Photonic Analog Quantum Simulation of (1+1)-Dimensional $U(1)$ Lattice Gauge Theory with Dynamical MatterPhotonic Analog Quantum Simulation of (1+1)-Dimensional $U(1)$ Lattice Gauge Theory with Dynamical Matter

Nathan R. Gonzalez, Thea Budde, Klemen Kersic +5 more

We propose a photonic scheme for analog quantum simulation of a $U(1)$ Lattice Gauge Theory (LGT) with dynamical matter based on the Jaynes-Cummings-Hubbard (JCH) model. Here, an array of interacting cavities in the strong-coupling regime of cavity Quantum Electrodynamics is mapped onto the alternating matter and gauge-field sites of the spin-1/2 Quantum Link Model. In contrast to other analog LGT quantum simulation methods, our approach implements the desired gauge-invariant dynamics through the hopping of polaritonic excitations among the array sites. The hopping is mapped to the gauge theory via precise tuning of polaritonic resonances in individual cavities. Using exact diagonalization, we show that the real-time evolution of the JCH model accurately replicates that of a Quantum Link Model. Finally, we discuss feasible routes to the beyond-classical simulation capability with scalable implementations in photonic and superconducting systems. This provides a novel route towards understanding the real-time dynamics of lattice gauge theories with matter in higher dimensions.We propose a photonic scheme for analog quantum simulation of a $U(1)$ Lattice Gauge Theory (LGT) with dynamical matter based on the Jaynes-Cummings-Hubbard (JCH) model. Here, an array of interacting cavities in the strong-coupling regime of cavity Quantum Electrodynamics is mapped onto the alternating matter and gauge-field sites of the spin-1/2 Quantum Link Model. In contrast to other analog LGT quantum simulation methods, our approach implements the desired gauge-invariant dynamics through the hopping of polaritonic excitations among the array sites. The hopping is mapped to the gauge theory via precise tuning of polaritonic resonances in individual cavities. Using exact diagonalization, we show that the real-time evolution of the JCH model accurately replicates that of a Quantum Link Model. Finally, we discuss feasible routes to the beyond-classical simulation capability with scalable implementations in photonic and superconducting systems. This provides a novel route towards understanding the real-time dynamics of lattice gauge theories with matter in higher dimensions.

hep-latCross-listedarXiv:2606.02756Jun 3, 20260 citations

Hybrid Quantum Monte Carlo Simulations of an Unconstrained U(1) Lattice Gauge Theory with Fermionic Matter

Ahlqvist Edwin

We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.We study a compact U(1) lattice gauge theory using a self-built Hybrid Monte Carlo (HMC) program. The starting point is the parton construction of the Heisenberg spin chain where the spins are fractionalized into spinons coupled to an emergent compact U(1) gauge field. Here we do not impose Gauss's law, such that the Hamiltonian describes an unconstrained lattice gauge theory. We make theoretical calculations of the ground-state phase diagram and identify an emergent SO(4) symmetry in the strong-coupling limit. Furthermore, the weak coupling limit corresponds to frozen gauge fields which results in a free fermionic phase that is unstable in one dimension. The phase diagram is supported by carrying out HMC simulations which also allow us to study the dynamical generation of Gauss's law at low energy scales. We find that the theory accurately predicts the numerical findings and establish that HMC works as a method for simulating unconstrained gauge theories in (1+1)-dimensions.

Jan 1, 20260 citations

Photonic Analog Quantum Simulation of (1+1)-Dimensional

U(1)

Lattice Gauge Theory with Dynamical Matter

We propose a photonic scheme for analog quantum simulation of a

U(1)

Lattice Gauge Theory (LGT) with dynamical matter based on the Jaynes-Cummings-Hubbard (JCH) model. Here, an array of interacting cavities in the strong-coupling regime of cavity Quantum Electrodynamics is mapped onto the alternating matter and gauge-field sites of the spin-1/2 Quantum Link Model. In contrast to other analog LGT quantum simulation methods, our approach implements the desired gauge-invariant dynamics through the hopping of polaritonic excitations among the array sites. The hopping is mapped to the gauge theory via precise tuning of polaritonic resonances in individual cavities. Using exact diagonalization, we show that the real-time evolution of the JCH model accurately replicates that of a Quantum Link Model. Finally, we discuss feasible routes to the beyond-classical simulation capability with scalable implementations in photonic and superconducting systems. This provides a novel route towards understanding the real-time dynamics of lattice gauge theories with matter in higher dimensions.