Renormalization group analysis of the Anderson model on random regular graphs.

We present a renormalization group (RG) analysis of the problem of Anderson localization on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The RG equations necessarily involve two parameters (one being the changing connectivity of subtrees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the nonmonotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence.

Localization and Melting of Interfaces in the Two-Dimensional Quantum Ising Model.

We study the nonequilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model-a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles.

Constraint-Induced Delocalization.

We study the impact of quenched disorder on the dynamics of locally constrained quantum spin chains, that describe 1D arrays of Rydberg atoms in both the frozen (Ising-type) and dressed (XY-type) regime. Performing large-scale numerical experiments, we observe no trace of many-body localization even at large disorder. Analyzing the role of quenched disorder terms in constrained systems we show that they act in two, distinct and competing ways: as an on-site disorder term for the basic excitations of the system, and as an interaction between excitations.

Impact of jamming criticality on low-temperature anomalies in structural glasses.

We present a mechanism for the anomalous behavior of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a cross-over temperature above which the specific heat scales linearly with temperature, while below it, a cubic scaling is displayed. This relies on two crucial features of the phase diagram: () the marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling; and () the vicinity of the classical jamming critical point, as the cross-over temperature gets lowered when approaching it.