Search

We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms. [ABSTRACT FROM AUTHOR]

Nuclei colliding at very high energy create a strong, quasiclassical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromoelectric and chromomagnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For example, we find that the ratio of longitudinal to transverse pressure very early in the system behaves as pL/pT = −[1−...(Qτ)²]/[1−1/a(Qτ)²] + ...(Qτ)4, where τ is the longitudinal proper time, Q is related to the saturation scales Qs of the two nuclei, and a = ln(Q²/m²) with m a scale to be defined later. Our results are generally applicable if τ ≲ 1/Q. As already discussed in a previous paper, the transverse energy flow Si of the gluon field exhibits hydrodynamiclike contributions that follow transverse gradients of the energy density ∇iɛ. In addition, a rapidity-odd energy flow also emerges from the non-Abelian analog of Gauss' law and generates nonvanishing angular momentum of the field. We discuss the space-time picture that emerges from our analysis and its implications for observables in heavy-ion collisions. [ABSTRACT FROM AUTHOR]

We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete coefficients proportional to the corresponding topological charges. Applying the theory to the effective nonlinear sigma models for topological Fermi points with disorders in the framework of replica approach, we derive rigorously the Wess-Zumino terms with the topological charges being their levels in the two complex symmetry classes of A and AIII. Intriguingly, two nontrivial examples of quadratic Fermi points with the topological charge 2 are respectively illustrated for the classes A and AIII.We also address a qualitative connection of topological charges of Fermi points in the real symmetry classes to the topological terms in the nonlinear sigma models, based on the one-to-one classification correspondence. [ABSTRACT FROM AUTHOR]

Non-Abelian gauge potentials are quite relevant in subatomic physics, but they are relatively rare in a condensed matter context. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunneling microscopy and spectroscopy. At a magic twisted angle, θ ≈ (1.11 ± 0.05)°, a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, is observed in the tunneling density of states due to the action of the non-Abelian gauge fields. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunneling peaks with energy spacing δE ≈ νF/D ≈ 70 meV (here νF is the Fermi velocity of graphene and D is the period of the moir'e patterns). This indicates that the non-Abelian gauge potentials in twisted graphene bilayers confine low-energy electrons into a triangular array of quantum dots following the modulation of the moiré patterns. Our results also directly demonstrate that the Fermi velocity in twisted bilayers can be tuned from about 106 m/s to zero by simply reducing the twisted angle of about 2°. [ABSTRACT FROM AUTHOR]

Recent theoretical insights into the possibility of non-Abelian phases in ν = 2/3 fractional quantum Hall states revived the interest in the numerical phase diagram of the problem. We investigate the effect of various kinds of two-body interlayer couplings on the (330) bilayer state and exactly solve the Hamiltonian for up to 14 electrons on sphere and torus geometries. We consider interlayer tunneling, short-ranged repulsive/attractive pseudopotential interactions, and Coulomb repulsion. We find a 6-fold ground-state degeneracy on the torus when the interlayer hollow-core interaction is dominant. To identify the topological nature of this phase we measure the orbital-cut entanglement spectrum, quasihole counting, topological entanglement entropy, and wave-function overlap. Comparing the numerical results to the theoretical predictions, we interpret this 6-fold ground-state degeneracy phase to be the non-Abelian bilayer Fibonacci state. [ABSTRACT FROM AUTHOR]

The interplay between bulk spin-orbit coupling and electron-electron interactions produces umklapp scattering in the helical edge states of a two-dimensional topological insulator. If the chemical potential is at the Dirac point, umklapp scattering can open a gap in the edge state spectrum even if the system is time-reversal invariant. We determine the zero-energy bound states at the interfaces between a section of a helical liquid which is gapped out by the superconducting proximity effect and a section gapped out by umklapp scattering. We show that these interfaces pin charges which are multiples of e/2, giving rise to a Josephson current with 8π periodicity. Moreover, the bound states, which are protected by time-reversal symmetry, are fourfold degenerate and can be described as Z4 parafermions. We determine their braiding statistics and show how braiding can be implemented in topological insulator systems. [ABSTRACT FROM AUTHOR]

