Statistical Majorana Bound State Spectroscopy.

Tunnel spectroscopy data for the detection of Majorana bound states (MBS) is often criticized for its proneness to misinterpretation of genuine MBS with low-lying Andreev bound states. Here, we suggest a protocol removing this ambiguity by extending single shot measurements to sequences performed at varying system parameters. We demonstrate how such sampling, which we argue requires only moderate effort for current experimental platforms, resolves the statistics of Andreev side lobes, thus providing compelling evidence for the presence or absence of a Majorana center peak.

Emergence of Fermi's Golden Rule.

Fermi's golden rule applies in the limit where an initial quantum state is weakly coupled to a continuum of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing; this question arises in a number of recently investigated many-body systems. For different symmetry classes, we analytically and/or numerically calculate the universal crossovers in the average decay of the initial state as the level spacing is varied, with the golden rule emerging in the limit of a continuum. Among the corrections to the exponential decay of the initial state given by Fermi's golden rule is the appearance of the spectral form factor in the longtime regime for small but nonzero level spacing.

Transmon platform for quantum computing challenged by chaotic fluctuations.

From the perspective of many-body physics, the transmon qubit architectures currently developed for quantum computing are systems of coupled nonlinear quantum resonators. A certain amount of intentional frequency detuning ('disorder') is crucially required to protect individual qubit states against the destabilizing effects of nonlinear resonator coupling. Here we investigate the stability of this variant of a many-body localized phase for system parameters relevant to current quantum processors developed by the IBM, Delft, and Google consortia, considering the cases of natural or engineered disorder. Applying three independent diagnostics of localization theory - a Kullback-Leibler analysis of spectral statistics, statistics of many-body wave functions (inverse participation ratios), and a Walsh transform of the many-body spectrum - we find that some of these computing platforms are dangerously close to a phase of uncontrollable chaotic fluctuations.

Quantum Ergodicity in the Many-Body Localization Problem.

We generalize Page's result on the entanglement entropy of random pure states to the many-body eigenstates of realistic disordered many-body systems subject to long-range interactions. This extension leads to two principal conclusions: first, for increasing disorder the "shells" of constant energy supporting a system's eigenstates fill only a fraction of its full Fock space and are subject to intrinsic correlations absent in synthetic high-dimensional random lattice systems. Second, in all regimes preceding the many-body localization transition individual eigenstates are thermally distributed over these shells. These results, corroborated by comparison to exact diagonalization for an SYK model, are at variance with the concept of "nonergodic extended states" in many-body systems discussed in the recent literature.

Sachdev-Ye-Kitaev Non-Fermi-Liquid Correlations in Nanoscopic Quantum Transport.

Electronic transport in nanostructures, such as long molecules or 2D exfoliated flakes, often goes through a nearly degenerate set of single-particle orbitals. Here we show that in such cases a conspiracy of the narrow band and strong e-e interactions may stabilize a non-Fermi-liquid phase in the universality class of the complex Sachdev-Ye-Kitaev (SYK) model. Focusing on signatures in quantum transport, we demonstrate the existence of anomalous power laws in the temperature dependent conductance, including algebraic scaling T^{3/2} in the inelastic cotunneling channel, separated from the conventional Fermi liquid T^{2} scaling via a quantum phase transition. The relatively robust conditions under which these results are obtained indicate that the SYK non-Fermi-liquid universality class might not be as exotic as previously thought.

Quantum Criticality of Granular Sachdev-Ye-Kitaev Matter.

We consider granular quantum matter defined by Sachdev-Ye-Kitaev dots coupled via random one-body hopping. Within the framework of Schwarzian field theory, we identify a zero-temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping. The critical hopping strength scales inversely with the number of degrees of freedom on the dots. The increase of temperature out of either phase induces a crossover into a regime of strange metallic behavior.

Nonergodic Extended States in the Sachdev-Ye-Kitaev Model.

We analytically study spectral correlations and many body wave functions of a Sachdev-Ye-Kitaev model deformed by a random Hamiltonian diagonal in Fock space. Our main result is the identification of a wide range of intermediate coupling strengths where the spectral statistics is of Wigner-Dyson type, while wave functions are nonuniformly distributed over Fock space. The structure of the theory suggests that such manifestations of nonergodic extendedness may be a prevalent phenomenon in many body chaotic quantum systems.

Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders.

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our Letter is that, in practice, they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications.

Vanishing Density of States in Weakly Disordered Weyl Semimetals.

