Source-linked AI summary
Machine learning quantum phases of matter beyond the fermion sign problem
Peter Broecker, Juan Carrasquilla, Roger G. Melko, Simon Trebst
TL;DR
The paper addresses the difficulty of extracting fermionic phase information with QMC when sign fluctuations make conventional statistical analysis exponentially hard. It combines auxiliary-field QMC with CNN classification of Green’s functions and finds that this identifies phase transitions even in sign-problematic systems.
Problem
The fermion sign problem makes conventional QMC estimation of observables exponentially hard in system size and inverse temperature.
Method
The authors sample fermionic systems with auxiliary-field QMC and train a CNN state function on Green’s functions rather than directly estimating thermodynamic observables.
Results
The CNN distinguishes phases and locates transitions in spinful and sign-problematic spinless Hubbard models, including U ≈ 4.1 ± 0.1 and Vc ≈ 0.7 ± 0.1.
Takeaways & Limitations
Green’s-function-based QMC plus machine learning provides a general framework for discriminating fermionic phases despite severe sign problems.
Abstract
from arXiv · showhide
State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems. Using auxiliary-field quantum Monte Carlo (QMC) simulations to sample the many-fermion system, we show that the Green's function (but not the auxiliary field) holds sufficient information to allow for the distinction of different fermionic phases via a CNN. We demonstrate that this QMC + machine learning approach works even for systems exhibiting a severe fermion sign problem where conventional approaches to extract information from the Green's function, e.g.~in the form of equal-time correlation functions, fail. We expect that this capacity of hierarchical machine learning techniques to circumvent the fermion sign problem will drive novel insights into some of the most fundamental problems in statistical physics.
C OC · sign(WC) · |WC| P
The paper replaces conventional observable estimation in sign-problematic QMC with CNN classification of sampled configurations, finding that Green’s functions—not auxiliary fields—contain sufficient information to distinguish fermionic phases and locate transitions. The approach works across spinful and severely sign-problematic spinless Hubbard models, including through transfer learning.
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- The proposed state function replaces direct expectation-value estimation with supervised CNN classification of configurations sampled using absolute QMC weights.
- The auxiliary-field representation fails to distinguish the spinful model’s reference phases, whereas the Green’s function enables CNN discrimination and locates the transition at U ≈ 4.1 ± 0.1.
- For the half-filled spinless model, adding configuration signs or complex phases yields no notable predictive improvement over the bare Green’s function, whose transition estimate agrees well with Monte Carlo results.
- The same approach identifies a one-third-filled spinless transition around Vc ≈ 0.7 ± 0.1, matching a recent estimate from entanglement calculations.
- Transfer learning from the sign-problem-free spinful model reliably distinguishes phases of the sign-problematic spinless model and provides a rough transition estimate.
- The authors conclude that Green’s-function machine learning can complement conventional methods and may help map phase diagrams across quantum many-body systems.