Gapped domain walls, as topological line defects between (2 + 1)D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which (2 + 1)D topological orders must have gapless edge modes, namely, which (1 + 1)D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix W, whose entries are the fusion-space dimensions Wia, to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries. [ABSTRACT FROM AUTHOR]

We relate the ground state degeneracy of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase into a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence with the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The ground state degeneracy resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin- Tao-Wu charge-pumping argument for Abelian fractional quantum Hall states to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a nontrivial cycle can pump a condensed anyon from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation. [ABSTRACT FROM AUTHOR]

We present a wide class of partially integrable lattice models with two-spin interactions which generalize the Kitaev honeycomb model. These models have a conserved quantity associated with each plaquette, conserved large loop operators on the torus, and topological degeneracy. We introduce a "slave-genon" approach which generalizes the Majorana fermion approach in the Kitaev model. The Hilbert space of our spin model can be embedded in an enlarged Hilbert space of non-Abelian twist defects, referred to as genons. In the enlarged Hilbert space, the spin model is exactly reformulated as a model of non-Abelian genons coupled to a discrete gauge field. We discuss in detail a particular Z3 generalization, and we show that in a certain limit the model is analytically tractable and produces a non-Abelian topological phase with chiral parafermion edge states. [ABSTRACT FROM AUTHOR]

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G's cohomology group H4(G,R/Z) in three-dimensional space and one-dimensional time (3 + 1D). We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 + 1D twisted gauge theory can be characterized by a representation of a modular transformation group, SL(3,Z). We express the SL(3,Z) generators Sxyz and Txy in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sxy and Txy of an SL(2,Z) subgroup to study the dimensional reduction of the 3D topological order C3D to a direct sum of degenerate states of 2D topological orders of in different flux b sectors: C3D = bC2Db. The 2D topological orders C2Db are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3(b), dimensionally reduced from the 4-cocycle ω4. We show that the SL(2,Z) generators, Sxy and Txy, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics. [ABSTRACT FROM AUTHOR]

We propose a general framework of nonlinear optics induced by non-Abelian Berry curvature in time-reversal-invariant (TRI) insulators. We find that the third-order response of a TRI insulator under optical and terahertz light fields is directly related to the integration of the non-Abelian Berry curvature over the Brillouin zone. We apply the result to insulators with rotational symmetry near the band edge. Under resonant excitations, the optical susceptibility is proportional to the flux of the Berry curvature through the iso-energy surface, which is equal to the Chern number of the surface times 2π. For the III-V compound semiconductors, microscopic calculations based on the six-band model give a third-order susceptibility with the Chern number of the iso-energy surface equal to 3. [ABSTRACT FROM AUTHOR]

We describe the braiding statistics of topological twist defects in fractional quantum Hall (FQH) states. In particular, we study Abelian bosonic (mmn) FQH states with bilayer symmetries. Twist defects are staircases that lift orbiting quasiparticles from one layer to another. These point defects exhibit semiclassical non-Abelian characteristics. We develop a procedure to evaluate consistent basis transformations (F symbols) of the defect fusion theory. Unlike quantum anyonic excitations of a topological phase, the exchange and braiding statistics of twist defects is not characterized by modular transformations, but instead a subcollection known as congruent transformations. We also characterize the projective nature of unitary braiding operations and relate it to the global Z 2 bilayer symmetry. [ABSTRACT FROM AUTHOR]

String-net models allow us to systematically construct and classify (2+1 )-dimensional [(2+1 )D] topologically ordered states which can have gapped boundaries. We can use a simple ideal string-net wave function, which is described by a set of F-matrices [or more precisely, a unitary fusion category (UFC)], to study all the universal properties of such a topological order. In this paper, we describe a finite computational method, Q-algebra approach, that allows us to compute the non-Abelian statistics of the topological excitations [or more precisely, the unitary modular tensor category (UMTC)], from the string-net wave function (or the UFC). We discuss several examples, including the topological phases described by twisted gauge theory [i.e., twisted quantum double Dα(G)]. Our result can also be viewed from an angle of holographic bulk-boundary relation. The (1 + 1 (-dimensional [(1 + 1 )D] anomalous topological orders, that can appear as edges of (2+1 )D topological states, are classified by UFCs which describe the fusion of quasiparticles in (1+ 1)D. The (1 +1 )D anomalous edge topological order uniquely determines the (2+1)D bulk topological order (which are classified by UMTC). Our method allows us to compute this bulk topological order (i.e., the UMTC) from the anomalous edge topological order (i.e., the UFC). [ABSTRACT FROM AUTHOR]

