arXiv subjects

Fiona Burnell

Publications and source records attributed to Fiona Burnell.

7 recordsLinked to original sources

arXiv2024

Prethermal stability of eigenstates under high frequency Floquet driving

Systems subject to high-frequency driving exhibit Floquet prethermalization, that is, they heat exponentially slowly on a time scale that is large in the drive frequency, $τ_{\rm h} \sim \exp(ω)$. Nonetheless, local observables can decay much faster via energy conserving processes, which are expected to cause a rapid decay in the fidelity of an initial state. Here we show instead that the fidelities of eigenstates of the time-averaged Hamiltonian, $H_0$, display an exponentially long lifetime over a wide range of frequencies -- even as generic initial states decay rapidly. When $H_0$ has quantum scars, or highly excited-eigenstates of low entanglement, this leads to long-lived non-thermal behavior of local observables in certain initial states. We present a two-channel theory describing the fidelity decay time $τ_{\rm f}$: the interzone channel causes fidelity decay through energy absorption i.e. coupling across Floquet zones, and ties $τ_{\rm f}$ to the slow heating time scale, while the intrazone channel causes hybridization between states in the same Floquet zone. Our work informs the robustness of experimental approaches for using Floquet engineering to generate interesting many-body Hamiltonians, with and without scars.

cond-mat.stat-mech↗

arXiv2022

Composing topological domain walls and anyon mobility

Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a framework for decomposing stacks of multiple domain walls into superselection sectors - i.e., into fundamental domain wall types that cannot be mixed by any local operators. Such a decomposition can be understood using an alternate framework in the case that the topological order is anomaly-free, in the sense that it can be realized by a commuting projector lattice model. By placing these Witt equivalences in the context of a 3-category of potentially anomalous (2+1)D topological orders, we develop a framework for computing the decomposition of parallel topological domain walls into indecomposable superselection sectors, extending the previous understanding to topological orders with non-trivial anomaly. We characterize the superselection sectors in terms of domain wall particle mobility, which we formalize in terms of tunnelling operators. The mathematical model for the 3-category of topological orders is the 3-category of fusion categories enriched over a fixed unitary modular tensor category.

cond-mat.str-el↗

arXiv2020

From tunnels to towers: quantum scars from Lie Algebras and q-deformed Lie Algebras

We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with `spectrum generating algebras' that can be used to lift the degeneracy of the scar states and promote them to equally spaced `towers'. Our framework applies to several known models with scars, but we also introduce new models with scars that transform as irreducible representations of symmetries such as SU(3) and $q$-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present new examples of generalized AKLT models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-like models into our framework.

cond-mat.stat-mech↗

arXiv2017

How does a locally constrained quantum system localize?

At low energy, the dynamics of excitations of many physical systems are locally constrained. Examples include frustrated anti-ferromagnets, fractional quantum Hall fluids and Rydberg atoms in the blockaded regime. Can such locally constrained systems be fully many-body localized (MBL)? In this article, we answer this question affirmatively and elucidate the structure of the accompanying quasi-local integrals of motion. By studying disordered spin chains subject to a projection constraint in the $z$-direction, we show that full MBL is stable at strong $z$-field disorder and identify a new mechanism of localization through resonance at strong transverse disorder. However MBL is not guaranteed; the constraints can `frustrate' the tendency of the spins to align with the transverse fields and lead to full thermalization or criticality. We further provide evidence that the transition is discontinuous in local observables with large sample-to-sample variations. Our study has direct consequences for current quench experiments in Rydberg atomic chains.

cond-mat.dis-nn↗

arXiv2016

Symmetry enriched string-nets: Exactly solvable models for SET phases

We construct exactly solvable models for a wide class of symmetry enriched topological (SET) phases. Our construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group $G$ and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. Our models are designed so that they have a special property: if we couple them to a dynamical lattice gauge field with gauge group $G$, the resulting gauge theories are equivalent to modified string-net models. This property is what allows us to analyze our models in generality. As an example, we present a model for a phase with the same anyon excitations as the toric code and with a $\mathbb{Z}_2$ symmetry which exchanges the $e$ and $m$ type anyons. We further illustrate our construction with a number of additional examples.

cond-mat.str-el↗

arXiv2015

Time reversal invariant gapped boundaries of the double semion state

The boundary of a fractionalized topological phase can be gapped by condensing a proper set of bosonic quasiparticles. Interestingly, in the presence of a global symmetry, such a boundary can have different symmetry transformation properties. Here we present an explicit example of this kind, in the double semion state with time reversal symmetry. We find two distinct cases where the semionic excitations on the boundary can transform either as time reversal singlets or as time reversal (Kramers) doublets, depending on the coherent phase factor of the Bose condensate. The existence of these two possibilities are demonstrated using both field theory argument and exactly solvable lattice models. Furthermore, we study the domain walls between these two types of gapped boundaries and find that the application of time reversal symmetry tunnels a semion between them.

cond-mat.str-el↗

arXiv2005

The Abundance of Kaluza-Klein Dark Matter with Coannihilation

In Universal Extra Dimension models, the lightest Kaluza-Klein (KK) particle is generically the first KK excitation of the photon and can be stable, serving as particle dark matter. We calculate the thermal relic abundance of the KK photon for a general mass spectrum of KK excitations including full coannihilation effects with all (level one) KK excitations. We find that including coannihilation can significantly change the relic abundance when the coannihilating particles are within about 20% of the mass of the KK photon. Matching the relic abundance with cosmological data, we find the mass range of the KK photon is much wider than previously found, up to about 2 TeV if the masses of the strongly interacting level one KK particles are within five percent of the mass of the KK photon. We also find cases where several coannihilation channels compete (constructively and destructively) with one another. The lower bound on the KK photon mass, about 540 GeV when just right-handed KK leptons coannihilate with the KK photon, relaxes upward by several hundred GeV when coannihilation with electroweak KK gauge bosons of the same mass is included.

hep-ph↗