Gauge Theory Couplings on Anisotropic Lattices

Abstract

The advantage of simulating lattice field theory with quantum computers is hamstrung by the limited resources that induce large errors from finite volume and sizable lattice spacings. Previous work has shown how classical simulations near the Hamiltonian limit can be used for setting the lattice spacings in real-time through analytical continuation, thereby reducing errors in quantum simulations. In this work, we derive perturbative relations between bare and renormalized quantities in Euclidean spacetime at any anisotropy factor -- the ratio of spatial to temporal lattice spacings -- and in any spatial dimension for $U(N)$ and $SU(N)$. This reduces the required classical preprocessing for quantum simulations. We find less than $10\%$ discrepancy between our perturbative results and those from existing nonperturbative determinations of the anisotropy for $SU(2)$ and $U(1)$ gauge theories. For the discrete groups ${\mathbb{Z}}_{10}$, ${\mathbb{Z}}_{100}$ and $\mathbb{BI}$, we perform lattice Monte Carlo simulations to extract anisotropy factors and observe similar agreement with our perturbative results.

10 pages, 8 figures

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Cited by in corpus (9)

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• From square plaquettes to triamond lattices for SU(2) gauge theory
• Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory
• Lattice Holography on a Quantum Computer