We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, suc...We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, such as the Ising model,Hamiltonian model of quantum Hall effect, fermion pairing model, Kitaev honeycomb lattice model, and so on, are the short-range coupling cases of this knot lattice model. The long-range coupling knot lattice model bears Abelian and nonAbelian anyons, and shows integral and fractional filling states like the quantum Hall system. The fusion rules of anyons are explicitly demonstrated by braiding crossing states. The eigenstates of quantum models can be represented by a multilayer link lattice pattern whose topology is characterized by the linking number. This topological linking number offers a new quantity to explain and predict physical phenomena in conventional quantum models. For example, a convection flow loop is introduced into the well-known Bardeen–Cooper–Schrieffer fermion pairing model to form a vortex dimer state that offers an explanation of the pseudogap state of unconventional superconductors, and predicts a fractionally filled vortex dimer state. The integrally and fractionally quantized Hall conductance in the conventional quantum Hall system has an exact correspondence with the linking number in this multi-knot lattice model. The real-space knot pattern in the topological insulator model has an equivalent correspondence with the Lissajous knot in momentum space. The quantum phase transition between different quantum states of the quantum spin model is also directly quantified by the change of topological linking number, which revealed the topological character of phase transition. Circularized photons in an optical fiber network are a promising physical implementation of this multi-knot lattice, and provide a different path to topological quantum computation.展开更多
By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three...By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11304062)
文摘We proposed an entangled multi-knot lattice model to explore the exotic statistics of anyons. Long-range coupling interaction is a fundamental character of this knot lattice model. The short-range coupling models, such as the Ising model,Hamiltonian model of quantum Hall effect, fermion pairing model, Kitaev honeycomb lattice model, and so on, are the short-range coupling cases of this knot lattice model. The long-range coupling knot lattice model bears Abelian and nonAbelian anyons, and shows integral and fractional filling states like the quantum Hall system. The fusion rules of anyons are explicitly demonstrated by braiding crossing states. The eigenstates of quantum models can be represented by a multilayer link lattice pattern whose topology is characterized by the linking number. This topological linking number offers a new quantity to explain and predict physical phenomena in conventional quantum models. For example, a convection flow loop is introduced into the well-known Bardeen–Cooper–Schrieffer fermion pairing model to form a vortex dimer state that offers an explanation of the pseudogap state of unconventional superconductors, and predicts a fractionally filled vortex dimer state. The integrally and fractionally quantized Hall conductance in the conventional quantum Hall system has an exact correspondence with the linking number in this multi-knot lattice model. The real-space knot pattern in the topological insulator model has an equivalent correspondence with the Lissajous knot in momentum space. The quantum phase transition between different quantum states of the quantum spin model is also directly quantified by the change of topological linking number, which revealed the topological character of phase transition. Circularized photons in an optical fiber network are a promising physical implementation of this multi-knot lattice, and provide a different path to topological quantum computation.
文摘By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.
