ZN Gauge theories on a lattice and quantum memory

Chenyang Wang, Jim Harrington, John P. Preskill

Giovanni Cataldi

Anuj Apte

This thesis investigates gauge theories by combining theoretical analysis of non-invertible symmetries with computational simulations using neural network quantum states. We first investigate (3+1)d ZN gauge theories with non-invertible duality symmetries that arise from gauging one-form symmetries. These symmetries impose strict constraints on renormalization group flows, often prohibiting symmetry-preserving gapped phases. Our proof demonstrates that a self-dual theory with ZN one-form symmetry must either remain gapless or break self-duality, except when N = k²ℓ with –1 as a quadratic residue modulo ℓ. Lattice gauge theories provide concrete realizations of these constraints. We then focus on the development of neural network quantum states for studying lattice gauge theories. By implementing gauge-invariant neural networks, we compute ground-state wavefunctions for ZN lattice gauge theories in (2+1)d. For Z2 gauge theory, we characterize the continuous confinement transition and identify critical exponents consistent with the Ising universality class. In the Z3 case we observe a weakly first-order transition between the confined and deconfined phases. For both theories, we compute order and disorder parameters and verify the linear confining potential in the confining phase. These results demonstrate that neural network methods provide a powerful tool for studying quantum field theories computationally. By combining these simulations with symmetry-based analysis, this work uncovers new insights into the nonperturbative dynamics and phase structure of gauge theories.

M. Bögli

Yoshiteru Tamura, Kiyoshi Kudo, T. Hashimoto

We introduce the mutual information to the Zn lattice gauge theory for testing the degree of correlations. It is shown that our simulation result for the plaquettes gives a clear peak on the critical point.

Kaustubh Roy, Elio J. König

Motivated by the exotic phenomenology of certain quantum materials and recent advances in programmable quantum emulators, we here study fermions and bosons in ZN lattice gauge theories. We introduce a family of exactly soluble models, and characterize their orthogonal (semi)metallic ground states, the excitation spectrum, and the correlation functions. We further study integrability-breaking perturbations using an appropriately derived set of Feynman diagrammatic rules and borrowing physics associated to Anderson's orthogonality catastrophe. In the context of the ground states, we revisit Luttinger's theorem following Oshikawa's flux insertion argument and furthermore demonstrate the existence of a Luttinger surface of zeros in the fermionic Green's function. Upon inclusion of perturbations, we address the transition from the orthogonal metal to the normal state by condensation of certain excitations in the gauge sectors, so-called “ e particles.” We furthermore discuss the effect of dynamics in the dual “ m -particle” excitations, which ultimately leads to the formation of charge-neutral hadronic N -particle bound states. We present analytical arguments for the most important phases and estimates for phase boundaries of the model. Specifically, and in sharp distinction to quasi-one-dimensional ZN lattice gauge theories, renormalization group arguments imply that the phase diagram does not include an emergent deconfining U(1) phase in the limit of large number of fermion flavors. Therefore, in regards to lattice QED problems, ZN quantum emulators with N<∞ can at best be used for approximate solutions at intermediate length scales. Published by the American Physical Society 2024