We introduce a broad class of simple models for quantum Hall states based on the expansion of their parent Hamiltonians near the one-dimensional limit of "thin cylinders," i.e., when one dimension Ly of the Hall surface becomes comparable to the magnetic length lB. Formally, the models can be viewed as topological generalizations of the 1D Hubbard model with center-of-mass-preserving hopping of multiparticle clusters. In some cases, we show that the models can be exactly solved using elementary techniques, and yield simple wave functions for the ground states as well as the entire neutral excitation spectrum. We study a large class of Abelian and non-Abelian states in this limit, including the Read-Rezayi Zk series, as well as states deriving from nonunitary or irrational conformal field theories: the "Gaffnian," "Haffnian," Haldane-Rezayi, and the "permanent" state. We find that the thin-cylinder limit of unitary (rational) states is "classical": their effective Hamiltonians reduce to only Hartree-type terms, the ground states are trivial insulators, and excitation gaps result from simple electrostatic repulsion. In contrast, for states deriving from nonunitary or irrational conformal field theories, the thin-cylinder limit is found to be intrinsically quantum; it contains hopping terms that play an important role in the structure of the ground states and in the energetics of the low-lying neutral excitations. [ABSTRACT FROM AUTHOR]

Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-Abelian anyonic chains. These phases display protected anyonic end modes. We consider spin-1/2 su(2)k chains at any level k, focusing on the most prominent examples: the case k = 2 describes Ising anyons (equivalent to Majorana fermions) and k = 3 corresponds to Fibonacci anyons. The method we develop is quite general and rests on a deep connection between boundary conformal field theory and topological symmetry. This method tightly constrains the nature of the topological insulating phases of these chains for general k. Emergent anyons which arise at domain walls are shown to have the same braiding properties as the physical quasiparticles. This suggests a "solid-state" topological quantum computation scheme in which emergent anyons are braided by tuning the couplings of non-Abelian quasiparticles in a fixed network. [ABSTRACT FROM AUTHOR]

We propose a scheme to induce Z3 parafermion modes, exotic zero-energy bound states that possess non-Abelian statistics. We consider a minimal setup consisting of a bundle of four tunnel coupled nanowires hosting spinless electrons that interact strongly with each other. The hallmark of our setup is that it relies only on simple one-dimensional wires, a uniform magnetic field, and strong interactions, but does not require the presence of superconductivity or exotic quantum Hall phases. [ABSTRACT FROM AUTHOR]

We propose a method to detect a signature of non-Abelian statistics in a one-dimensional (ID) superconducting wire by tuning the effective coupling between a pair of Majorana particles. Our experiment requires a single wire with two segments in the topological superconducting phase and a total of four Majorana particles. We show that an appropriately timed "pulse" in the coupling between the two middle Majoranas leads to a coherent rotation of the two qubits associated with the pairs of Majoranas in the two topological superconducting segments, in much the same way that an appropriate-length pulse of a transverse magnetic field can be used to rotate spins in nuclear magnetic resonance. This can be exploited both to probe the correlations of the Majoranas and to manipulate the Majorana qubits in these 1D wires. We discuss the experimental requirements for such a coherent rotation to be observable when the wire system is coupled to a fermionic bath. [ABSTRACT FROM AUTHOR]

The topological order is encoded in the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order for topological band models through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice models with bosonic particles. We identify multiple independent minimal entangled states (MESs) in the ground state manifold on a torus. The extracted modular S matrix from MESs faithfully demonstrates the Ising anyon or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings unambiguously demonstrate the topological nature of the quantum states for these flatband models without using the knowledge of model wave functions. [ABSTRACT FROM AUTHOR]

The article discusses the study which builds the non-Abelian topological order for topological band models using entanglement entropy measurement. The study involves non-Abelian Moore-Read and Read-Rezayi states' quasiparticle statistics on lattice models with bosonic particles. The study identifies multiple independent minimal entangled states (MESs) in torus's ground state manifolds in which a modular S matrix from MESs was extracted and demonstrates Fibonacci quasiparticle.

