相关论文: Quantum loop models and the non-abelian toric code

We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model…

Inspired by the topological insulator circuit proposed and experimentally verified by Jia., et al. \cite{1}, we theoretically realized the topological Lieb lattice, a line centered square lattice with rich topological properties, in a…

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, Abelian U(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information…

Although the topological order is known as a quantum order in quantum many-body systems, it seems that there is not a one-to-one correspondence between topological phases and quantum phases. As a well-known example, it has been shown that…

Non-Abelian anyons are fractional excitations of gapped topological models believed to describe certain topological superconductors or quantum Hall states. Here, we provide the first numerical evidence that they emerge as independent…

We study a generalization of Kitaev's abelian toric code model defined on CW complexes. In this model qudits are attached to $n$ dimensional cells and the interaction is given by generalized star and plaquette operators. These are defined…

Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…

Gaining insight about ensembles of magnetic configurations, that could originate the confining string tension between quarks, constitutes a major concern in current lattice investigations. This interest also applies to a different approach,…

We describe four closely related Hubbard-like models (models A, B, C and D) of particles that can hop on a 2D Kagome lattice interacting via Coulomb repulsion. The particles can be either bosons (models A and B) or (spinless) fermions…

We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…

Topological quantum computation relies on control of non-Abelian anyons for inherently fault-tolerant storage and processing of quantum information. By now, blueprints for topological qubits are well developed for electrically active…

We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids - spin-analogues of fractional non-Abelian quantum Hall states- with gapped bulk and gapless chiral edge excitations described…

We study theoretically the topological quantum phase transition in Cavity QED lattice. We predict the condition for non-topological phase to the topological phase transition conditions for three different model Hamiltonians in cavity QED…

Ring exchange is an elementary interaction for modeling unconventional topological matters which hold promise for efficient quantum information processing. We report the observation of four-body ring-exchange interactions and the…

We construct SU($N$) toric code model describing the dynamics of SU($N$) electric and magnetic fluxes on a two dimensional torus. We show that the model has $N^2$ topologically distinct ground states $|\psi_0\rangle_{({\mathsf p},{\mathsf…

Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and…

We exactly solve a four-site spin model with site-dependent Kitaev's coupling in a tetrahedron by means of an analytical diagonalization. The non-abelian fusion rules of eigen vortex excitations in this small lattice model are explicitly…

Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host…

The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin-spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows…

We construct in the K matrix formalism concrete examples of symmetry enriched topological phases, namely intrinsically topological phases with global symmetries. We focus on the Abelian and non-chiral topological phases and demonstrate by…