arXiv subjects

Vasilii Iugov

Publications and source records attributed to Vasilii Iugov.

4 recordsLinked to original sources

arXiv2026

Tropical WKB asymptotics of NRS coordinates for opers in $SU(2)$, $N_f=4$ theory

We study the semiclassical limit of SL_2-opers on the four-punctured sphere in Nekrasov-Rosly-Shatashvili Darboux coordinates. Using exact Wentzel-Kramers-Brillouin (WKB) connection formulae, we express the trace coordinates of the corresponding SL_2(C) character variety as finite Laurent sums of Voros exponentials. Tropicalizing these formulae and the NRS relations gives a chamberwise integer affine linear system for the leading logarithms of the NRS coordinates. In chambers where this system is unimodular and the selected cycles form a primitive symplectic pair, the leading asymptotics agree, up to flavor-period shifts, with Seiberg-Witten periods of the N=2 SU(2) theory with N_f=4 fundamental hypermultiplets. We verify this mechanism in a sample chamber and in the weak-coupling degeneration. No global coordinate-independent recovery theorem is claimed; non-unimodular or degenerate chambers are treated as limitations of the chosen NRS chart. In the weak-coupling degeneration, we show that the NRS chart can be chosen compatibly with the plumbing limit so that the resulting chamber is unimodular and non-degenerate away from tropical walls.

hep-th↗

arXiv2025

Yang-Mills flows for multilayered graphene

We clarify the origin of magic angles in twisted multilayered graphene using Yang-Mills flows in two dimensions. We relate the effective Hamiltonian describing the electrons in the multilayered graphene to the ${\bar\partial}_{A}$ operator on a two dimensional torus coupled to an $SU(N)$ gauge field. Despite the absence of a characteristic class such as $c_{1}$ relevant for the quantum Hall effect, we show that there are topological invariants associated with the zero modes occuring in a family of Hamiltonians. The flatbands in the spectrum of the effective Hamiltonian are associated with Yang-Mills connections, studied by M.Atiyah and R.Bott long time ago. The emergent $U(1)$ magnetic field with nonzero flux is presumably responsible for the observed Hall effect in the absence of (external) magnetic field. We provide a numeric algorithm transforming the original single-particle Hamiltonian to the direct sum of ${\bar\partial}_{A}$ operators coupled to abelian gauge fields with non-zero $c_1$'s. Our perspective gives a simple bound for magic angles: if the gauge field $A(α)$ is such that the YM energy $\Vert F_{A(α)} \Vert^2$ is smaller than that of $U(1)$ magnetic flux embedded into $SU(2)$, then $α$ is not magic.

hep-th↗

arXiv2025

Two-dimensional topological paramagnets protected by $\mathbb{Z}_3$ symmetry: Properties of the boundary Hamiltonian

We systematically study gapless edge modes corresponding to $\mathbb{Z}_3$ symmetry-protected topological (SPT) phases of two-dimensional three-state Potts paramagnets on a triangular lattice. First, we derive microscopic lattice models for the gapless edge and, using the density-matrix renormalization group (DMRG) approach, investigate the finite-size scaling of the low-lying excitation spectrum and the entanglement entropy. Based on the obtained results, we identify the universality class of the critical edge, namely the corresponding conformal field theory and the central charge. Finally, we discuss the inherent symmetries of the edge models and the emergent winding number symmetry. As a result, one-dimensional chains with this symmetry form a model that supports gapless excitations due to its tricritical symmetry. Numerically, we show that low-energy states in the continuous limit of the edge model can be described by conformal field theory (CFT) with central charge $c=1$, given by the coset $SU_k(3)/SU_k(2)$ CFT at level k=1.

cond-mat.str-el↗

arXiv2023

$Z_3$ and $(\times Z_3)^3$ symmetry protected topological paramagnets

We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by $(\times Z_3)^3\equiv Z_3\times Z_3\times Z_3$ symmetry and smaller $Z_3$ symmetry. We derive microscopic models for the gapless edge, uncover their symmetries, and analyze the conformal properties. We study the properties of the gapless edge by employing the numerical density-matrix renormalization group (DMRG) simulation and exact diagonalization. We discuss the corresponding conformal field theory, its central charge, and the scaling dimension of the corresponding primary field. We argue that the low energy limit of our edge modes is defined by the $SU_k(3)/SU_k(2)$ coset conformal field theory with the level $k=2$. The discussed two-dimensional models realize a variety of symmetry-protected topological phases, opening a window for studies of the unconventional quantum criticalities between them.

cond-mat.str-el↗