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We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon $g-2$ Theory Initiative to update the Standard Model prediction., Comment: Contribution to the US Community Study on the Future of Particle Physics (Snowmass 2021)

We numerically evaluate the entanglement spectrum (singular value decomposition of the wavefunction) of paired states of fermions in two dimensions that break parity and time-reversal symmetries, focusing on the spin-polarized $p_x+ip_y$ case. The entanglement spectrum of the weak-pairing (BCS) phase contains a Majorana zero mode, indicating non-Abelian topological order. In contrast, for the strong-pairing (BEC) phase, we find no such mode, consistent with Abelian topological order., Comment: 4 pages, 4 figures; submitted version

Systems with spin-orbit coupling do not conserve "bare" spin current $\bf{j}$. A recent proposal for a conserved spin current $\bf{J}$ [J. Shi {\it et.al} Phys. Rev. Lett. {\bf 96}, 076604 (2006)] does not flow persistently in equilibrium. We suggest another conserved spin current $\bar{\bf{J}}$ that may flow persistently in equilibrium. We give two arguments for the instability of persistent current of the form $\bf{J}$: one based on the equations of motions and another based on a variational construction using Lieb-Schulz-Mattis twist operators. In the absence of spin-orbit coupling, the three forms of spin current coincide., Comment: 5 pages; added references, simplified notation, clearer introduction

We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the phase diagram, with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyper-scaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half filling, the fidelity metric is expected to diverge as U^{-4} when U is sent to zero., Comment: 8 pages, 4 figures, added results on the hyper-scaling form of the fidelity metric

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered 1D bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet.

The reduction of 2D superconducting or antiferromagnetic order by random dilution is studied as a model for the 2D diluted Heisenberg antiferromagnet (DHAF) La$_2$Cu$_{1-p}$(Zn,Mg)$_p$O$_4$ and randomly inhomogeneous 2D suerconductors. We show in simplified models that long-range order can persist at the percolation threshold despite the presence of disordered one-dimensional segments, contrary to the classical case. When long-range order persists to the percolation threshold, charging effects (in the superconductor) or frustrating interactions (in the antiferromagnet) can dramatically modify the stiffness of the order. This quantum destruction of stiffness is used to model neutron scattering data on La$_2$Cu$_{1-p}$(Zn,Mg)$_p$O$_4$. In a certain simplified model, there is a sharp stiffness transition between ``stiff'' and ``floppy'' ordered phases., Comment: 4 pages, 3 figures