An improved algorithm for dynamical triangulations and simulations of finer lattices

TL;DR

This paper presents a rejection-free algorithm for Euclidean dynamical triangulations that enables simulations at finer lattices, revealing geometries consistent with semiclassical Euclidean de Sitter space and improving agreement with classical solutions.

Contribution

A novel rejection-free algorithm for dynamical triangulations that improves simulation efficiency and allows exploration of finer lattices while maintaining detailed balance.

Findings

Simulations at finer lattice spacings show geometries resembling Euclidean de Sitter space.

The new algorithm maintains detailed balance with all proposed moves accepted.

Results at smaller lattice spacings align better with classical de Sitter solutions.

Abstract

We introduce a new algorithm for the simulation of Euclidean dynamical triangulations that mimics the Metropolis-Hastings algorithm, but where all proposed moves are accepted. This rejection-free algorithm allows for the factorization of local and global terms in the action, a condition needed for efficient simulation of theories with global terms, while still maintaining detailed balance. We test our algorithm on the $2d$ Ising model, and against results for EDT obtained with standard Metropolis. Our new algorithm allows us to simulate EDT at finer lattice spacings than previously possible, and we find geometries that resemble semiclassical Euclidean de Sitter space in agreement with earlier results at coarser lattices. The agreement between lattice data and the classical de Sitter solution continues to get better as the lattice spacing decreases.