We study a quantum point contact in the fractional quantum Hall regime at Landau level filling factors v = 1/3 and 5/2. By using exact diagonalizations in the cylinder geometry, we identify the edge modes in the presence of a parabolic confining potential. By changing the sign of the potential, we can access both the tunneling through the bulk of the fluid and the tunneling between spatially separated droplets. This geometry is realized in the quantum point contact geometry for two-dimensional electron gases. In the case of the model Moore-Read Pfaffian state at filling factor v = 5/2, we identify the conformal towers of many-body eigenstates including the non-Abelian sector. By a Monte-Carlo technique, we compute the various scaling exponents that characterize the edge modes. In the case of hard-core interactions whose ground states are exact model wave functions, we find equality of neutral and charged velocities, both bosonic and fermionic, for the Pfaffian state [ABSTRACT FROM AUTHOR]

We study the dynamics of color fields as generated by simple configurations of relativistic particles with Abelian and non-Abelian [SU(2)] charges in the classical limit. We find that chromodynamic (non-Abelian) systems generally show Coulomb-like features by analogy with electrodynamics. A peculiar feature in the non-Abelian case is the additional strength of the chromoelectric and chromomagnetic fields caused by the contribution of changing the color charge. This change of color SU(2) charges results in a rotation of the color vector, which is getting very fast at close partonic distances. The presence of this non-Abelian additional term in the chromoelectric and chromomagnetic fields creates a color charge glow, which is manifested as a distinct color wave disturbance arising due to the finite distance at which the color interaction becomes active. This situation may be relevant to the hadronization phase in ultrarelativistic heavy-ion collisions, where the partonic state is governed by strong local color fluctuations. [ABSTRACT FROM AUTHOR]

Following an earlier construction of exactly soluble lattice models for Abelian fractional topological insulators in two and three dimensions, we construct here an exactly soluble lattice model for a non-Abelian v = 1 quantum Hall state and a non-Abelian topological insulator in two dimensions. We show that both models are topologically ordered, exhibiting fractionalized charge, ground-state degeneracy on the torus, and protected edge modes. The models feature non-Abelian vortices which carry fractional electric charge in the quantum Hall case and spin in the topological insulator case. We analyze the statistical properties of the excitations in detail and discuss the possibility of extending this construction to three-dimensional non-Abelian topological insulators [ABSTRACT FROM AUTHOR]

It is well known that the three-dimensional (3D) electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry preserving, at the expense of having surface-topological order. In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian. We show that the surface-topological order provides a complete nonperturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topological Mott insulators. [ABSTRACT FROM AUTHOR]

Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Zd gauge group and non-Abelian Kitaev D(G) models on different geometries. Focusing on the special case of Z2 gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wave function for the Z2 theory away from the exactly solvable limit, and to demonstrate the confining or deconfining phase transition of the Wilson loop order parameter. [ABSTRACT FROM AUTHOR]

We develop an approach to realizing a topological phase transition and non-Abelian braiding statistics with dynamically induced Floquet Majorana fermions (FMFs). When the periodic driving potential does not break fermion parity conservation, FMFs can encode quantum information. Quasienergy analysis shows that a stable FMF zero mode and two other satellite modes exist in a wide parameter space with large quasienergy gaps, which prevents transitions to other Floquet states under adiabatic driving. We also show that in the asymptotic limit FMFs preserve non-Abelian braiding statistics and, thus, behave like their equilibrium counterparts. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices. [ABSTRACT FROM AUTHOR]

