Scalable approach to many-body localization via quantum data
This work addresses a bottleneck in quantum many-body physics for researchers by providing a scalable method to study MBL, though it is incremental as it builds on existing neural network techniques.
The authors tackled the computational challenge of analyzing many-body localization (MBL) in quantum systems by proposing a neural network-based learning approach that efficiently estimates indicators like the adjacent gap ratio and entropic quantities, enabling extrapolation from smaller to larger system sizes.
We are interested in how quantum data can allow for practical solutions to otherwise difficult computational problems. A notoriously difficult phenomenon from quantum many-body physics is the emergence of many-body localization (MBL). So far, is has evaded a comprehensive analysis. In particular, numerical studies are challenged by the exponential growth of the Hilbert space dimension. As many of these studies rely on exact diagonalization of the system's Hamiltonian, only small system sizes are accessible. In this work, we propose a highly flexible neural network based learning approach that, once given training data, circumvents any computationally expensive step. In this way, we can efficiently estimate common indicators of MBL such as the adjacent gap ratio or entropic quantities. Our estimator can be trained on data from various system sizes at once which grants the ability to extrapolate from smaller to larger ones. Moreover, using transfer learning we show that already a two-dimensional feature vector is sufficient to obtain several different indicators at various energy densities at once. We hope that our approach can be applied to large-scale quantum experiments to provide new insights into quantum many-body physics.