Photonic Simulation of Majorana-Based Jones Polynomials.

By braiding non-Abelian anyons it is possible to realize fault-tolerant quantum algorithms through the computation of Jones polynomials. So far, this has been an experimentally formidable task. In this Letter, a photonic quantum system employing two-photon correlations and nondissipative imaginary-time evolution is utilized to simulate two inequivalent braiding operations of Majorana zero modes.

Chiral Spin-Chain Interfaces Exhibiting Event-Horizon Physics.

The interface between different quantum phases of matter can give rise to novel physics, such as exotic topological phases or nonunitary conformal field theories. Here we investigate the interface between two spin chains in different chiral phases. Surprisingly, the mean field theory approximation of this interacting composite system is given in terms of Dirac fermions in a curved space-time geometry.

Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation.

Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions the system can be effectively described by a rich variety of topologically massive gauge theories. Among these effective theories, we obtain an extended Chern-Simons theory with higher order derivatives as well as two coupled Chern-Simons theories.

Specific heat of 2D interacting Majorana fermions from holography.

Majorana fermions are a fascinating medium for discovering new phases of matter. However, the standard analytical tools are very limited in probing the non-perturbative aspects of interacting Majoranas in more than one dimensions. Here, we employ the holographic correspondence to determine the specific heat of a two-dimensional interacting gapless Majorana system.

Photonic implementation of Majorana-based Berry phases.

Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies alike. The exotic statistics of anyons realized in physical systems can be interpreted as a topological version of geometric phases. However, non-Abelian statistics has not yet been demonstrated in the laboratory.

Topological Quantum Liquids with Long-Range Couplings.

Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological properties. We demonstrate that, even though topological phases are intimately linked to the notion of locality, the infinite-range couplings give rise to topological zero and nonzero energy Majorana end modes depending on the boundary conditions of the system.

Optimal free descriptions of many-body theories.

Interacting bosons or fermions give rise to some of the most fascinating phases of matter, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids and Mott insulators. Although these systems are promising for technological applications, they also present conceptual challenges, as they require approaches beyond mean-field and perturbation theory. Here we develop a general framework for identifying the free theory that is closest to a given interacting model in terms of their ground-state correlations.

Simulating the exchange of Majorana zero modes with a photonic system.

The realization of Majorana zero modes is in the centre of intense theoretical and experimental investigations. Unfortunately, their exchange that can reveal their exotic statistics needs manipulations that are still beyond our experimental capabilities. Here we take an alternative approach.

Induced topological phases at the boundary of 3D topological superconductors.

We present tight-binding models of 3D topological superconductors in class DIII that support a variety of winding numbers. We show that gapless Majorana surface states emerge at their boundary in agreement with the bulk-boundary correspondence. At the presence of a Zeeman field, the surface states become gapped and the boundary behaves as a 2D superconductor in class D.

Entropic barriers for two-dimensional quantum memories.

Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses.

Abelian Chern-Simons-Maxwell theory from a tight-binding model of spinless fermions.

Abelian Chern-Simons-Maxwell theory can emerge from the bosonization of the (2+1)-dimensional Thirring model that describes interacting Dirac fermions. Here we show how the Thirring model manifests itself in the low energy limit of a two-dimensional tight-binding model of spinless fermions. To establish that, we employ a modification of Haldane's model, where the "doubling" of fermions is rectified by adiabatic elimination.

Bringing order through disorder: localization of errors in topological quantum memories.

Anderson localization emerges in quantum systems when randomized parameters cause the exponential suppression of motion. Here we consider this phenomenon in topological models and establish its usefulness for protecting topologically encoded quantum information. For concreteness we employ the toric code.

Quantum walks with non-Abelian anyons.

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface, by modeling it with a discrete time quantum walk. During the evolution, the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants.

Cold atom simulation of interacting relativistic quantum field theories.

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model.

Graphene with geometrically induced vorticity.

At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes.

Geometric phases and criticality in spin systems.

A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behaviour is presented. This opens up the way for the use of geometric phases as a tool to probe regions of criticality without having to undergo a quantum phase transition. As a concrete example, a spin-1/2 chain with XY interactions is considered and the corresponding geometric phases are analysed.

Geometric phases and criticality in spin-chain systems.

A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that corresponds to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated.

Three-spin interactions in optical lattices and criticality in cluster Hamiltonians.

We demonstrate that in a triangular configuration of an optical lattice of two atomic species a variety of novel spin-1/2 Hamiltonians can be generated. They include effective three-spin interactions resulting from the possibility of atoms tunneling along two different paths. This motivates the study of ground state properties of various three-spin Hamiltonians in terms of their two-point and n-point correlations as well as the localizable entanglement.

Quantum computation with a one-dimensional optical lattice.

We present an economical dynamical control scheme to perform quantum computation on a one-dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the lattice. They can be activated by external laser beams resulting in a two-qubit phase gate or in an exchange interaction.