共查询到20条相似文献,搜索用时 15 毫秒
1.
We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Zp) gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n dimensional vector space which we call Hn. The Zp gauge particles act on the vertex particles and thus Hn can be thought of as a C(Zp) module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n and p, though we believe this feature holds for all n>p. We will see that non-Abelian anyons of the quantum double of C(S3) are obtained as part of the vertex excitations of the model with n=6 and p=3. Ising anyons are obtained in the model with n=4 and p=2. The n=3 and p=2 case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Zp. This makes them possible candidates for realizing quantum computation. 相似文献
2.
We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z2)n-graded commutative associative algebra A. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonné determinant of quaternionic matrices, but in general our quaternionic determinant is different. We show that the graded determinant of purely even (Z2)n-graded matrices of degree 0 is polynomial in its entries. In the case of the algebra A=H of quaternions, we calculate the formula for the Berezinian in terms of a product of quasiminors in the sense of Gelfand, Retakh, and Wilson. The graded trace is related to the graded Berezinian (and determinant) by a (Z2)n-graded version of Liouville’s formula. 相似文献
3.
We consider an extension of the standard model (SM) with three SU(2) scalar doublets and discrete S3⊗Z2 symmetries. The irreducible representation of S3 has a singlet and a doublet, and here we show that the singlet corresponds to the SM-like Higgs and the two additional SU(2) doublets forming a S3 doublet are inert. In general, in a three scalar doublet model, with or without S3 symmetry, the diagonalization of the mass matrices implies arbitrary unitary matrices. However, we show that in our model these matrices are of the tri-bimaximal type. We also analyzed the scalar mass spectra and the conditions for the scalar potential is bounded from below at the tree level. We also discuss some phenomenological consequences of the model. 相似文献
4.
We study heterotic asymmetric orbifold models. By utilizing the lattice engineering technique, we classify (22,6)-dimensional Narain lattices with right-moving non-Abelian group factors which can be starting points for Z3 asymmetric orbifold construction. We also calculate gauge symmetry breaking patterns. 相似文献
5.
We show that a quantized Berry phase in Bloch momentum space can serve as a topological order parameter to the quantum phases of a gapped spin chain system with time-reversal invariance. Specifically, we study this approach analytically in a class of XY spin-1/2 chain with multiple sites interactions in a transverse field. In order to derive a proper definition of the Berry curvature in a two-dimensional parameter space, we performed a local gauge transformation to the spin chain system by a twist operator, which endows the Hamiltonian of the system with the topology of a torus T2 without changing its energy spectrum. We show that a topological Z2 order parameter can be obtained as a quantized Berry phase by a loop integral of the Berry gauge potential along quarter of the Brillouin zone, which determines the zero-temperature phase diagram of the system. 相似文献
6.
Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric–magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids , which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the Z2-symmetric toric code, SO(2N)1 and SU(3)1 state as well as the S3-symmetric SO(8)1 state and a non-Abelian chiral state we call the “4-Potts” state. 相似文献
7.
We discuss three Hamiltonians, each with a central-field part H0 and a PT-symmetric perturbation igz. When H0 is the isotropic Harmonic oscillator the spectrum is real for all g because H is isospectral to H0+g2/2. When H0 is the Hydrogen atom then infinitely many eigenvalues are complex for all g. If the potential in H0 is linear in the radial variable r then the spectrum of H exhibits real eigenvalues for 0<g<gc and a PT phase transition at gc. 相似文献
8.
We propose a six-dimensional Universal Extra Dimensions (UED) model compactified on a real projective plane RP2, a two-sphere with its antipodal points being identified. We utilize the Randjbar-Daemi–Salam–Strathdee spontaneous sphere compactification with a monopole configuration of an extra UX(1) gauge field that leads to a spontaneous radius stabilization. Unlike the sphere and the S2/Z2 orbifold compactifications, the massless UX(1) gauge boson is safely projected out. We show how a compactification on a non-orientable manifold results in a chiral four-dimensional gauge theory by utilizing 6D chiral gauge and Yukawa interactions. The resultant Kaluza–Klein mass spectra are distinct from the ordinary UED models compactified on torus. We briefly comment on the anomaly cancellation and also on a possible dark matter candidate in our model. 相似文献
9.
We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable Si=±1 on the i-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable Jij=±1 describes a state of the synaptic connection between j-th and i-th neurons. The gauge symmetry allows for a self-coupling energy among Jij’s such as JijJjkJki, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of Jij, (II) a quenched model with full connections where Jij is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III). 相似文献
10.
We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H and transverse magnetic field Ω. Using the effective-field theory (EFT) with correlation in cluster with N=1 spin we calculate the thermodynamic properties as a function of temperature with values H and Ω fixed. The model consists of ferromagnetic interaction Jx in the x direction and antiferromagnetic interaction Jy in the y direction, and it is found that for H/Jy∈[0,2] the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=Jx/Jy=1 (isotropic square lattice). 相似文献
11.
Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z) in He-like atomic ions for the range of (fractional) nuclear charges Z lying between the known critical value Zc=0.911 at which I(Z) tends to zero and Z=2. They showed that it is possible to fit I(Z) to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of Zc for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z) for these series. 相似文献
12.
A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3. We propose to use the probabilistic and unambiguous state extraction scheme as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity fX to display quantum features, i.e., we find a threshold CX for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successful then we find a filterable outcome with average fidelity fX,0 that can be greater than fX. In addition, we find the threshold concurrence of the channel CX,0 in order for the average fidelity fX,0 to display quantum features and surprisingly, the threshold concurrence CX,0 can be less than CX. Even more, we find some special cases for which the threshold values become zero. 相似文献
13.
The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T), frequency (w), Onsager coefficient (γ) and external magnetic field (H) near the second-order (Tc) and first-order (Tt) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α). Our investigations revealed that only one peak is obtained near Tt and three peaks are found near Tc when the Onsager coefficient is varied at a given constant frequency for q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4 and 6 near Tc. The sound attenuation peaks are observed near Tt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear. 相似文献
14.
15.
The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric 2F1, 1F1 and 0F1 functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins. 相似文献
16.
In this paper we study the infinitesimal deformations of the Z3-color Lie superalgebra Ln,m,p. By means of these deformations all filiform Z3-color Lie superalgebras can be obtained. In particular, we give a method that will allow us to determine the dimension of the subspaces that are composed by linearly integrable deformations. 相似文献
17.
We continue the study of U(1) vortices with cholesteric vacuum structure. A new class of solutions is found which represent global vortices of the internal spin field. These spin vortices are characterized by a non-vanishing angular dependence at spatial infinity, or winding. We show that despite the topological Z2 behavior of SO(3) windings, the topological charge of the spin vortices is of the Z type in the cholesteric. We find these solutions numerically and discuss the properties derived from their low energy effective field theory in 1+1 dimensions. 相似文献
18.
Alexander Moroz 《Annals of Physics》2014,340(1):252-266
The Rabi model describes the simplest interaction between a cavity mode with a frequency ωc and a two-level system with a resonance frequency ω0. It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to Δ=ω0/(2ωc)=0, which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy ?, which are orthogonal on an equidistant lattice. A non-zero value of Δ leads to non-classical discrete orthogonal polynomials ?k(?) and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model. The number of ca. 1350 calculable energy levels per parity subspace obtained in double precision (cca 16 digits) by an elementary stepping algorithm is up to two orders of magnitude higher than is possible to obtain by Braak’s solution. Any first n eigenvalues of the Rabi model arranged in increasing order can be determined as zeros of ?N(?) of at least the degree N=n+nt. The value of nt>0, which is slowly increasing with n, depends on the required precision. For instance, nt?26 for n=1000 and dimensionless interaction constant κ=0.2, if double precision is required. Given that the sequence of the lth zeros xnl’s of ?n(?)’s defines a monotonically decreasing discrete flow with increasing n, the Rabi model is indistinguishable from an algebraically solvable model in any finite precision. Although we can rigorously prove our results only for dimensionless interaction constant κ<1, numerics and exactly solvable example suggest that the main conclusions remain to be valid also for κ≥1. 相似文献
19.
S. Sakhi 《Physica A》2013
This paper examines the multicritical behavior of a generalized U(N1)×U(N2) Ginzburg–Landau theory containing two multicomponent complex fields which couple differently to two gauge fields described by two Maxwell terms and one mixed-Chern–Simons term. This model is relevant to the dynamics of Cooper pairs and vortices in a self-dual Josephson junction array system near its superconductor–insulator transition. We develop a renormalization group flow at fixed dimension and obtain the beta functions at one loop when both disorder fields are critical. Two sets of infrared-stable charged fixed points solutions are found for N>Nc: partially charged solutions with respect to the gauge fields exist with Nc=35.6, and fully charged solutions exist with Nc=12.16. We show that fine tuning the ratio of the two energy scales in the model has the effect of reducing the critical number Nc and thus enlarges the region where the quantum phase transition is continuous. It is also found that the decoupled fixed point which is stable in the neutral case is no longer attainable in the presence of fluctuating gauge fields. We probe the conductivity at the critical point and show that it has a universal character determined by the renormalization group infrared-stable fixed-point values of the gauge couplings. 相似文献
20.
We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo–Kobayashi–Maskawa (CKM) unitarity triangle, α≈90°. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5), a discrete family symmetry such as A4 or S4, a shaping symmetry including products of Z2 and Z4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of α≈90° by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1–3 texture zeros that satisfy the “phase sum rule” and lepton mass matrices that satisfy the “lepton mixing sum rule” together with a new prediction that the leptonic CP violating oscillation phase is close to either 0°, 90°, 180°, or 270° depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors. 相似文献