Related papers: Kitaev models based on unitary quantum groupoids

In this paper, we give a generalization of Kitaev's stabilizer code based on chain complex theory of bicommutative Hopf algebras. Due to the bicommutativity, the Kitaev's stabilizer code extends to a broader class of spaces, e.g. finite…

In this paper, we will introduce Quantum Toric Varieties which are (non-commutative) generalizations of ordinary toric varieties where all the tori of the classical theory are replaced by quantum tori. Quantum toric geometry is the…

We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the…

In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the previous cotangent…

We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…

We study groups generated by three half-turns in the Lobachevsky $3$-space and their quotient orbifolds. These generalized triangle groups are closely related to the arbitrary 2-generator Kleinian groups. Our main result is a classification…

Integrable multistate or multiflavor/color models were recently introduced. They are generalizations of models corresponding to the defining representations of the U_q(sl(m)) quantum algebras. Here I show that a similar generalization is…

Fusion surface models, as introduced by Inamura and Ohmori, extend the concept of anyon chains to 2+1 dimensions, taking fusion 2-categories as their input. In this work, we construct and analyze fusion surface models on the honeycomb…

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general…

We conjecture that appropriate K-theoretic Gromov-Witten invariants of complex flag manifolds G/B are governed by finite-difference versions of Toda systems constructed in terms of the Langlands-dual quantized universal enveloping algebras…

We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…

Categorified quantum groups play an increasing role in quantum topology and representation theory. The Steenrod algebra is a fundamental component of algebraic topology. In this paper we show that categorified quantum groups can be extended…

We introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the formalism to the generalized Seiberg-Witten equations and show…

We combine tensor-network approaches and high-order linked-cluster expansions to investigate the quantum phase diagram of the antiferromagnetic Kitaev's honeycomb model in a magnetic field for general spin values. For the pure Kitaev model,…

We generalize the asymptotic faithfulness of the skein quantum $SU(2)$ representations of mapping class groups of orientable closed surfaces to skein $SU(3)$. Skein quantum representations of mapping class groups are different from the…

We establish the equivalence between $U(1)$ Chern-Simons and Reshetikhin-Turaev TQFTs associated with finite quadratic modules. For gauge group $U(1)$ and even level $k$, we prove that the corresponding Chern-Simons TQFT is naturally…

Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest…

After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We…

In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in [WW1].

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…