We introduce a novel class of low-dimensional topological tight-binding models that allow for bound states that are fractionally charged fermions and exhibit non-Abelian braiding statistics. The proposed model consists of a double (single) ladder of spinless (spinful) fermions in the presence of magnetic fields. We study the system analytically in the continuum limit as well as numerically in the tight-binding representation. We find a topological phase transition with a topological gap that closes and reopens as a function of system parameters and chemical potential. The topological phase is of the type BDI and carries two degenerate midgap bound states that are localized at opposite ends of the ladders. We show numerically that these bound states are robust against a wide class of perturbations. [ABSTRACT FROM AUTHOR]

We propose a discrete model—the twisted quantum double model—of 2D topological phases based on a finite group G and a 3-cocycle α over G. The detailed properties of the ground states are studied, and we find that the ground-state subspace can be characterized in terms of the twisted quantum double Dα(G) of G. When α is the trivial 3-cocycle, the model becomes Kitaev's quantum double model based on the finite group G, in which the elementary excitations are known to be classified by the quantum double D (G) of G. Our model can be viewed as a Hamiltonian extension of the Dijkgraaf-Witten topological gauge theories to the discrete graph case with gauge group being a finite group. We also demonstrate a duality between a large class of Levin-Wen string-net models and certain twisted quantum double models, by mapping the string-net 6j symbols to the corresponding 3-cocycles. [ABSTRACT FROM AUTHOR]

The search for Majorana fermions in p-wave paired fermionic systems has recently moved to the forefront of condensed matter research. Here we propose an alternative route and show theoretically that Majorana-like modes can be realized and probed in a driven-dissipative system of strongly correlated photons consisting of a chain of tunnel-coupled cavities, where p-wave pairing effectively arises from the interplay between strong on-site interactions and two-photon parametric driving. The nonlocal nature of these exotic modes could be demonstrated through cross-correlation measurements carried out at the ends of the chain--revealing a strong photon-bunching signature--and their non-Abelian properties could be simulated through tunnel-braid operations. [ABSTRACT FROM AUTHOR]

Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagome lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-Abelian gauge fields. [ABSTRACT FROM AUTHOR]

We study the composite charged spin texture (CST) over the Moore-Read quantum Hall state that arises when a collection of elementary CSTs is moved to the same location. Following an algebraic approach based on the characteristic pair correlations of the Moore-Read state, we find that the spin texture associated with a composite CST is set by the fusion sector of the underlying non-Abelian quasiparticles. This phenomenon provides a novel way to read out the quantum register of a non-Abelian topologically ordered phase. [ABSTRACT FROM AUTHOR]

We consider the exchange statistics of vortices, each of which traps an odd number (N) of Majorana fermions. We assume that the fermions in a vortex transform in the vector representation of the SO(A') group. Exchange of two vortices turns out to be non-Abelian, and the corresponding operator is further decomposed into two parts: a part that is essentially equivalent to the exchange operator of vortices having a single Majorana fermion in each vortex, and a part representing the Coxeter group. Similar decomposition was already found in the case with N = 3, and the result shown here is a generalization to the case with an arbitrary odd N. We can obtain the matrix representation of the exchange operators in the Hubert space that is constructed by using Dirac fermions nonlocally defined by Majorana fermions trapped in separated vortices. We also show that the decomposition of the exchange operator implies tensor-product structure in its matrix representation. [ABSTRACT FROM AUTHOR]

We propose a model for inflation consisting of an axionic scalar field coupled to a set of three non-Abelian gauge fields. Our model's novel requirement is that the gauge fields begin inflation with a rotationally invariant vacuum expectation value (VEV) that is preserved through identification of SU(2) gauge invariance with rotations in three dimensions. The gauge VEV interacts with the background value of the axion, leading to an attractor solution that exhibits slow roll inflation even when the axion decay constant has a natural value (< MPl). Assuming a sinusoidal potential for the axion, we find that inflation continues until the axionic potential vanishes. The speed at which the axion moves along its potential is modulated by its interactions with the gauge VEV, rather than being determined by the slope of its bare potential. For sub-Planckian axion decay constants vanishingly small tensor to scalar ratios are predicted, a direct consequence of the Lyth bound. The parameter that controls the interaction strength between the axion and the gauge fields requires a technically natural tuning of …(100). [ABSTRACT FROM AUTHOR]

