Adam Smith

Disorder-Free Localization

The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.

Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.

Neutron scattering signatures of the 3D hyperhoneycomb Kitaev quantum spin liquid

Motivated by recent synthesis of the hyperhoneycomb material β−Li2IrO3, we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalized degrees of freedom are Majorana fermions and emergent flux loops. The properties of this 3D model are known to differ in important ways from those of its 2D counterpart—it has a finite-temperature phase transition, as well as distinct features in the Raman response. We show, however, that the qualitative behavior of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs.

Majorana spectroscopy of three-dimensional Kitaev spin liquids

We analyze the dynamical response of a range of three-dimensional Kitaev quantum spin liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines, or Weyl points. We find that the behavior of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a nonvanishing density of states, to the phase shifts encountered in the corresponding x-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalize, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.

Dynamics of a lattice gauge theory with fermionic matter—minimal quantum simulator with time-dependent impurities in ultracold gases

We propose a minimal cold atomic gas quantum simulator for studying the real-time dynamics of a

Eye-Gaze Patterns as Students Study Worked-out Examples in Mechanics.

mathbb{Z}_2

Silicon nanoparticle electronic switches

lattice gauge theory minimally coupled to fermionic matter. Using duality transformations we show that dynamical correlators of the gauge field can be obtained by measuring the dynamics of two pairs of impurities in a lattice of free fermions. We provide a protocol for the implementation of this minimal setting in a cold atomic gas experiment and predict a number of unusual experimental features in the integrable limit of the gauge theory. Finally, we show how the experimental setting can easily be extended to non-integrable regimes for exploring strongly interacting gauge theories beyond the capabilities of classical computers.