Simulating CDT quantum gravity

TL;DR

This paper introduces Monte Carlo simulation techniques for nonperturbative lattice quantum gravity using Causal Dynamical Triangulations, detailing implementation, optimization, and data analysis in 2D and 3D.

Contribution

It provides a detailed, practical guide and open-source code for simulating CDT quantum gravity, including move implementation, data management, and observable measurement.

Findings

Effective Monte Carlo move implementation for CDT

Optimized data storage strategies for dynamical lattices

Guidelines for tuning and measuring observables in simulations

Abstract

We provide a hands-on introduction to Monte Carlo simulations in nonperturbative lattice quantum gravity, formulated in terms of Causal Dynamical Triangulations (CDT). We describe explicitly the implementation of Monte Carlo moves and the associated detailed-balance equations in two and three spacetime dimensions. We discuss how to optimize data storage and retrieval, which are nontrivial due to the dynamical nature of the lattices, and how to reconstruct the full geometry from selected stored data. Various aspects of the simulation, including tuning, thermalization and the measurement of observables are also treated. An associated open-source C++ implementation code is freely available online.