Steve Simon

Abstract:

We study classical dimers on two-dimensional quasiperiodic Ammann-Beenker (AB) tilings. Using the discrete scale-symmetry of quasiperiodic tilings, we prove that each infinite tiling admits “perfect matchings”, where every vertex is touched by one dimer. We show the appearance of so-called monomer pseudomembranes. These are sets of edges, which collectively host exactly one dimer, which bound certain eightfold-symmetric regions of the tiling. Regions bounded by pseudomembranes are matched together in a way that resembles perfect matchings of the tiling itself. These structures emerge at all scales, suggesting the preservation of collective dimer fluctuations over long distances. We provide numerical evidence, via Monte Carlo simulations, of dimer correlations consistent with power laws over a hierarchy of different lengthscales. We also find evidence of rich monomer correlations, with monomers displaying a pattern of attraction and repulsion to different regions within pseudomembranes, along with signatures of deconfinement within certain annular regions of the tiling.

Abstract:

Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr2RuO4 can be tuned through a single Van Hove point, resulting in strong enhancement of both Tc and Hc2. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously. Here, we achieve a record uniaxial stress of 3.2 GPa along the c axis of Sr2RuO4. Hc2 increases, as expected for increasing density of states, but unexpectedly Tc falls. As a first attempt to explain this result, we present three-dimensional calculations in the weak interaction limit. We find that within the weak-coupling framework there is no single order parameter that can account for the contrasting effects of in-plane versus c-axis uniaxial stress, which makes this new result a strong constraint on theories of the superconductivity of Sr2RuO4.

Abstract:

We study the excitations that emerge upon doping the translationally invariant correlated insulating states in magic-angle twisted bilayer graphene at various integer filling factors ν. We identify parameter regimes where these are excitations associated with skyrmion textures in the spin or pseudospin degrees of freedom, and explore both short-distance pairing effects and the formation of long-range ordered skyrmion crystals. We perform a comprehensive analysis of the pseudospin skyrmions that emerge upon doping insulators at even ν, delineating the regime in parameter space where these are the lowest-energy charged excitations by means of self-consistent Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key ingredient behind a recent proposal of skyrmion superconductivity. Building upon this, we construct hopping models to extract the effective masses of paired skyrmions, and discuss our findings and their implications for skyrmion superconductivity in relation to experiments, focusing on the dome-shaped dependence of the transition temperature on the twist angle. We also investigate the properties of spin skyrmions about the quantized anomalous Hall insulator at ν=+3. In both cases, we demonstrate the formation of robust spin or pseudospin skyrmion crystals upon doping to a finite density away from integer filling.

Abstract:

We develop techniques to probe the dynamics of quantum information, and implement them experimentally on an IBM superconducting quantum processor. Our protocols adapt shadow tomography for the study of time evolution channels rather than of quantum states, and rely only on single-qubit operations and measurements. We identify two unambiguous signatures of quantum information scrambling, neither of which can be mimicked by dissipative processes, and relate these to many-body teleportation. By realizing quantum chaotic dynamics in experiment, we measure both signatures, and support our results with numerical simulations of the quantum system. We additionally investigate operator growth under this dynamics, and observe behaviour characteristic of quantum chaos. As our methods require only a single quantum state at a time, they can be readily applied on a wide variety of quantum simulators.