The Brillouin zone of the clean Weyl semimetal contains points at which the density of states (DOS) vanishes. Previous work suggested that below a certain critical concentration of impurities this feature is preserved including in the presence of disorder. This result got criticized for its neglect of rare disorder fluctuations which might bind quantum states and hence generate a finite DOS. We here show that in spite of their existence these states are so fragile that their contribution effectively vanishes when averaged over continuous disorder distributions. This means that the integrity of the nodal points remains protected for weak disorder.

Field Theory Approach to Many-Body Localization.

We introduce an analytic approach to many-body localization (MBL) in random spin chains. We consider MBL within a first quantized framework where it becomes a localization phenomenon in the high-dimensional lattice defined by the Hilbert space of the clean system. Designed in analogy with the field-theory description of single particle localization, our approach describes wave package propagation on that lattice after a disorder average has been performed and the system is controlled by only a few universal parameters. We discuss the stability of an ergodic weak disorder and a localized strong disorder phase, respectively, and demonstrate that the latter is protected by mechanisms which put MBL outside the universality class of Anderson localization.

Sinai Diffusion at Quasi-1D Topological Phase Transitions.

We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indices. Focusing on the example of thermal transport in class D ("Majorana") quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations-a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.

A review of sigma models for quantum chaotic dynamics.

We review the construction of the supersymmetric sigma model for unitary maps, using the color-flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization.

Effective Field Theory of the Disordered Weyl Semimetal.

In disordered Weyl semimetals, mechanisms of topological origin lead to the protection against Anderson localization, and at the same time to different types of transverse electromagnetic response-the anomalous Hall and the chiral magnetic effect. We here apply field theory methods to discuss the manifestation of these phenomena at length scales that are beyond the scope of diagrammatic perturbation theory. Specifically, we show how an interplay of symmetry breaking and the chiral anomaly leads to a field theory containing two types of topological terms. Generating the unconventional response coefficients of the system, these terms remain largely unaffected by disorder, i.e., information on the chirality of the system remains visible even at large length scales.

Geometric quantum noise of spin.

The presence of geometric phases is known to affect the dynamics of the systems involved. Here, we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nanomagnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application, we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

Multiterminal Coulomb-Majorana junction.

We study multiple helical nanowires in proximity to a common mesoscopic superconducting island, where Majorana fermion bound states are formed. We show that a weak finite charging energy of the center island may dramatically affect the low-energy behavior of the system. While for strong charging interactions, the junction decouples the connecting wires, interactions lower than a nonuniversal threshold may trigger the flow towards an exotic Kondo fixed point. In either case, the ideally Andreev reflecting fixed point characteristic for infinite capacitance (grounded) devices gets destabilized by interactions.

Incoherent scatterer in a Luttinger liquid: a new paradigmatic limit.

We address the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. The asymptotic behavior at zero temperature is governed by a new stable fixed point: A Goldstone mode dominates the low energy dynamics, leading to universal behavior. This limit is marked by equal probabilities for forward and backward scattering. Notwithstanding this nontrivial scattering pattern, we find that the shot noise as well as cross-current correlations vanish. We thus present a paradigmatic picture of an impurity in the Luttinger model, alternative to the Kane-Fisher picture.

Quantum chaos and effective thermalization.

We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a "quantum smoothened" approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.

Class D spectral peak in Majorana quantum wires.

Proximity coupled spin-orbit quantum wires purportedly support midgap Majorana states at critical points. We show that, in the presence of disorder, these systems generate a second band center anomaly, which is of different physical origin but shares key characteristics with the Majorana state: it is narrow in width, insensitive to magnetic fields, carries unit spectral weight, and is rigidly tied to the band center. Depending on the parity of the number of subgap quasiparticle states, a Majorana mode does or does not coexist with the impurity peak. The strong "entanglement" between the two phenomena may hinder an unambiguous detection of the Majorana by spectroscopic techniques.

Theory of the Anderson transition in the quasiperiodic kicked rotor.

We present the first microscopic theory of transport in quasiperiodically driven environments ("kicked rotors"), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of a dimensionless Planck constant h: for irrational values of h/(4π) they fall into the universality class of disordered electronic systems and we describe the corresponding localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a "supermetal." We discuss the ensuing possibility of a metal-supermetal quantum phase transition.

Rare events in population genetics: stochastic tunneling in a two-locus model with recombination.

We study the evolution of a population in a two-locus genotype space, in which the negative effects of two single mutations are overcompensated in a high-fitness double mutant. We discuss how the interplay of finite population size N and sexual recombination at rate r affects the escape times t(esc) to the double mutant. For small populations demographic noise generates massive fluctuations in t(esc). The mean escape time varies nonmonotonically with r, and grows exponentially as lnt(esc)∼N(r-r(*))(3/2) beyond a critical value r(*).