Height models and random tiling are well-studied objects in classical statistical mechanics and combinatorics that lead to many interesting phenomena, such as arctic curve, limit shape and Kadar-Parisi-Zhang scaling. We introduce quantum dynamics to the classical hexagonal dimer, 6- and 19-vertex models to construct frustration-free Hamiltonians with unique ground state being a superposition of tiling configurations subject to a particular boundary configuration. The local Hilbert space is enlarged with a color degree of freedom to generate long range entanglement that makes area law violation of entanglement entropy possible. The scaling of entanglement entropy between half systems is analysed with the surface tension theory of random surfaces and under a q-deformation that weighs random surfaces in the ground state superposition by the volume below, it undergoes a phase transition from area law to volume scaling. At the critical point, the scaling is L logL due to the so-called "entropic repulsion” of Gaussian free fields conditioned to be positive. An exact holographic tensor network description of the ground state is proposed with one extra dimension perpendicular to the lattice. I will also discuss inhomogeneous deformations to obtain sub-volume intermediate scaling and possible generalisations to higher dimension.
Collective cell movement is critical to the emergent properties of many multicellular systems including microbial self-organization in biofilms, wound healing, and cancer metastasis. However, even the best-studied systems lack a complete picture of how diverse physical and chemical cues act upon individual cells to ensure coordinated multicellular behavior. Myxococcus xanthus is a model bacteria famous for its coordinated multicellular behavior resulting in dynamic patterns formation. For example, when starving millions of cells coordinate their movement to organize into fruiting bodies – aggregates containing tens of thousands of bacteria. Relating these complex self-organization patterns to the behavior of individual cells is a complex-reverse engineering problem that cannot be solved solely by experimental research. In collaboration with experimental colleagues, we use a combination of quantitative microscopy, image processing, agent-based modeling, and kinetic theory PDEs to uncover the mechanisms of emergent collective behaviors.
Exchange-antisymmetric pair wavefunctions in fermionic systems hold the promise of new types of quantum simulations, topological quantum gates, and exotic few-body states. However, p-wave and other antisymmetric interactions are weak in naturally occurring systems, and their enhancement via Feshbach resonances in ultracold systems has been limited by three-body loss. Here we revisit p-wave interactions in the presence of strong confinement.In a first scenario, we study the two-body correlation strength of quasi-one-dimensional (q1D) ensembles of spin-polarized fermionic potassium. The strength and spatial symmetry of interactions are tuned by a nearby p-wave Feshbach resonance and by confinement anisotropy. Surprisingly, we find a scattering channel that has even particle-exchange parity along the q1D axis. These emergent s-wave collisions are enabled by orbital singlet wave functions in the transverse directions, which also confer high-momentum components to low-energy q1D collisions.In a second scenario, we create isolated pairs of spin-polarised fermionic atoms in a multi-orbital three-dimensional optical lattice. We measure elastic p-wave interaction energies of strongly interacting pairs of atoms and find pair lifetimes to be up to fifty times larger than in free space. We demonstrate that on-site interaction strengths can be widely tuned but collapse onto a universal single-parameter curve when rescaled by the harmonic energy and length scales of a single lattice site. Since three-body processes are absent in this scenario, we are able to observe elastic unitary p-wave interactions for the first time. Observations are compared both to an analytic solution for two harmonically confined atoms interacting via a p-wave pseudopotential, and to numerical solutions using an ab-initio interaction potential.
