Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model

Abstract

We investigate a non-Abelian SU$(2)$ quantum link model in $2+1$ dimensions on a hexagonal lattice using tensor network methods. We determine the static quark potential for a wide range of bare coupling values and find that the theory is confining. We also probe the existence of a Lüscher term and find a clear signal with a $g^2$ dependent coefficient, in qualitative agreement with a strong coupling expansion. Correspondingly, the width of the strings scales logarithmically with the string length again for all $g^2$-values, providing evidence for a rough string, with no indication for a roughening transition.

v3: minor revisions to match published version

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• The Width of the Confining String in Yang-Mills Theory
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• Digitising SU(2) Gauge Fields and the Freezing Transition
• Continuum limit of string formation in 3-d SU(2) LGT
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• From Decay to Complete Breaking: Pulling the Strings in SU(2) Yang-Mills Theory
• Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition and Free Theory
• Hidden order and symmetry protected topological states in quantum link ladders
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension
• Dynamics in Hamiltonian Lattice Gauge Theory: Approaching the Continuum Limit with Partitionings of SU$(2)$