Complex Langevin and machine learning approaches to the non-linear sigma model with a topological term

One of the central challenges in computational approaches to many-body quantum systems is the presence of the sign problem. This work investigates the phase transitions of disordered quantum materials via the nonlinear sigma model with a finite topological term—which contains a complex term—using two methods: complex Langevin and unsupervised learning. Complex Langevin has had great success in Lattice QCD and is becoming more widely used in low-energy quantum systems, but does not always converge to a valid solution. Unsupervised learning is rapidly growing as a popular model, but there remain concerns about reproducibility in machine learning research applications. This work serves as a comparative study of these two methods in treating systems with a sign problem, in order to elucidate the strengths and pitfalls of each method and gain a deeper understanding of phase coexistence and phase transitions in disordered quantum materials.<!-- notionvc: 915a463d-43f1-489d-ba26-238c75db0f8f -->