相关论文: Internal Levin-Wen models

We study the $t-V-V'$ model in one dimension at half-filling. It is known that for large enough $V$ fixed, as $V'$ is varied, the system goes from a charge-density wave into a Luttinger liquid, then a bond-order, and then a second charge…

The search for artificial structure with tunable topological properties is an interesting research direction of today's topological physics. Here, we introduce a scheme to realize `topological semimetal states' with a three-dimensional…

Topological matter is a popular topic in both condensed matter and cold atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in…

We revisit the Hitchin integrable system whose phase space is the bundle cotangent to the moduli space $N$ of holomorphic $SL_2$-bundles over a smooth complex curve of genus two. $N$ may be identified with the 3-dimensional projective space…

We present a detailed analysis of the classical Dicke-Jaynes-Cummings-Gaudin integrable model, which describes a system of $n$ spins coupled to a single harmonic oscillator. We focus on the singularities of the vector-valued moment map…

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase -- an interaction-driven topological insulator -- using cold atoms in an optical Lieb lattice. To this end, we study a…

For a topological space $X$, we introduce a criterion for the $\rm FI$ module $H^i({\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \times…

Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged…

A binary interface defect is any interface between two (not necessarily invertible) domain walls. We compute all possible binary interface defects in Kitaev's $\mathbb{Z}/p\mathbb{Z}$ model and all possible fusions between them. Our methods…

Topological photonics was embarked from realizing the first-order chiral state in gyromagnetic media, but its higher-order states were mostly studied in dielectric lattice instead. In this paper we theoretically unveil a hierarchy of…

We study composite solitons, consisting of domain walls and vortex lines attaching to the walls in two-component Bose-Einstein condensates. When the total density of two components is homogeneous, the system can be mapped to the O(3)…

A state sum construction on closed manifolds \'{a} la Kuperberg can be used to construct the partition functions of $3D$ lattice gauge theories based on involutory Hopf algebras, $\mathcal{A}$, of which the group algebras, $\mathbb{C}G$,…

We present a reconfigurable topological photonic system consisting of a 2D lattice of coupled ring resonators, with two sublattices of site rings coupled by link rings, which can be accurately described by a tight-binding model. Unlike…

A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with…

In an array of coupled cavities where the cavities are doped with an atomic V-system, and the two excited levels couple to cavity photons of different polarizations, we show how to construct various spin models employed in characterizing…

We study the topological phases in spin-orbit coupled dipolar bosons in a one-dimensional optical lattice. The magnetic dipolar interactions between atoms give rise to the inter-site interactions. In the Mott-insulating regime, this system…

Motivated by group-theoretical questions that arise in the context of asymptotic symmetries in gravity, we study model spaces and their quantization from the viewpoint of constrained Hamiltonian systems. More precisely, we propose that a…

We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel…

We study a class of two-dimensional spin models with the Kitaev-type couplings in mosaic structure lattices to implement topological orders. We show that they are exactly solvable by reducing them to some free Majorana fermion models with…

We study several integrable Hamiltonian systems on the moduli spaces of meromorphic functions on Riemann surfaces (the Riemann sphere, a cylinder and a torus). The action-angle variables and the separated variables (in Sklyanin's sense) are…