Simone Tibaldi, Giuseppe Magnifico, Davide Vodola, Elisa Ercolessi
SciPost Phys. 14, 005 (2023) ·
published 19 January 2023
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The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, t-distributed stochastic neighbor embedding and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.
SciPost Phys. 1, 010 (2016) ·
published 27 October 2016
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The many-body localization (MBL) transition is a quantum phase transition
involving highly excited eigenstates of a disordered quantum many-body
Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive
entanglement entropies and fluctuations) to "localized" (exhibiting area-law
scaling of entanglement and fluctuations). The MBL transition can be driven by
the strength of disorder in a given spectral range, or by the energy density at
fixed disorder - if the system possesses a many-body mobility edge. Here we
propose to explore the latter mechanism by using "quantum-quench spectroscopy",
namely via quantum quenches of variable width which prepare the state of the
system in a superposition of eigenstates of the Hamiltonian within a
controllable spectral region. Studying numerically a chain of interacting
spinless fermions in a quasi-periodic potential, we argue that this system has
a many-body mobility edge; and we show that its existence translates into a
clear dynamical transition in the time evolution immediately following a quench
in the strength of the quasi-periodic potential, as well as a transition in the
scaling properties of the quasi-stationary state at long times. Our results
suggest a practical scheme for the experimental observation of many-body
mobility edges using cold-atom setups.
