Detector observables pose a fundamental challenge for nonperturbative lattice methods due to their intrinsically real-time and asymptotic nature. We propose quantum simulation platforms as an ideal setting for studying these observables. Using quantum spin systems as a demonstration, we construct lattice detector operators and establish their connection to continuum energy-flow observables. We demonstrate this framework in the $1+1$ -dimensional quantum Ising model, where finite lattice calculations show quantitative agreement with conformal field theory expectations at criticality. These results support the interpretation of the lattice flow operators as regulated counterparts of continuum detectors in the scaling and asymptotic limits, providing a concrete route toward realizing high-energy collider physics on table-top quantum platforms.Detector observables pose a fundamental challenge for nonperturbative lattice methods due to their intrinsically real-time and asymptotic nature. We propose quantum simulation platforms as an ideal setting for studying these observables. Using quantum spin systems as a demonstration, we construct lattice detector operators and establish their connection to continuum energy-flow observables. We demonstrate this framework in the $1+1$-dimensional quantum Ising model, where finite lattice calculations show quantitative agreement with conformal field theory expectations at criticality. These results support the interpretation of the lattice flow operators as regulated counterparts of continuum detectors in the scaling and asymptotic limits, providing a concrete route toward realizing high-energy collider physics on table-top quantum platforms.

hep-phCross-listedarXiv:2609.17664Sep 17, 20260 citations

The classical limit of quantum spin systems

Élliott H. Lieb

Communications in Mathematical PhysicsDec 1, 1973476 citations

The Classical Limit of Quantum Spin Systems

Élliott H. Lieb

Springer eBooksJan 1, 197331 citations

The Fate of Crystalline Topological Phenomena in the Continuum

Rajas Chari, Taylor L. Hughes

The continuum limit is a widely used theoretical construct for obtaining continuum field-theories of crystalline systems. We study the formulation of a continuum limit for gapped bosonic phases and ask whether their topological properties survive passage to the continuum. Using methods in algebraic topology and category theory, we give a rigorous formulation of the continuum limit and construct a surjective global map relating crystalline topological phases across all finite point-group symmetries to continuum invertible topological phases. Consequently, we find that some lattice phases admit no continuum limit, while distinct lattice phases that do admit a continuum limit can share the same continuum image, hence implying that some lattice topological data can collapse. Conversely, we find that every continuum invertible phase admits a faithful crystalline realization. In addition to the general framework, we apply it to several examples, including studies of a 2D rotation-symmetric phase, higher-order topological phases, and the mixed spin-lattice anomaly of the deconfined quantum critical point between an antiferromagnet and valence bond solid.The continuum limit is a widely used theoretical construct for obtaining continuum field-theories of crystalline systems. We study the formulation of a continuum limit for gapped bosonic phases and ask whether their topological properties survive passage to the continuum. Using methods in algebraic topology and category theory, we give a rigorous formulation of the continuum limit and construct a surjective global map relating crystalline topological phases across all finite point-group symmetries to continuum invertible topological phases. Consequently, we find that some lattice phases admit no continuum limit, while distinct lattice phases that do admit a continuum limit can share the same continuum image, hence implying that some lattice topological data can collapse. Conversely, we find that every continuum invertible phase admits a faithful crystalline realization. In addition to the general framework, we apply it to several examples, including studies of a 2D rotation-symmetric phase, higher-order topological phases, and the mixed spin-lattice anomaly of the deconfined quantum critical point between an antiferromagnet and valence bond solid.

arXiv:2608.11302Aug 11, 20260 citations

1+1

-dimensional quantum Ising model, where finite lattice calculations show quantitative agreement with conformal field theory expectations at criticality. These results support the interpretation of the lattice flow operators as regulated counterparts of continuum detectors in the scaling and asymptotic limits, providing a concrete route toward realizing high-energy collider physics on table-top quantum platforms.