arXiv subjects

Shiyu Cao

Publications and source records attributed to Shiyu Cao.

3 recordsLinked to original sources

arXiv2026

On the Asymptotics of the Volume of Hitchin Moduli Spaces

Let $X$ be a compact Riemann surface of genus $g\geq2$, and let $\M$ be the moduli space of rank-two trace-free Higgs bundles with fixed determinant of odd degree. For the normalization of the Hitchin metric used in this paper, we prove that the volume of geodesic ball in the Hitchin moduli space is given by $$ \Vol_{g_{L^2}}B_{L^2}(p,R) =\frac{2^{4g-3}\pi^{9g-9}}{(3g-3)!}\,R^{6g-6}+o(R^{6g-6}) $$ for every $p\in\M$. We also determine the leading asymptotics of Hamiltonian sublevel volumes and exponentially weighted volumes. The proof combines homogeneity of the hyperk\"ahler volume form with metric asymptotics on the regular Hitchin locus. Symplectic reduction and the Prym polarization evaluate the coefficient, which is independently recovered by equivariant localization.

math.DG↗

arXiv2026

On minimally 1-tough $(K_1\cup P_4)$-free graphs

Agraph G is minimally t-tough if the toughness of G is t and the deletion of any edge from G decreases its toughness, where t is a positive real number. It is conjectured that every $(K_1\cup P_4)$-free 1-tough graph is hamiltonian. In this paper, we characterize the structure of minimally 1-tough $(K_1\cup P_4)$-free graphs, and thus show that the above conjecture is true for minimally 1-tough graphs. Furthermore, it is also proved that the Kriesell's conjecture which states that each minimally 1-tough graph has a vertex of degree 2 holds for minimally 1-tough $(K_1\cup P_4)$-free graphs.

math.CO↗

arXiv2026

Topological quantum color code model on infinite lattice

The color code model is a crucial instance of a Calderbank-Shor-Steane (CSS)-type topological quantum error-correcting code, which notably supports transversal implementation of the full Clifford group. Its robustness against local noise is rooted in the structure of its topological excitations. From the perspective of quantum phases of matter, it is essential to understand these excitations in the thermodynamic limit. In this work, we analyze the color code model on an infinite lattice within the quasi-local $C^{*}$-algebra framework, using a cone-localized Doplicher-Haag-Roberts (DHR) analysis. We classify its irreducible anyon superselection sectors and construct explicit string operators that generate anyonic excitations from the ground state. We further examine the fusion and braiding properties of these excitations. Our results show that the topological order of the color code is described by $\mathsf{Rep}(D(\mathbb{Z}_2 \times \mathbb{Z}_2)) \simeq \mathsf{Rep}(D(\mathbb{Z}_2)) \boxtimes \mathsf{Rep}(D(\mathbb{Z}_2))$, which is equivalent to a double layer of the toric code and consistent with established analyses on finite lattices. We also establish the existence and uniqueness of the KMS state at every finite inverse temperature and derive an explicit description of the corresponding thermal distribution of stabilizer excitations.

quant-ph↗