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arXiv:2512.11068 · Physical review. D/Physical review. D.

Asymptotic-freedom and massive glueballs in a qubit-regularized SU(2) gauge theory

Rui Xian Siew, Shailesh Chandrasekharan, Tanmoy Bhattacharya

hep-latcond-mat.str-elhep-thnucl-thquant-phSubmitted Dec 11, 2025• Announced Dec 15, 2025• 0 citations• Revised Jan 20, 2026 (v3)
v1 · Dec 11, 2025v2 · Jan 12, 2026v3 · Jan 20, 2026
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Abstract

We argue that a simple qubit-regularized $\mathrm{SU}(2)$ lattice gauge theory (LGT) on a plaquette chain serves as a pseudo-one-dimensional toy model for Yang-Mills (YM) theory in three spatial dimensions. We map the chain Hamiltonian to the Transverse Field Ising Model (TFIM) in a uniform magnetic field and demonstrate that it can be tuned to a continuum limit in which the short-distance physics is governed by the asymptotically free Ising conformal field theory (CFT) describing free Majorana fermions, while the long-distance regime contains massive excitations of the $E_8$ quantum field theory (QFT) that can be interpreted as one-dimensional analogues of glueballs. Furthermore, we find $\sqrtσ/m_1 = 0.249(1)$ where $σ$ is the string tension between two static quarks and $m_1$ is the mass of the lightest glueball.

Journal reference
Phys. Rev. D 113, 114522 (2026)
DOI
10.1103/2cy4-cp7f
Comments
8 pages, 9 figures. Computed the space-time asymmetry factor required to correctly compute the universal ratio involving the string tension. Added Supplementary Material, one figure, and two references. Corrected a typo in the Supplementary Material

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We argue that a simple qubit-regularized SU(2)\mathrm{SU}(2)SU(2) lattice gauge theory (LGT) on a plaquette chain serves as a pseudo-one-dimensional toy model for Yang-Mills (YM) theory in three spatial dimensions. We map the chain Hamiltonian to the Transverse Field Ising Model (TFIM) in a uniform magnetic field and demonstrate that it can be tuned to a continuum limit in which the short-distance physics is governed by the asymptotically free Ising conformal field theory (CFT) describing free Majorana fermions, while the long-distance regime contains massive excitations of the E8E_8E8​ quantum field theory (QFT) that can be interpreted as one-dimensional analogues of glueballs. Furthermore, we find σ/m1=0.249(1)\sqrtσ/m_1 = 0.249(1)σ​/m1​=0.249(1) where σσσ is the string tension between two static quarks and m1m_1m1​ is the mass of the lightest glueball.
We show that a simple qubit-regularized SU(3)\mathrm{SU}(3)SU(3) lattice gauge theory on a plaquette chain admits a continuum limit with massive gauge-invariant excitations, providing a minimal toy model of strong interactions without quarks. By mapping the plaquette-chain Hamiltonian to the three-state quantum clock model in a magnetic field, we demonstrate that the theory can be tuned to a continuum limit governed at short distances by the Z3\mathbb{Z}_3Z3​ parafermion conformal field theory, which serves as the ultraviolet fixed point. A small relevant magnetic perturbation then drives the system to a massive continuum quantum field theory in the infrared, featuring relativistic particles. In this continuum theory we compute two universal ratios: the mass ratio of the lightest massive particles with opposite charge conjugation, m−/m+=1.459(2)m^{-}/m^{+} = 1.459(2)m−/m+=1.459(2), and σ/m+=0.2648(2)\sqrtσ/m^{+} = 0.2648(2)σ​/m+=0.2648(2), where σσσ denotes the string tension between a static quark and antiquark.
We construct simple qubit-regularized Hamiltonian lattice gauge theories formulated in the monomer--dimer--tensor-network (MDTN) basis that are free of sign problems in the pure gauge sector. These models naturally realize both confined and deconfined phases. Using classical Monte Carlo methods, we investigate the associated finite-temperature phase transitions and show that they exhibit the expected universality classes of conventional SU(N) lattice gauge theories in various spacetime dimensions. Furthermore, we argue that second-order quantum phase transitions separating the confined and deconfined phases are likely to exist. Such critical points would provide a nonperturbative route to defining continuum limits of qubit-regularized gauge theories, potentially allowing Yang--Mills theory and related continuum gauge theories to emerge from finite-dimensional lattice constructions.
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String Breaking Dynamics and Glueball Formation in a 2+12+12+1D Lattice Gauge Theory
With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the 2+12+12+1D Z2\mathbb{Z}_2Z2​ LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.
We construct simple qubit-regularized Hamiltonian lattice gauge theories formulated in the monomer--dimer--tensor-network (MDTN) basis that are free of sign problems in the pure gauge sector. These models naturally realize both confined and deconfined phases. Using classical Monte Carlo methods, we investigate the associated finite-temperature phase transitions and show that they exhibit the expected universality classes of conventional SU(N) lattice gauge theories in various spacetime dimensions. Furthermore, we argue that second-order quantum phase transitions separating the confined and deconfined phases are likely to exist. Such critical points would provide a nonperturbative route to defining continuum limits of qubit-regularized gauge theories, potentially allowing Yang--Mills theory and related continuum gauge theories to emerge from finite-dimensional lattice constructions.
Traditional SU ( N ) lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) V λ of the SU ( N ) gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps { λ ℓ } and monomer tensors on sites labeled by { λ s } . These tensors naturally define a local site Hilbert space, H s g , on which gauge transformations act. Gauss’s law introduces an additional index α s = 1 , 2 , … , D ( H s g ) that labels an orthonormal basis of the gauge-invariant subspace of H s g . This monomer-dimer tensor-network (MDTN) basis, | { λ s } , { λ ℓ } , { α s } ⟩ , of the physical Hilbert space enables the construction of new qubit-regularized SU ( N ) gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2) and SU(3) gauge theory in d = 2 and d = 3 spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in d = 1 , we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.