Measurement-Induced Phase Transition for Free Fermions above One Dimension.

A theory of the measurement-induced entanglement phase transition for free-fermion models in d>1 dimensions is developed. The critical point separates a gapless phase with ℓ^{d-1}lnℓ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with ℓ^{d-1} scaling, where ℓ is a size of the subsystem. The problem is mapped onto an SU(R) replica nonlinear sigma model in d+1 dimensions, with R→1. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for d=1+ε with ε≪1. Further, we carry out a numerical study of the transition for a d=2 model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, ν≈1.4.

Slow Many-Body Delocalization beyond One Dimension.

We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and timescales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder W_{c}(L,d) as a function of length L and width d. In the quasi-1D case W_{c} has a finite large-L limit at fixed d, which increases strongly with d. In the 2D case W_{c}(L,L) grows with L. The results are consistent with the avalanche picture of the many-body localization transition.

Giant Magnetoresistance in Carbon Nanotubes with Single-Molecule Magnets TbPc2.

We present experimental results and a theoretical model for the gate-controlled spin-valve effect in carbon nanotubes with side-attached single-molecule magnets TbPc2 (Terbium(III) bis-phthalocyanine). These structures show a giant magnetoresistance up to 1000% in experiments on single-wall nanotubes that are tunnel-coupled to the leads. The proposed theoretical model combines the spin-dependent Fano effect with Coulomb blockade and predicts a spin-spin interaction between the TbPc2 molecules, mediated by conducting electrons via the charging effect. This gate-tuned interaction is responsible for the stable magnetic ordering of the inner spins of the molecules in the absence of magnetic field. In the case of antiferromagnetic arrangement, electrons with either spin experience the scattering by the molecules, which results in blocking the linear transport. In strong magnetic fields, the Zeeman energy exceeds the effective antiferromagnetic coupling and one species of electrons is not scattered by molecules, which leads to a much lower total resistance at the resonant values of gate voltage, and hence to a supramolecular spin-valve effect.

Hanbury Brown-Twiss interference of anyons.

We present a study of a Hanbury Brown-Twiss interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate Hanbury Brown-Twiss cross correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmutation from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought of as intermediate between bosons and fermions.

Electron-electron interaction in the magnetoresistance of graphene.

We investigate the magnetotransport in large area graphene Hall bars epitaxially grown on silicon carbide. In the intermediate field regime between weak localization and Landau quantization, the observed temperature-dependent parabolic magnetoresistivity is a manifestation of the electron-electron interaction. We can consistently describe the data with a model for diffusive (magneto)transport that also includes magnetic-field-dependent effects originating from ballistic time scales. We find an excellent agreement between the experimentally observed temperature dependence of magnetoresistivity and the theory of electron-electron interaction in the diffusive regime. We can further assign a temperature-driven crossover to the reduction of the multiplet modes contributing to electron-electron interaction from 7 to 3 due to intervalley scattering. In addition, we find a temperature-independent ballistic contribution to the magnetoresistivity in classically strong magnetic fields.

Quantum critical fluctuations in disordered d-wave superconductors.

To explain the strong quasiparticle damping in the cuprates, Sachdev and collaborators proposed to couple the system to a critically fluctuating id(xy)- or is-order parameter mode. Here we generalize the approach to the presence of static disorder. In the id case, the order parameter dynamics becomes diffusive, but otherwise much of the phenomenology of the clean case remains intact. In contrast, the interplay of disorder and is-order parameter fluctuations leads to a secondary superconductor transition, with a critical temperature exponentially sensitive to the impurity concentration.