Extend the Levin-Wen model to two-dimensional topological orders with gapped boundary junctions

Abstract

A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of realizing topological quantum computation. To facilitate the study of such boundary defects, in this paper, we construct an exactly solvable Hamiltonian model of topological orders with gapped boundary junctions, where the boundary defects reside, by placing the Levin-Wen model on a disk, whose gapped boundary is separated into multiple segments by junctions. We derive a formula of the ground state degeneracy and an explicit ground-state basis of our model. We propose the notion of mobile and immobile charges on the boundary and find that they are quantum observables and label the ground-state basis. Our model is computation friendly.

Characterizing the ambiguity in topological entanglement entropy

“…Topological entanglement entropy can be systematically and analytically studied using the effective theories of topological orders, which are generally classified into two different kinds: the Chern-Simons (CS) theory [3], including the K-matrix theory [4,5], and the lattice models such as the Levin-Wen (LW) model [6][7][8][9][10] and the quantum double (QD) model [11][12][13][14][15]. In the lattice models, the overall Hilbert space is inherently structured as JHEP03(2024)074 a tensor product of the Hilbert spaces of local degrees of freedom (d.o.f.…”

Characteristic properties of a composite system of topological phases separated by gapped domain walls via an exactly solvable Hamiltonian model

“…Although a categorical description provides a crucial understanding of a 2+1D topological order, it focuses on the topological properties and omits some details of the topological system, specifically the local internal degrees of freedom of anyons that are not preserved under local perturbations. To overcome this limitation, one can represent the topological order through an exactly solvable lattice model given certain input data [1][2][3][12][13][14][15][16][17][18][19][20][21][22][23]. The lattice model explicitly provides the wavefunctions of elementary excitation states and uncovers the internal degrees of freedom using the input data, which are not apparent in a categorical theory.…”