannier functions that are maximally localized help in understanding many\nproperties of crystalline materials. In the absence of topological\nobstructions, they are at least exponentially localized. In some cases such as\nflat-band Hamilt…
View article: Topology and Broken Symmetry in Floquet Systems
Topology and Broken Symmetry in Floquet Systems Open
Floquet systems are governed by periodic, time-dependent Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However, this unhappy state o…
View article: Topology and Broken Symmetry in Floquet Systems
Topology and Broken Symmetry in Floquet Systems Open
Floquet systems are governed by periodic, time-dependent, Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However this unhappy state o…
View article: Finite-wave-vector electromagnetic response in lattice quantum Hall systems
Finite-wave-vector electromagnetic response in lattice quantum Hall systems Open
In a quantum Hall system, the finite-wavevector Hall conductivity displays an\nintriguing dependence on the Hall viscosity, a coefficient that describes the\nnon-dissipative response of the fluid to a velocity gradient. In this paper, we\n…
View article: Chiral flow in one-dimensional Floquet topological insulators
Chiral flow in one-dimensional Floquet topological insulators Open
We propose a bulk topological invariant for one-dimensional Floquet systems\nwith chiral symmetry which quantifies the particle transport on each sublattice\nduring the evolution. This chiral flow is physically motivated, locally\ncomputab…
View article: Interacting Floquet topological phases in three dimensions
Interacting Floquet topological phases in three dimensions Open
In two dimensions, interacting Floquet topological phases may arise even in the absence of any protecting symmetry, exhibiting chiral edge transport that is robust to local perturbations. We explore a similar class of Floquet topological p…
View article: Periodic table for Floquet topological insulators
Periodic table for Floquet topological insulators Open
Dynamical phases with novel topological properties are known to arise in\ndriven systems of free fermions. In this paper, we obtain a `periodic table' to\ndescribe the phases of such time-dependent systems, generalizing the periodic\ntable…
View article: Floquet topological phases with symmetry in all dimensions
Floquet topological phases with symmetry in all dimensions Open
Dynamical systems may host a number of remarkable symmetry-protected phases that are qualitatively different from their static analogs. In this work, we consider the phase space of symmetry-respecting unitary evolutions in detail and ident…
View article: Floquet Topological Order in Interacting Systems of Bosons and Fermions
Floquet Topological Order in Interacting Systems of Bosons and Fermions Open
Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We find that these drives have surprising many-body analogs, corresponding to class A, which exhibit anomalous…
View article: Floquet topological phases with symmetry in all dimensions
Floquet topological phases with symmetry in all dimensions Open
Dynamical systems may host a number of remarkable symmetry-protected phases that are qualitatively different from their static analogs. In this work, we consider the phase space of symmetry-respecting unitary evolutions in detail and ident…
View article: Floquet Topological Order in Interacting Systems of Bosons and Fermions
Floquet Topological Order in Interacting Systems of Bosons and Fermions Open
Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We find that these drives have surprising many-body analogs, corresponding to class A, which exhibit anomalous…
View article: Stability of Anomalous Floquet Edge Unitaries
Stability of Anomalous Floquet Edge Unitaries Open
It has recently been shown that periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We obtain many-body versions of such drives, corresponding to class A, which e…
View article: Abelian Floquet symmetry-protected topological phases in one dimension
Abelian Floquet symmetry-protected topological phases in one dimension Open
Time-dependent systems have recently been shown to support novel types of\ntopological order that cannot be realised in static systems. In this paper, we\nconsider a range of time-dependent, interacting systems in one dimension that\nare p…
View article: Abelian Floquet SPT Phases in 1D
Abelian Floquet SPT Phases in 1D Open
Time-dependent systems have recently been shown to support novel types of topological order that cannot be realised in static systems. In this paper, we consider a range of time-dependent, interacting systems in one dimension that are prot…
View article: Fractional Chern insulators in bands with zero Berry curvature
Fractional Chern insulators in bands with zero Berry curvature Open
Even if a noninteracting system has zero Berry curvature everywhere in the\nBrillouin zone, it is possible to introduce interactions that stabilise a\nfractional Chern insulator. These interactions necessarily break time-reversal\nsymmetry…
View article: The Hofstadter model and other fractional chern insulators
The Hofstadter model and other fractional chern insulators Open
Fractional Chern insulators (FCIs) are strongly correlated, topological phases of matter that may exist on a lattice in the presence of broken time-reversal symmetry. This thesis explores the link between FCI states and the quantum Hall ef…