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1. Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory

   https://doi.org/10.3390/quantum7020018  

   Baul, Anshumitra; Fotso, Herbert; Terletska, Hanna; Tam, Ka-Ming; Moreno, Juana (June 2025, Quantum Reports)

   Modeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising avenue of research is to combine many-body physics with machine learning for the classification of distinct phases. We present a workflow that synergizes quantum computing, many-body theory, and quantum machine learning (QML) for studying strongly correlated systems. In particular, it can capture a putative quantum phase transition of the stereotypical strongly correlated system, the Hubbard model. Following the recent proposal of the hybrid quantum-classical algorithm for the two-site dynamical mean-field theory (DMFT), we present a modification that allows the self-consistent solution of the single bath site DMFT. The modified algorithm can be generalized for multiple bath sites. This approach is used to generate a database of zero-temperature wavefunctions of the Hubbard model within the DMFT approximation. We then use a QML algorithm to distinguish between the metallic phase and the Mott insulator phase to capture the metal-to-Mott insulator phase transition. We train a recently proposed quantum convolutional neural network (QCNN) and then utilize the QCNN as a quantum classifier to capture the phase transition region. This work provides a recipe for application to other phase transitions in strongly correlated systems and represents an exciting application of small-scale quantum devices realizable with near-term technology. 

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2. Low-temperature dielectric anomaly arising from electronic phase separation at the Mott insulator-metal transition

   https://doi.org/10.1038/s41535-020-00307-0  

   Pustogow, A.; Rösslhuber, R.; Tan, Y.; Uykur, E.; Böhme, A.; Wenzel, M.; Saito, Y.; Löhle, A.; Hübner, R.; Kawamoto, A.; et al (December 2021, npj Quantum Materials)

   null (Ed.)

   Abstract Coulomb repulsion among conduction electrons in solids hinders their motion and leads to a rise in resistivity. A regime of electronic phase separation is expected at the first-order phase transition between a correlated metal and a paramagnetic Mott insulator, but remains unexplored experimentally as well as theoretically nearby T  = 0. We approach this issue by assessing the complex permittivity via dielectric spectroscopy, which provides vivid mapping of the Mott transition and deep insight into its microscopic nature. Our experiments utilizing both physical pressure and chemical substitution consistently reveal a strong enhancement of the quasi-static dielectric constant ε 1 when correlations are tuned through the critical value. All experimental trends are captured by dynamical mean-field theory of the single-band Hubbard model supplemented by percolation theory. Our findings suggest a similar ’dielectric catastrophe’ in many other correlated materials and explain previous observations that were assigned to multiferroicity or ferroelectricity. 

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3. Connecting Complex Electronic Pattern Formation to Critical Exponents

   https://doi.org/10.3390/condmat6040039  

   Liu, Shuo; Carlson, Erica W.; Dahmen, Karin A. (December 2021, Condensed Matter)

   Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin–Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems. 

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4. Mott-moiré excitons

   https://doi.org/10.1103/PhysRevB.107.195151  

   Huang, Tsung-Sheng; Chou, Yang-Zhi; Baldwin, Christopher L.; Wu, Fengcheng; Hafezi, Mohammad (May 2023, Physical Review B)

   We develop a systematic theory for excitons subject to Fermi-Hubbard physics in moiré twisted transition metal dichalcogenides (TMDs). Specifically, we consider excitons from two moiré bands with a Mott-insulating valence band sustaining 120 spin order. These “Mott-moiré excitons,” which are achievable in twisted TMD heterobilayers, are bound states of a magnetic polaron in the valence band and a free electron in the conduction band. We find significantly narrower exciton bandwidths in the presence of Hubbard physics, serving as a potential experimental signature of strong correlations. We also demonstrate the high tunability of Mott-moiré excitons through the dependence of their binding energies, diameters, and bandwidths on the moiré period. In addition, we study bound states between charges outside of the strongly correlated moiré band and find that these as well exhibit signatures of spin correlation. Our work provides guidelines for future exploration of strongly correlated excitons in triangular Hubbard systems such as twisted TMD heterobilayers. 

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5. Spontaneous Supercrystal Formation During a Strain‐Engineered Metal–Insulator Transition

   https://doi.org/10.1002/adma.202403873  

   Gorobtsov, Oleg Yu; Miao, Ludi; Shao, Ziming; Tan, Yueze; Schnitzer, Noah; Goodge, Berit Hansen; Ruf, Jacob; Weinstock, Daniel; Cherukara, Mathew; Holt, Martin Victor; et al (August 2024, Advanced Materials)

   Abstract Mott metal–insulator transitions possess electronic, magnetic, and structural degrees of freedom promising next‐generation energy‐efficient electronics. A previously unknown, hierarchically ordered, and anisotropic supercrystal state is reported and its intrinsic formation characterized in‐situ during a Mott transition in a Ca₂RuO₄thin film. Machine learning‐assisted X‐ray nanodiffraction together with cryogenic electron microscopy reveal multi‐scale periodic domain formation at and below the film transition temperature (T_Film ≈ 200–250 K) and a separate anisotropic spatial structure at and aboveT_Film. Local resistivity measurements imply an intrinsic coupling of the supercrystal orientation to the material's anisotropic conductivity. These findings add a new degree of complexity to the physical understanding of Mott transitions, opening opportunities for designing materials with tunable electronic properties. 

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