Robust Spectral π Pairing in the Random-Field Floquet Quantum Ising Model.

Motivated by an experiment on a superconducting quantum processor [X. Mi et al., Science 378, 785 (2022).SCIEAS0036-807510.1126/science.abq5769], we study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The pairings derive from Majorana zero and π modes when writing the spin model in Jordan-Wigner fermions. Both splittings have log-normal distributions with random transverse fields. In contrast, random longitudinal fields affect the zero and π splittings in drastically different ways. While zero pairings are rapidly lifted, the π pairings are remarkably robust, or even strengthened, up to vastly larger disorder strengths. We explain our results within a self-consistent Floquet perturbation theory and study implications for boundary spin correlations. The robustness of π pairings against longitudinal disorder may be useful for quantum information processing.

Resistivity Tensor of Vortex-Lattice States in Josephson Junction Arrays.

Two-dimensional Josephson junction arrays frustrated by a perpendicular magnetic field are predicted to form a cascade of distinct vortex lattice states. Here, we show that the resistivity tensor provides both structural and dynamical information on the vortex-lattice states and intervening phase transitions, which allows for experimental identification of these symmetry-breaking ground states. We illustrate our general approach by a microscopic theory of the resistivity tensor for a range of magnetic fields exhibiting a rich set of vortex lattices as well as transitions to liquid-crystalline vortex states.

Hilbert Space Geometry of Random Matrix Eigenstates.

The geometry of multiparameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the Hilbert space geometry of eigenstates of parameter-dependent random matrix ensembles, deriving the full probability distribution of the quantum geometric tensor for the Gaussian unitary ensemble. Our analytical results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We discuss relations to Levy stable distributions and compare our results to numerical simulations of random matrix ensembles as well as electrons in a random magnetic field.