Dihedral non-Abelian Lattice Gauge Theories: Physics and Quantum Simulation

Lattice gauge theories provide a first-principles, non-perturbative formulation of the fundamental interactions of the Standard Model, and their Hamiltonian reformulation on a quantum simulator offers a promising route to regimes---real-time dynamics, finite baryon density---that lie beyond the reach of Euclidean Monte Carlo methods. With the ultimate goal of overcoming these shortcomings, over the last decade, quantum simulations of Abelian lattice gauge theories have expanded from the first proofs of principle to the experimental study of confinement and string breaking by pair production. One of the next frontiers lies in the simulation of non-Abelian theories, which are significantly more demanding both in local Hilbert space dimension and in symmetry-protection requirements, and ultimately essential for addressing open problems in high-energy physics. In this thesis, we investigate dihedral non-Abelian lattice gauge theories D_N---whose small order and finite local dimension make D₃ and D₄ natural targets for near-term quantum platforms---as a minimal yet physically rich arena for the study of non-Abelian gauge dynamics. After introducing dihedral groups and the associated lattice gauge theories, we propose a gauge-fixed ladder model that reduces the effective dimensionality while preserving the essential physics. We use it to show that the D₃ theory on a ladder displays a smooth crossover---rather than a sharp phase transition---between electric- and magnetic-dominated regimes, with the nonstabilizerness peaking in the crossover region. Furthermore, we introduce a formulation of the model compatible with the analysis of the Eigenstate Thermalization Hypothesis. We then study string breaking in pure-gauge D_N ladders in the presence of static charges through tensor-network DMRG simulations in the rishon formalism. We show that for odd $N$ static charges are screened by gluelumps---charge-glueball bound states enabled by the trivial centre of the group---while for even $N$ a fundamental flux string persists. Turning to the quantum-simulation side, we introduce a dynamical post-selection (DPS) protocol in which the local gauge charges are tested by mid-circuit measurements on auxiliary registers, and we show that gauge protection emerges through a sharp quantum Zeno transition in the spectrum of an associated Liouvillian. We verify the generality of this picture on \mathbb{Z}₂, \mathbb{Z}₃, and truncated $U(1)$ gauge groups, identifying an optimal window of measurement frequencies that survives also in the presence of noisy measurements. Finally, we benchmark DPS against an alternative post-processed symmetry verification scheme on a two-plaquette D₃ model designed for state-of-the-art qudit hardware. We find that both protocols significantly improve the reconstructed dynamics, with DPS tracking the exact evolution over longer times. Taken together, the results of this thesis position dihedral gauge theories as a concrete stepping stone from Abelian proofs of principle toward genuinely non-Abelian quantum simulation on near-term devices.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2026

Author dc:creator

• Ballini, Edoardo

Contributors dc:contributor

• Hauke, Philipp Hans Juergen
• Wauters, Matteo Michele

• LGTs, Quantum Simulation, Quantum Computation, non-Abelian LGTs, Dihedral groups
• Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
• Settore PHYS-02/A - Fisica teorica delle interazioni fondamentali, modelli, metodi matematici e applicazioni
• Settore PHYS-04/A - Fisica teorica della materia, modelli, metodi matematici e applicazioni

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Creative commons
• license uri:http://creativecommons.org/licenses/by-nc/4.0/

Language dc:language

eng

Handle dc:identifier

https://hdl.handle.net/11572/491110

OAI identifier oai:identifier

oai:iris.unitn.it:11572/491110