In materials, the two principal interactions are the electron-phonon and the electron-electron Coulomb interaction. While even each of them separately can lead to intricate collective phenomena, many interesting phenomena emerge when these interactions are both present and of comparable strength. For example, the combined influence of both interactions is widely considered fundamental to unconventional superconductivity, organic semiconductors, and twistronics. Understanding how quantum phonons interact with strongly correlated electrons is one of the key challenges in quantum materials research. Theoretical exploration of systems with both interactions, however, is often limited by the unbounded nature of the phonon Hilbert space and the complex many-body correlations involved.

Our group investigates strong coupling regimes where phonons contribute to the dynamics in non-perturbative ways. We apply a range of quantum many-body methods — exact diagonalization, quantum Monte Carlo, and density-matrix renormalization group — to model these systems. Beyond standard approaches, we are advancing hybrid variational-numerical methods that use non-Gaussian transformations to unitarily disentangle the electron and phonon subsystems in a dressed-state framework. This approach allows us to simulate strongly dressed states and fluctuating orders that lack mean-field analogs. In addition, we are interested in spectroscopic techniques that quantify the influence of quantum phonons and phonon-mediated interactions.

Characterizing and controlling entanglement are central to quantum technology advancements, yet they pose distinct challenges in materials. Unlike quantum optics or quantum simulators, materials do not allow for precise manipulation of single electrons or twin-state interference experiments. Instead, we focus on entanglement witness approaches through spectroscopies accessible in solid-state environments. Fluctuations of spectroscopic observables provide a lower bound on many-body entanglement. Our work in entanglement witnesses spans both distinguishable spin modes and indistinguishable fermions and bosons, employing diverse spectral techniques.

We also explore fluctuating “orders” that arise without symmetry breaking. In strongly correlated materials, interactions can induce observable properties, such as single-particle gaps, that mimic the signatures of broken-symmetry phases while maintaining symmetry. This phenomenon is especially pronounced in low-dimensional or nanoscale materials. We utilize quantum many-body simulations and machine-learning methods to differentiate these fluctuating states from true broken-symmetry phases. Our interests include fluctuating superconductivity, fluctuating spin states, and fluctuating structural transitions.

Unconventional superconductivity describes pairing phenomena that remain elusive within the BCS theory framework. A prominent example is high-temperature superconductivity in cuprates, where strong electronic correlations are believed to play a key role in the pairing mechanism. Beyond cuprates, unconventional pairing has been observed in a variety of systems, including specific transition-metal compounds, heavy-fermion systems, and recently explored moiré materials. Our research leverages quantum many-body techniques to analyze superconductivity and related phases in strongly correlated models relevant to these materials, aiming to unravel the complexities of unconventional pairing.

While our work builds on Hubbard-like models, we delve into additional factors that might work in tandem with electronic correlations to stabilize Cooper pairs. For instance, phonon-mediated interactions may enhance the d-wave pairing driven by strong correlations, helping to establish long-range order. Furthermore, charge-transfer characteristics and multi-orbital effects introduce new dimensions to the pairing mechanism, each contributing in unique ways to stabilizing the superconducting state. Together, these factors provide potential control mechanisms, guiding efforts to design and manipulate superconductors.

Electronic states confined to low-dimensional systems are often prone to correlation effects and quantum fluctuations, which can be controlled through mechanisms like gating, surface doping, substrates, and moiré superstructures. These tunable systems offer a valuable setting for exploring complex properties in quantum many-body physics. Notably, low-dimensional platforms are particularly well-suited for comparison between theoretical and experimental results, as quantum many-body methods tend to yield high reliability in these settings.

Our research explores the exotic properties of 1D and 2D correlated systems, including fractionalization, entanglement, and fluctuation phenomena. These wavefunction-level properties often manifest as distinctive signatures in dynamical response functions, creating direct experimental parallels. By mapping theoretical models to measurable dynamical features, we aim to bridge the gap between theoretical understanding and empirical validation of complex quantum states.