相关论文: The complete set of infinite volume ground states …
This dissertation discusses some properties of topologically ordered states as they appear in the setting of infinite quantum spin systems. We begin by studying the set of infinite volume ground states for Kitaev's abelian quantum double…
Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this…
The ground states of an abstract model in quantum field theory are investigated. By means of the asymptotic field theory, we give a necessary and sufficient condition for that the expectation value of the number operator of ground states is…
We give a complete classification of the anyon sectors of Kitaev's quantum double model on the infinite triangular lattice and for finite gauge group $G$, including the non-abelian case. As conjectured, the anyon sectors of the model…
We consider a theory of superselection sectors for infinite quantum spin systems, describing charges that can be approximately localized in cone-like regions. The primary examples we have in mind are the anyons (or charges) in topologically…
We study ground-state and thermodynamic properties of an $S=1$ Kitaev model. We first clarify the existence of global parity symmetry in addition to the local symmetry on each plaquette, which enables us to perform the large scale…
This paper focuses on the generalized version of the quantum double model on arbitrary $N$-dimensional simplicial complexes with finite local regularity. The core of our analysis is a detailed characterization of the frustration-free ground…
The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is…
We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition $(A,B)$ of the lattice…
We set up a general structure for the analysis of ``frustration-free ground states'', or ``zero-energy states'', i.e., states minimizing each term in a lattice interaction individually. The nesting of the finite volume ground state spaces…
In this paper, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S=S_G+S_F, with S_F the…
We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $\alpha$ over $G$. The detailed properties of the ground states are studied, and we find that the…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
We model an atom-molecule Bose-Einstein condensate (AMBEC) using simplified set of coupled Gross-Pitaevskii equations (GPE), where we neglect the background (elastic) scattering length of the atoms. We analyze the ground state numerically…
In this comprehensive study of Kitaev's abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the…
We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of…
We introduce a frustration-free, one-dimensional model of spinless fermions with hopping, p-wave superconducting pairing and alternating chemical potentials. The model possesses two exactly degenerate ground states even for finite system…
We prove Haag duality for conelike regions in the ground state representation corresponding to the translational invariant ground state of Kitaev's quantum double model for finite abelian groups. This property says that if an observable…
We generalize the classical one dimensional Potts model to the case where the symmetry group is a non-Abelian finite group. It turns out that this new model has a quantum nature in that its spectrum of energy eigenstates consists of…
Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all…