Complexity Powered Machine Intelligent Classification of Quantum Many-Body Dynamics

TL;DR

This work introduces a complexity boosted distance measure that captures the inherent complexity of dynamic evolution series in different quantum many-body phases and leads to remarkable improvements of unsupervised manifold learning of quantum many-body dynamics.

Abstract

Identifying and classifying quantum phases from measurable time series in many-body dynamics have significant values, yet face formidable challenges, requiring profound knowledge of physicists. Here, to achieve a pure data-driven machine intelligent classification, we introduce a complexity boosted distance measure that captures the inherent complexity of dynamic evolution series in different quantum many-body phases. Significantly, the introduction of complexity-boosted distance leads to remarkable improvements of unsupervised manifold learning of quantum many-body dynamics, which are exemplified in discrete time crystal model, Aubry-André model, and quantum east model. Our method does not require any prior knowledge and exhibits effectiveness even in imperfect, disordered, and noisy situations that are challenging for human scientists. Successful classification of dynamic phases in many-body systems holds the potential to enable crucial applications, including identification of tsunamis, earthquakes, catastrophes and future trends in finance.

Figures (3)

• Figure 1: Schematic framework of complexity-powered quantum dynamics analysis. a, Temporal evolution of quantum many-body dynamical processes; b, TFC quantification via configuration-space stretching metrics; c, Frequency-dependent complexity scaling: TFC increases with the dominance of high-frequency components; d, Frequency amplification mechanism: complexity enhances inter-series frequency discrimination, while power boosting exponentially magnifies these distinctions; e, Classification performance based on the TFCAD framework demonstrates progressive improvement as $\beta$ parameters are augmented (see Supplemental Material [SM Sec.1] SM).
• Figure 2: The unsupervised phase classification of DTC model. a, Floquet dynamics of DTC under dual-pulse driving: global rotation ($\hat{H}_1$) followed by disorder-enhanced nearest-neighbor coupling ($\hat{H}_2$); b, Site-1 Z-operator expectation value evolution; c, The two-dimensional phase diagram is generated through the application of the TFCAD framework to dynamical sequences acquired under systematically varied driving field strengths $g$ and interaction parameters $J_{typ}$. The cluster boundaries marked by the black crosses is consistent with the theoretical phase diagram (the orange / red / green / blue region represents the $0\pi$ paramagnetic / ferromagnetic / paramagnetic / $\pi$ ferromagnetic phase); d, The LE data collected at $J_{\text{typ}}=0.3\pi$ for $g=0.145\pi$ (red square), $g=0.185\pi$ (red diamond), and $g=0.325\pi$ (blue triangle) in panel (c) correspond to the three easily confusable cases in the $\beta=0$ regime; e, The classification results are derived from data represented by the blue dotted line in panel (c) (corresponding to varying g at fixed $J_\text{typ} = 0.3\pi$), which were used to generate the categorical mapping. The low-dimensional representation is constructed through an orthogonal transformation of the transfer matrix's second and third eigenstates: $\bar{\phi}_{2} = \cos\alpha\phi_2-\sin\alpha\phi_3$ and $\bar{\phi}_{3}= \sin\alpha\phi_2+\cos\alpha\phi_3$, where the parameter $\log(\beta)$ spans $-\infty$ to $2$. The inset in panel (e) displays the first six eigenvalues of the transfer matrix.
• Figure 3: The unsupervised clustering of AA model.a, LE data for $V=0$ at three disorder strengths: $h=1.85$ (blue squares), $h=2.05$ (red diamonds), and $h=2.35$ (red triangles); b, First six eigenvalues of transfer matrix $\hat{\mathbf{P}}$ computed using Euclidean distance (upper panel) and TFCAD (lower panel); c, Low-dimensional representation constructed from the second eigenstates of $\hat{\mathbf{P}}$ , classified via Euclidean metric (light shades) and TFCAD (dark shades). $S$ (orange curves) quantify clustering quality for $h$-parameterized configurations; d, First six eigenvalues of $\hat{\mathbf{P}}$ using TFCAD (upper panel); low-dimensional representation derived from the third eigenstates (TFCAD-classified, color-coded) with corresponding $S$ (orange curves); e, Two-dimensional phase diagram reconstructed from time-dependent density matrix renormalization group (t-DMRG) simulations, with classifications performed using the TFCAD framework.