We consider the effect of quenched spatial disorder on systems of interacting, pinned non-Abelian anyons as might arise in disordered Hall samples at filling fractions v = 5/2 or v = 12/5. In one spatial dimension, such disordered anyon models have previously been shown to exhibit a hierarchy of infinite randomness phases. Here, we address systems in two spatial dimensions and report on the behavior of Ising and Fibonacci anyons under the numerical strong-disorder renormalization group (SDRG). In order to manage the topology-dependent interactions generated during the flow, we introduce a planar approximation to the SDRG treatment. We characterize this planar approximation by studying the flow of disordered hard-core bosons and the transverse field Ising model, where it successfully reproduces the known infinite randomness critical point with exponent &psgr; &ap; 0.49. Our main conclusion for disordered anyon models in two spatial dimensions is that systems of Ising anyons as well as systems of Fibonacci anyons do not realize infinite randomness phases, but flow back to weaker disorder under the numerical SDRG treatment. [ABSTRACT FROM AUTHOR]

We compute the nonequilibrium stress tensor induced by a heavy quark moving through weakly coupled QCD plasma at the speed of light and compare the result to N = 4 super-Yang-Mills theory at strong coupling. The QCD Boltzmann equation is reformulated as a Fokker-Planck equation in a leading logarithmic approximation, which is used to compute the induced stress. The transition from nonequilibrium at short distances to equilibrium at long distances is analyzed with first- and second-order hydrodynamics. Even after accounting for the obvious differences in shear lengths, the strongly coupled theory is significantly better described by hydrodynamics at subasymptotic distances. We argue that this difference between the kinetic and the anti-de Sitter space/conformal field theories is related to the second-order hydrodynamic coefficient &tgr;&pgr; &tgr;&pgr; is numerically large in units of the shear length for theories based on the Boltzmann equation. [ABSTRACT FROM AUTHOR]

We study the effect of spatial modulations in the interlayer hopping of graphene bilayers, such as those that arise upon shearing or twisting. We show that their single-particle physics, characterized by charge accumulation and recurrent formation of zero-energy bands as the pattern period L increases, is governed by a non-Abelian gauge potential arising in the low-energy electronic theory due to the coupling between layers. We show that such gauge-type couplings give rise to a potential that, for certain discrete values of L, spatially confines states at zero energy in particular regions of the moiré patterns. We also draw the connection between the recurrence of the flat zero-energy bands and the non-Abelian character of the potential. [ABSTRACT FROM AUTHOR]

We construct models of interacting itinerant non-Abelian anyons moving along one-dimensional chains, focusing, in particular, on itinerant Ising anyon chains, and derive effective anyonic t-J models for the low-energy sectors. Solving these models by exact diagonalization, we find a fractionalization of the anyons into charge and (non-Abelian) anyonic degrees of freedom--a generalization of spin-charge separation of electrons which occurs in Luttinger liquids. A detailed description of the excitation spectrum by combining spectra for charge and anyonic sectors requires a subtle coupling between charge and anyonic excitations at the microscopic level (which we also find to be present in Luttinger liquids), despite the macroscopic fractionalization. [ABSTRACT FROM AUTHOR]

I present a family of one-dimensional bosonic liquids analogous to non-Abelian fractional quantum Hall states. A new quantum number is introduced to characterize these liquids, the chiral momentum, which differs from the usual angular or linear momentum in one dimension. As their two-dimensional counterparts, these liquids minimize a ¿-body hard-core interaction with the minimum total chiral momentum. They exhibit global order, with a hidden organization of the particles in k identical copies of a one-dimensional Laughlin state. For k = 2 the state is a p-wave paired phase corresponding to the Pfaffian quantum Hall state. By imposing conservation of the total chiral momentum, an exact parent Hamiltonian is derived which involves long-range tunnehng and interaction processes with an amplitude decaying with the chord distance. This family of non-AbeUan liquids is shown to be in formal correspondence with a family of spin-j liquids which are total singlets made out of k indistinguishable resonating valence bond states. The corresponding spin Hamiltonians are obtained. [ABSTRACT FROM AUTHOR]