Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2502.15636

Spin-$s$ $Q$-systems: Twist and Open Boundaries

Yi-Jun He·Jue Hou·Yi-Chao Liu·Zi-Xi Tan
View original source ↗Read source document ↗Export metadata ↓

Abstract

In integrable spin chains, the spectral problem can be solved by the method of Bethe ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations. In this work, we systematically investigate the spin-$s$ XXX chain with twisted and open boundary conditions using the rational $Q$-system, which is a powerful tool to solve Bethe equations. We establish basic frameworks of the rational $Q$-system and confirm its completeness numerically in both cases. For twisted boundaries, we investigate the polynomiality conditions of the rational $Q$-system and derive physical conditions for singular solutions of Bethe equations. For open boundaries, we uncover novel phenomena such as hidden symmetries and magnetic strings under specific boundary parameters. Hidden symmetries lead to the appearance of extra degeneracies in the Hilbert space, while the magnetic string is a novel type of exact string configuration, whose length depends on the boundary magnetic fields. These findings, supported by both analytical and numerical evidences, offer new insights into the interplay between symmetries and boundary conditions.

Explore related subjects

hep-thcond-mat.stat-mechmath-phmath.MPnlin.SI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yi-Jun He, Jue Hou, Yi-Chao Liu, Zi-Xi Tan. 2025-07-05. Spin-$s$ $Q$-systems: Twist and Open Boundaries. https://doi.org/10.21468/scipostphyscore.8.3.057

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Off-shell recursion for all-loop planar integrands in Yang-Mills theory

In this paper, we develop in detail the off-shell recursion for planar loop integrands in Yang-Mills theory. Starting from the classical equations of motion solved with the perturbiner method, we derive an exact transfer-matrix representation of the pure-gluon sector. We then include the ghost contributions to the loop kernels based on \cite{Tao:2025fch}. Finally, as an example, we work out the two-loop recursion in detail and conclude a general recursion strategy for two-loop planar integrands whose external legs are gluons.

hep-th↗
arXiv2026

Criticality of ISCOs and AdS/CFT

We study the trajectories of massive particles in spherically symmetric black holes in arbitrary dimensions, and find certain universal features based on the topological classification of the fixed points. If the system admits a center, we find two possible outcomes: regardless of the value of the angular momentum, the center always survives, which is realized in global AdS spacetimes or, the center disappears below a critical value of angular momentum, which happens for various spherically symmetric black holes. For the latter case, we find that irrespective of the details of the black hole, there must always be a saddle point. Topological arguments show that there exists a certain critical value of energy, angular momentum and the angular velocity, where the center and the saddle coalesce. This happens at a special point in the parameter space where the trajectories are the limiting innermost stable circular orbits (ISCOs). At the critical point, conserved quantities show universal, van der Waals-like mean-field scaling typical of a second-order phase transition. The anomalous dimensions $γ$ of the double-twist operators in the CFT are found, both using AdS/CFT and through the the heavy-heavy-light-light four point correlators, giving negative and positive values for the center and saddle, respectively, including the emergence of certain non-analytic behaviour at the ISCO. For the center, we also find subleading corrections in $\frac{1}{Δ_H}$ to $γ$ in the dual CFT, and dsicuss the implications of our results.

hep-th↗
arXiv2026

Constraining F-theory Model Building with QCD Axions

In this paper, we investigate axion physics in 4D F-theory MSSM models. We derive the axion coupling term with QCD gauge fields and the axion potential from a top-down perspective, from both IIB superstring and the dual M-theory picture. For the explicit geometric model, we employ the "quadrillion" landscape of 4D F-theory models with the exact Standard Model chiral spectrum, and study simple base threefolds such as $\mathbb{P}^3$, $\mathbb{P}^1\times\mathbb{P}^2$, the generalized Hirzebruch threefold $\tilde{\mathbb{F}}_3$ and $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$. We derive exclusion constraints on the Kähler moduli space of the base threefold from the CP violation angle, the Standard Model gauge coupling constants and the stretched Kähler cone condition. We find stringent constraints on the set of base divisors that should be rigid or rigidified by the inclusion of flux. For the allowed regions of the parameter space, we estimate the typical mass of detectable QCD axions to be around $10^{-9}$eV, and the axion decay constant to be around $f_a\sim 10^{15}$GeV.

hep-th↗