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.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.

hep-latCross-listedarXiv:2512.11068Physical review. D/Physical review. D.Dec 15, 20250 citations

Theory of Spin Lattices and Lattice Gauge Models

J. W. Clark, MANFRED L. RISTIG

Springer eBooksJan 1, 19979 citations

Percolation as a confinement order parameter in Z 2 lattice gauge theories

Simon M. Linsel, Annabelle Bohrdt, Lukas Homeier +2 more

Lattice gauge theories (LGTs) were introduced in 1974 by Wilson to study quark confinement. These models have been shown to exhibit (de)confined phases, yet it remains challenging to define experimentally accessible order parameters. Here we propose percolation-inspired order parameters (POPs) to probe confinement of dynamical matter in ${\mathbb{Z}}_{2}$ LGTs using electric field basis snapshots accessible to quantum simulators. We apply the POPs to study a classical ${\mathbb{Z}}_{2}$ LGT and find a confining phase up to temperature $T=\ensuremath{\infty}$ in two dimensions (critical ${T}_{c}$ , i.e., finite- $T$ phase transition, in three dimensions) for any nonzero density of ${\mathbb{Z}}_{2}$ charges. Further, using quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice Fradkin-Shenker phase diagram at $T=0$ and explore the phase diagram at $T>0$ . The correlation length exponent coincides with the one of the three-dimensional Ising universality class and we determine the POP critical exponent characterizing percolation. Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators, making them suitable as a probe for quantum spin liquids.Lattice gauge theories (LGTs) were introduced in 1974 by Wilson to study quark confinement. These models have been shown to exhibit (de)confined phases, yet it remains challenging to define experimentally accessible order parameters. Here we propose percolation-inspired order parameters (POPs) to probe confinement of dynamical matter in ${\mathbb{Z}}_{2}$ LGTs using electric field basis snapshots accessible to quantum simulators. We apply the POPs to study a classical ${\mathbb{Z}}_{2}$ LGT and find a confining phase up to temperature $T=\ensuremath{\infty}$ in two dimensions (critical ${T}_{c}$, i.e., finite-$T$ phase transition, in three dimensions) for any nonzero density of ${\mathbb{Z}}_{2}$ charges. Further, using quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice Fradkin-Shenker phase diagram at $T=0$ and explore the phase diagram at $T>0$. The correlation length exponent coincides with the one of the three-dimensional Ising universality class and we determine the POP critical exponent characterizing percolation. Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators, making them suitable as a probe for quantum spin liquids.

arXiv:2401.08770Physical review. B./Physical review. BDec 2, 202410 citations

Phase transition in one-dimensional lattice gauge theories

Mohammad Khorrami

arXiv:hep-th/9412090International Journal of Theoretical PhysicsMar 1, 19961 citation

Digital quantum simulation of lattice gauge theories in three spatial dimensions

Julian Bender, Erez Zohar, Alessandro Farace +1 more

In the present work, we propose a scheme for the digital formulation of lattice gauge theories with dynamical fermions in 3 + 1 dimensions. All interactions are obtained as a stroboscopic sequence of two-body interactions with an auxiliary system. This enables quantum simulations of lattice gauge theories where the magnetic four-body interactions arising in two and more spatial dimensions are obtained without the use of perturbation theory, thus resulting in stronger interactions compared with analogue approaches. The simulation scheme is applicable to lattice gauge theories with either compact or finite gauge groups. The required bounds on the digitization errors in lattice gauge theories, due to the sequential nature of the stroboscopic time evolution, are provided. Furthermore, an implementation of a lattice gauge theory with a non-abelian gauge group, the dihedral group D 3 , is proposed employing the aforementioned simulation scheme using ultracold atoms in optical lattices.In the present work, we propose a scheme for the digital formulation of lattice gauge theories with dynamical fermions in 3 + 1 dimensions. All interactions are obtained as a stroboscopic sequence of two-body interactions with an auxiliary system. This enables quantum simulations of lattice gauge theories where the magnetic four-body interactions arising in two and more spatial dimensions are obtained without the use of perturbation theory, thus resulting in stronger interactions compared with analogue approaches. The simulation scheme is applicable to lattice gauge theories with either compact or finite gauge groups. The required bounds on the digitization errors in lattice gauge theories, due to the sequential nature of the stroboscopic time evolution, are provided. Furthermore, an implementation of a lattice gauge theory with a non-abelian gauge group, the dihedral group D 3 , is proposed employing the aforementioned simulation scheme using ultracold atoms in optical lattices.

arXiv:1804.02082New Journal of PhysicsAug 20, 2018113 citations

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.

{\mathbb{Z}}_{2}

LGTs using electric field basis snapshots accessible to quantum simulators. We apply the POPs to study a classical

{\mathbb{Z}}_{2}

LGT and find a confining phase up to temperature $T=\ensuremath{\infty}$ in two dimensions (critical

{T}_{c}

, i.e., finite-

T

phase transition, in three dimensions) for any nonzero density of

{\mathbb{Z}}_{2}

charges. Further, using quantum Monte Carlo we demonstrate that the POPs reproduce the square lattice Fradkin-Shenker phase diagram at

T=0

and explore the phase diagram at

T>0

. The correlation length exponent coincides with the one of the three-dimensional Ising universality class and we determine the POP critical exponent characterizing percolation. Our proposed POPs provide a geometric perspective of confinement and are directly accessible to snapshots obtained in quantum simulators, making them suitable as a probe for quantum spin liquids.