Vortices in two-dimensional superconductors with broken time-reversal and spin-rotation symmetry can bind states at zero excitation energy. These so-called Majorana bound states transform a thermal insulator into a thermal metal and may be used to encode topologically protected qubits. We identify an alternative mechanism for the formation of Majorana bound states, akin to the way in which Shockley states are formed on metal surfaces: An electrostatic line defect can have a pair of Majorana bound states at the end points. The Shockley mechanism explains the appearance of a thermal metal in vortex-free lattice models of chiral p-wave superconductors and (unlike the vortex mechanism) is also operative in the topologically trivial phase. DOI: 10.1103/PhysRevLett.105.046803 PACS numbers: 73.20.At, 73.20.Hb, 74.20.Àz, 74.25.fc Two-dimensional superconductors with spin-polarizedtriplet, p-wave pairing symmetry have the unusual property that vortices in the order parameter can bind a nondegenerate state with zero excitation energy [1][2][3][4]. Such a midgap state is called a Majorana bound state, because the corresponding quasiparticle excitation is a Majorana fermion-equal to its own antiparticle. A pair of spatially separated Majorana bound states encodes a qubit, in a way which is protected from local sources of decoherence [5]. Since such a qubit might form the building block of a topological quantum computer [6], there is an intensive search [7][8][9][10][11][12] for two-dimensional superconductors with the required combination of broken time-reversal and spinrotation symmetries (symmetry class D [13]).The generic Bogoliubov-de Gennes Hamiltonian H of a chiral p-wave superconductor is only constrained by particle-hole symmetry, x H Ã x ¼ ÀH. At low excitation energies E (to second order in momentum p ¼ Ài@@=@r) it has the form H ¼ Áðp x x þ p y y Þ þ ½UðrÞ þ p 2 =2m z ; (1) for a uniform (vortex-free) pair potential Á. The electrostatic potential U (measured relative to the Fermi energy) opens up a band gap in the excitation spectrum. At U ¼ 0 the superconductor has a topological phase transition (known as the thermal quantum Hall effect) between two localized phases, one with and one without chiral edge states [14][15][16][17].Our key observation is that the Hamiltonian (1) on a lattice has Majorana bound states at the two end points of a linear electrostatic defect. The mechanism for the production of these bound states goes back to Shockley [18]: The band gap closes and then reopens upon formation of the defect, and as it reopens a pair of states splits off from the band edges to form localized states at the end points of the defect [see Fig. 1]. Such Shockley states appear in systems as varied as metals and narrow-band semiconductors [19], carbon nanotubes [20], and photonic crystals [21]. In these systems they are unprotected and can be pushed out of the band gap by local perturbations. In a superconductor, particle-hole symmetry requires the spectrum to be AEE symmetric, so an isolated bound state is co...

We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.

We study the effects of dephasing noise on a prototypical many-body localized system -the XXZ spin 1/2 chain with a disordered magnetic field. At times longer than the inverse dephasing strength the dynamics of the system is described by a probabilistic Markov process on the space of diagonal density matrices, while all off-diagonal elements of the density matrix decay to zero. The generator of the Markovian process is a bond-disordered spin chain. The scaling variable is identified, and independence of relaxation on the interaction strength is demonstrated. We show that purity and von Neumann entropy are extensive, showing no signatures of localization, while the operator space entanglement entropy exhibits a logarithmic growth with time until the final saturation corresponding to localization breakdown, suggesting a many-body localized dynamics of the effective Markov process.

We investigate how the Kondo screening cloud builds up as a function of space and time. Starting from an impurity spin decoupled from the conduction band, the Kondo coupling is switched on at time t=0. We work at the Toulouse point where one can obtain exact analytical results for the ensuing spin dynamics at both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts building up in the wake of the impurity spin being transported to infinity. In this buildup process the impurity spin--conduction band spin susceptibility shows a sharp light cone due to causality, while the corresponding correlation function has a tail outside the light cone. At T=0 this tail has a power law decay as a function of distance from the impurity, which we interpret as due to initial entanglement in the Fermi sea.Comment: 10 pages, 9 figure