Harnessing Interpretable and Unsupervised Machine Learning to Address Big Data from Modern X-ray Diffraction

The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern x-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big data sets when a comprehensive analysis is beyond human reach. We report the development of a novel unsupervised machine learning approach, XRD Temperature Clustering (X-TEC), that can automatically extract charge density wave (CDW) order parameters and detect intra-unit cell (IUC) ordering and its fluctuations from a series of high-volume X-ray diffraction (XRD) measurements taken at multiple temperatures. We apply X-TEC to XRD data on a quasi-skutterudite family of materials, (Ca$_x$Sr$_{1-x}$)$_3$Rh$_4$Sn$_{13}$, where a quantum critical point arising from charge order is observed as a function of Ca concentration. We further apply X-TEC to XRD data on the pyrochlore metal, Cd$_2$Re$_2$O$_7$, to investigate its two much debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC-revealed selection rule that the Cd and Re displacements are approximately equal in amplitude, but out of phase. This discovery reveals a previously unknown involvement of $5d^2$ Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in-operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on-the-fly.

A DMRG Study of Superconductivity in the Triangular Lattice Hubbard Model

With the discovery of strong coupling physics and superconductivity in Moire superlattices, its essential to have an understanding of strong coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here we use density matrix renormalization group (DMRG) to investigate the domininant superconducting channels in the hole-doped triangular lattice Hubbard model over a range of repulsive interaction strengths. We find a clear transition from $p$-wave superconductivity at moderate on-site repulsion strength ($U/t = 2$) at filling above 1/4 ($n sim 0.65$) to $d$-wave superconductivity at strong on-site repulsion strength ($U/t = 10$) at filling below 1/4 ($n sim 0.4$). The unusual tunability that Moire superlattices offer in controlling $U/t$ would open up the opportunity to realize this transition between $d$-wave and $p$-wave superconductivity.

Machine learning out-of-equilibrium phases of matter

Neural network based machine learning is emerging as a powerful tool for obtaining phase diagrams when traditional regression schemes using local equilibrium order parameters are not available, as in many-body localized or topological phases. Nevertheless, instances of machine learning offering new insights have been rare up to now. Here we show that a single feed-forward neural network can decode the defining structures of two distinct MBL phases and a thermalizing phase, using entanglement spectra obtained from individual eigenstates. For this, we introduce a simplicial geometry based method for extracting multi-partite phase boundaries. We find that this method outperforms conventional metrics (like the entanglement entropy) for identifying MBL phase transitions, revealing a sharper phase boundary and shedding new insight into the topology of the phase diagram. Furthermore, the phase diagram we acquire from a single disorder configuration confirms that the machine-learning based approach we establish here can enable speedy exploration of large phase spaces that can assist with the discovery of new MBL phases. To our knowledge this work represents the first example of a machine learning approach revealing new information beyond conventional knowledge.

A DMRG study: Pair-density wave in spin-valley locked systems

Interest in modulated paired states, long sought since the first proposals by Fulde and Ferrell and by Larkin and Ovchinnikov, has grown recently in the context of strongly coupled superconductors under the name of pair density wave. However, there is little theoretical understanding of how such a state might arise out of strong coupling physics in simple models. Although density matrix renormalization group has been a powerful tool for exploring strong coupling modulation phenomena of spin and charge stripe in the Hubbard model and the t-J model, there has been no numerical evidence of PDW within these models using DMRG. Here we note that a system with inversion breaking, C3v point group symmetry may host a PDW-like state. Motivated by the fact that spin-valley locked band structure of hole-doped group VI transition metal dichalcogenides materializes such a setting, we use DMRG to study the superconducting tendencies in spin-valley locked systems with strong short-ranged repulsion. Remarkably we find robust evidence for a PDW and the first of such evidence within DMRG studies of a simple fermionic model.