Universal nonequilibrium signatures of Majorana zero modes in quench dynamics

The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of "quantum quench" to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${\cal L}(t)=| < \psi(0) | \psi(t) > |^2\sim t^{-\alpha}$ for large times after the quench, with a universal critical exponent $\alpha$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.Comment: 9 pages + appendices, 4 figures. v3: published versio

Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model

The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of Q by construction, it was only shown very recently that the spin representation can be promoted to the same level of generality. In this paper we show how to define the Potts model in terms of observables that simultaneously keep track of the spin and FK degrees of freedom. This is first done algebraically in terms of a transfer matrix that couples three different representations of a partition algebra. Using this, one can study correlation functions involving any given number of propagating spin clusters with prescribed colours, each of which contains any given number of distinct FK clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the Kac form h_{r,s}, with integer indices r,s that we determine exactly both in the bulk and in the boundary versions of the problem. In particular, we find that the set of points where an FK cluster touches the hull of its surrounding spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains this set to points where the neighbouring spin cluster extends to infinity, we show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table

Quantum Brownian motion in a quasiperiodic potential

We consider a quantum particle subject to Ohmic dissipation, moving in a bichromatic quasiperiodic potential. In a periodic potential the particle undergoes a zero-temperature localization-delocalization transition as dissipation strength is decreased. We show that the delocalized phase is absent in the quasiperiodic case, even when the deviation from periodicity is infinitesimal. Using the renormalization group, we determine how the effective localization length depends on the dissipation. We show that {a similar problem can emerge in} the strong-coupling limit of a mobile impurity moving in a periodic lattice and immersed in a one-dimensional quantum gas.Comment: 5+6 pages, 1 figur

Localization-protected order in spin chains with non-Abelian discrete symmetries

We study the non-equilibrium phase structure of the three-state random quantum Potts model in one dimension. This spin chain is characterized by a non-Abelian $D_3$ symmetry recently argued to be incompatible with the existence of a symmetry-preserving many-body localized (MBL) phase. Using exact diagonalization and a finite-size scaling analysis, we find that the model supports two distinct broken-symmetry MBL phases at strong disorder that either break the ${\mathbb{Z}_3}$ clock symmetry or a ${\mathbb{Z}_2}$ chiral symmetry. In a dual formulation, our results indicate the existence of a stable finite-temperature topological phase with MBL-protected parafermionic end zero modes. While we find a thermal symmetry-preserving regime for weak disorder, scaling analysis at strong disorder points to an infinite-randomness critical point between two distinct broken-symmetry MBL phases.Comment: 5 pages, 3 figures main text; 6 pages, 3 figures supplemental material; Version 2 includes a corrected the form of the chiral order parameter, and corresponding data, as well as larger system size numerics, with no change to the phase structur

Particle-hole symmetry, many-body localization, and topological edge modes

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders.Comment: 9 pages. 7 figure

alpha,beta-Unsaturated 2-Acyl-Imidazoles in Asymmetric Biohybrid Catalysis

International audienceα,β‐Unsaturated acylimidazoles have been used in a plethora of enantioselective transformations over the years and have unsurprisingly become privileged building blocks for asymmetric catalysis. Interestingly however, their use in asymmetric biohybrid catalysis as bidentate substrates able to interact with artificial metalloenzymes has only recently emerged, expanding considerably in the last few years. Easy to prepare and to post‐transform, α,β‐unsaturated acylimidazoles appear as leading synthons for the asymmetric construction of C−C and C−O bonds. This Minireview highlights the current and increasing interest of these key building blocks in the context of asymmetric biohybrid catalysis with the aim to stimulate further research into their still unexploited potential. The use of these α,β‐unsaturated acylimidazoles in metal‐catalyzed and organocatalyzed transformations will be covered in a back‐to‐back Minireview by Renata Marcia de Figueiredo, Jean‐Marc Campagne and co‐workers