Entanglement generation by adiabatic navigation in the space of symmetric multi-particle states

We propose a technique for robust and efficient navigation in the Hilbert space of entangled symmetric states of a multiparticle system with externally controllable linear and nonlinear collective interactions. A linearly changing external field applied along the quantization axis creates a network of well separated level crossings in the energy diagram of the collective states. One or more transverse pulsed fields applied at the times of specific level crossings induce adiabatic passage between these states. By choosing the timing of the pulsed field appropriately, one can transfer an initial product state of all N spins into (i) any symmetric state with n spin excitations and (ii) the N-particle analog of the Greenberger-Horne-Zeilinger state. This technique, unlike techniques using pulses of specific area, does not require precise knowledge of the number of particles and is robust against variations in the interaction parameters. We discuss potential applications in two-component Bose condensates and ion-trap systems.Comment: 7 pages, 6 figure

Efficient path sampling on multiple reaction channels

Due to the time scale problem, rare events are not accessible by straight forward molecular dynamics. The presence of multiple reaction channels complicates the problem even further. The feasibility of the standard free energy based methods relies strongly on the success in finding a proper reaction coordinate. This can be very difficult task in high-dimensional complex systems and even more if several distinct reaction channels exist. Moreover, even if a proper reaction coordinate can be found, ergodic sampling will be a challenge. In this article, we discuss the recent advancements of path sampling methods to tackle this problem. We argue why the path sampling methods, via the transition interface sampling technique, is less sensitive to the choice of reaction coordinate. Moreover, we review a new algorithm, parallel path swapping, that can dramatically improve the ergodic sampling of trajectories for the multiple reaction channel systems.Comment: 7 pages, 4 figures. Article submitted for the proceedings of the Conference on Computational Physics, Brussels 200

Wall-Crossing in Coupled 2d-4d Systems

We introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS states in an N=2 supersymmetric 4d gauge theory coupled to a supersymmetric surface defect. When the theory and defect are compactified on a circle, we get a 3d theory with a supersymmetric line operator, corresponding to a hyperholomorphic connection on a vector bundle over a hyperkahler space. The 2d-4d wall-crossing formula can be interpreted as a smoothness condition for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can be determined for 4d theories of class S, that is, for those theories obtained by compactifying the six-dimensional (0,2) theory with a partial topological twist on a punctured Riemann surface C. For such theories there are canonical surface defects. We illustrate with several examples in the case of A_1 theories of class S. Finally, we indicate how our results can be used to produce solutions to the A_1 Hitchin equations on the Riemann surface C.Comment: 170 pages, 45 figure

Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model

We study the gapped phase of Kitaev's honeycomb model (a $Z_2$ spin liquid) on a lattice with topological defects. We find that some dislocations and string defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a $Z_2$ gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a $Z_2$ vortex around one of the dislocations. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes. To facilitate these theoretical developments, we recast the degenerate perturbation theory for spins in the language of Majorana fermions.Comment: 15 pages, 7 figures; added a brief history of twists, references, and clarified the count of the topological degeneracy of the ground stat