Gauge protection in non-abelian lattice gauge theories

Abstract

Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge is the reliability of such schemes in non-Abelian gauge theories where local conservation laws do not commute. Here, we show through exact diagonalization that non-Abelian gauge invariance can be reliably controlled using gauge-protection terms that energetically stabilize the target gauge sector in Hilbert space, suppressing gauge violations due to unitary gauge-breaking errors. We present analytic arguments that predict a volume-independent protection strength $V$, which when sufficiently large leads to the emergence of an \textit{adjusted} gauge theory with the same local gauge symmetry up to least a timescale $\propto\sqrt{V/V_0^3}$. Thereafter, a \textit{renormalized} gauge theory dominates up to a timescale $\propto\exp(V/V_0)/V_0$ with $V_0$ a volume-independent energy factor, similar to the case of faulty Abelian gauge theories. Moreover, we show for certain experimentally relevant errors that single-body protection terms robustly suppress gauge violations up to all accessible evolution times in exact diagonalization, and demonstrate that the adjusted gauge theory emerges in this case as well. These single-body protection terms can be readily implemented with fewer engineering requirements than the ideal gauge theory itself in current ultracold-atom setups and NISQ devices.

A Restricted Path Integration Method

“…The mathematical form." a is expressed as follows: [1,2] ψ 0 e −βH ψ 0 ≈ 1 N dϕ 0 e −S(ϕ0)/ℏ ψ 0 (ϕ 0 ) (6) Among them, ψ 0 is the ground state of the Hamiltonian, H is the Hamiltonian, S(ϕ 0 ) is the amount of action on the time axis, ϕ 0 is the quantum field at time t = 0. The normalization constant is the value of N .…”

“…To apply this method to the Abelian U(1) local gauge theory in curved vacuum spacetime, we establish (1 1)-dimensional vacuum central symmetric curved spacetime using the zero geodesic of the Schwarschild metric. We then obtain the mass-U(1) gauge geodesicsal relation [1], which is a fundamental equation for this theory.…”

Floquet Engineering Heisenberg from Ising Using Constant Drive Fields for Quantum Simulation

“…This approach to simulating the XXZ-Heisenberg model is similar in spirit to recent proposals for simulating gauge theories by adding terms to the Hamiltonian that generate gauge symmetries [121][122][123][124][125]. In these proposals, an energy penalty for breaking gauge invariance decouples the gauge invariant sector from the rest of Hilbert space analogously to how dynamical decoupling can be used to decouple systems from their enviroment [124].…”

Toward Exploring Phase Diagrams of Gauge Theories on Quantum Computers with Thermal Pure Quantum States

“…where H ≡ 𝐻 + ∑ 𝑛 𝑓 (𝐺 𝑛 ), and 𝑓 (𝐺 𝑛 ) is chosen such that unphysical components are penalized during imaginary-time evolution [24,25]. This latter approach is what is investigated in this work.…”