Tensor electromagnetism and emergent elasticity in jammed solids.

The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how nonperiodic networks-apparently indistinguishable from a snapshot of a fluid-sustain shear. We present a stress-only theory of emergent elasticity for a nonthermal amorphous assembly of grains in a jammed solid, where each grain is subjected to mechanical constraints of force and torque balance. These grain-level constraints lead to the Gauss's law of an emergent U(1) tensor electromagnetism, which then accounts for the mechanical response of such solids. This formulation of amorphous elasticity has several immediate consequences. The mechanical response maps exactly to the static, dielectric response of this tensorial electromagnetism with the polarizability of the medium mapping to emergent elastic moduli. External forces act as vector electric charges, whereas the tensorial magnetic fields are sourced by momentum density. The dynamics in the electric and magnetic sectors naturally translate into the dynamics of the rigid jammed network and ballistic particle motion, respectively. The theoretical predictions for both stress-stress correlations and responses are borne out by the results of numerical simulations of frictionless granular packings in the static limit of the theory in both 2D and 3D.

Many-Body Chaos in Thermalized Fluids.

Linking thermodynamic variables like temperature T and the measure of chaos, the Lyapunov exponents λ, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we show that in thermalized flows λ∝sqrt[T], in agreement with results from frustrated spin systems. This suggests an underlying universality and provides evidence for recent conjectures on the thermal scaling of λ. We also reconcile seemingly disparate effects-equilibration on one hand and pushing systems out of equilibrium on the other-of many-body chaos by relating λ to T through the dynamical structures of the flow.

Emergent Elasticity in Amorphous Solids.

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids are governed by local conditions of mechanical equilibrium, i.e., force and torque balance of its constituents. Here we show that these constraints have the mathematical structure of a generalized electromagnetism, where the electrostatic limit successfully captures the anisotropic elasticity of amorphous solids. The emergence of elasticity from local mechanical constraints offers a new paradigm for systems with no broken symmetry, analogous to emergent gauge theories of quantum spin liquids. Specifically, our U(1) rank-2 symmetric tensor gauge theory of elasticity translates to the electromagnetism of fractonic phases of matter with the stress mapped to electric displacement and forces to vector charges. We corroborate our theoretical results with numerical simulations of soft frictionless disks in both two and three dimensions, and experiments on frictional disks in two dimensions. We also present experimental evidence indicating that force chains in granular media are subdimensional excitations of amorphous elasticity similar to fractons.

Signatures of a Spin-1/2 Cooperative Paramagnet in the Diluted Triangular Lattice of Y_{2}CuTiO_{6}.

We present a combination of thermodynamic and dynamic experimental signatures of a disorder driven dynamic cooperative paramagnet in a 50% site diluted triangular lattice spin-1/2 system: Y_{2}CuTiO_{6}. Magnetic ordering and spin freezing are absent down to 50 mK, far below the Curie-Weiss scale (-θ_{CW}) of ∼134 K. We observe scaling collapses of the magnetic field and temperature dependent magnetic heat capacity and magnetization data, respectively, in conformity with expectations from the random singlet physics. Our experiments establish the suppression of any freezing scale, if at all present, by more than 3 orders of magnitude, opening a plethora of interesting possibilities such as disorder stabilized long range quantum entangled ground states.

Interplay of Magnetism and Topological Superconductivity in Bilayer Kagome Metals.

The binary intermetallic materials, M_{3}Sn_{2} (M=3d transition metal) present a new class of strongly correlated systems that naturally allows for the interplay of magnetism and metallicity. Using first principles calculations we confirm that bulk Fe_{3}Sn_{2} is a ferromagnetic metal, and show that M=Ni and Cu are paramagnetic metals with nontrivial band structures. Focusing on Fe_{3}Sn_{2} to understand the effect of enhanced correlations in an experimentally relevant atomistically thin single kagome bilayer, our ab initio results show that dimensional confinement naturally exposes the flatness of band structure associated with the bilayer kagome geometry in a resultant ferromagnetic Chern metal. We use a multistage minimal modeling of the magnetic bands progressively closer to the Fermi energy. This effectively captures the physics of the Chern metal with a nonzero anomalous Hall response over a material relevant parameter regime along with a possible superconducting instability of the spin-polarized band resulting in a topological superconductor.

Light-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chain.

We find that the effects of a localized perturbation in a chaotic classical many-body system-the classical Heisenberg chain at infinite temperature-spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterized by the Lyapunov exponents and the butterfly speed, respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analyzing the scaling forms, we relate the growth, spread, and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang equation.

Temperature Dependence of the Butterfly Effect in a Classical Many-Body System.

We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterize many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered commutator. Due to the emergence of a spin-liquid phase, the chaotic dynamics extends all the way to zero temperature. We thus determine the full temperature dependence of two complementary aspects of the butterfly effect: the Lyapunov exponent, µ, and the butterfly speed, v_{b}, and study their interrelations with usual measures of spin dynamics such as the spin-diffusion constant, D, and spin-autocorrelation time, τ. We find that they all exhibit power-law behavior at low temperature, consistent with scaling of the form D∼v_{b}^{2}/µ and τ^{-1}∼T. The vanishing of µâˆ¼T^{0.48} is parametrically slower than that of the corresponding quantum bound, µâˆ¼T, raising interesting questions regarding the semiclassical limit of such spin systems.

Bosonic integer quantum Hall effect in an interacting lattice model.

We study a bosonic model with correlated hopping on a honeycomb lattice, and show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a prominent example of a symmetry-protected topological (SPT) phase. By using the infinite density matrix renormalization group method, we establish the existence of the BIQH phase by providing clear numerical evidence: (i) a quantized Hall conductance with |σ_{xy}|=2, (ii) two counterpropagating gapless edge modes. Our simple model is an example of a novel class of systems that can stabilize SPT phases protected by a continuous symmetry on lattices and opens up new possibilities for the experimental realization of these exotic phases.

Kagome Chiral Spin Liquid as a Gauged U(1) Symmetry Protected Topological Phase.

While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.

Tunneling conductance of graphene NIS junctions.

We show that, in contrast with conventional normal metal-insulator-superconductor (NIS) junctions, the tunneling conductance of a NIS junction in graphene is an oscillatory function of the effective barrier strength of the insulating region, in the limit of a thin barrier. The amplitude of these oscillations is maximum for aligned Fermi surfaces of the normal and superconducting regions and vanishes for a large Fermi surface mismatch. The zero-bias tunneling conductance, in sharp contrast to its counterpart in conventional NIS junctions, becomes maximum for a finite barrier strength. We also suggest experiments to test these predictions.