Research

Our group works on theoretical condensed matter physics with an emphasis on strongly correlated quantum systems. We develop analytical and numerical approaches to understand exotic quantum phases of matter and quantum phase transitions. We are always interested in exploring new directions. Below are four of our current main research directions.

Cuprate & Nickelate Superconductors

High-temperature superconductivity remains one of the central open problems in condensed matter physics. We develop new theoretical frameworks to understand the cuprate and the recently discovered nickelate superconductors.

• Ancilla theory of pseudogap metal in underdoped cuprates — We developed a mean-field theory that explains Fermi arcs and the pseudogap by hybridizing the electron with an ancilla fermion. Beyond mean field, we construct a variational wavefunction by introducing ancilla qubits and then projecting them out [49]. This provides, to our knowledge, the first wavefunction of the FL* phase within the Hilbert space of the one-band Hubbard model.
• Bilayer nickelate La₃Ni₂O₇ — We proposed a Type-II t–J model for superconducting La₃Ni₂O₇ [30] and showed that kinetic energy can drive strong pairing even when the attractive interaction from J_⊥ is canceled by a repulsive V [37] [p1]. Beyond mean field, J_⊥ penalizes the S=1 doublon state, frustrating single-electron motion so that pairing saves kinetic energy—a mechanism beyond the mean-field decoupling common to most other approaches. See [p7] for a review.
• Non-Fermi liquid criticality with Fermi surface volume jump — We aim to understand the quantum criticality between a pseudogap metal (with a small Fermi surface) and a Fermi liquid, and its connection to strange metal behavior. The second Fermi liquid (sFL) to Fermi liquid transition in a bilayer model [36] provides a wonderful example of a Fermi surface volume-changing transition without the distractions from symmetry breaking or fractionalization. We hope to gain new insights into the strange metal problem by first studying this bilayer model, and then applying the intuitions developed there to the single-layer model relevant to the cuprates.

Moiré Superlattices and 2D Materials

Moiré superlattices formed by stacking two-dimensional materials with a small twist angle or lattice mismatch can produce narrow bands in which the electron kinetic energy is strongly quenched relative to the Coulomb interaction. The resulting flat-band systems—which may or may not carry a Chern number—provide a highly tunable platform for realizing a remarkable variety of strongly correlated and topological quantum phases, including correlated insulators, unconventional superconductors, and integer and fractional quantum anomalous Hall states.

• Integer and fractional quantum anomalous Hall phases — We predicted nearly flat Chern bands in moiré superlattices [2] and fractional quantum anomalous Hall states in rhombohedral multilayer graphene in the moiréless limit [39]. We continue to explore possible fractional phases in moiré materials and multilayer graphene, as well as the quantum phase transitions between these topological states and conventional phases.
• Mott physics in strongly correlated topological bands — We are broadly interested in understanding the novel Mott physics that arises in topological flat bands [48] [p2]. A key distinction from conventional Mott insulators is the momentum-selective Mott gap: the Mott gap becomes small or vanishes at certain momentum points. Moreover, the Mott–Hubbard bands may themselves become topological, so that the final phase hosts charge edge modes coexisting with bulk localized spin moments.
• Theory of superconductivity for twisted bilayer graphene — We proposed a theory of superconductivity in twisted bilayer graphene based on pairing from a small Fermi surface [p9]. This approach naturally explains the two gap structure below T_c and the pseudogap above T_c observed in tunneling experiments.
• Chiral superconductivity — We are interested in understanding how chiral superconductivity can emerge in purely spinless models with Coulomb interaction alone. This question is potentially relevant to recent discoveries in pentalayer graphene and twisted MoTe₂. The chiral superconductor is particularly exciting because it likely hosts Majorana zero modes.

Fractional Phases

Fractionalization—where electrons collectively give rise to emergent quasiparticles carrying fractional quantum numbers—is a central theme in modern condensed matter physics.

• Quantum spin liquids — Quantum spin liquids are exotic states of matter that evade conventional symmetry-breaking order and host fractionalized excitations. We are particularly interested in realizing quantum spin liquids in moiré systems [18], where the high tunability offers new opportunities for their detection and control.
• Quantum Hall multilayers — Stacking quantum Hall layers enables exotic interlayer-coherent states such as fractional exciton condensates [28] and anyon superfluids [p5], opening a rich playground for engineering new topological phases through interlayer coherence.
• Deconfined quantum phase transitions — We investigated deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator [26], and studied phase transitions out of quantum Hall states in moiré materials [32].

Numerical Methods

In addition to analytical approaches, our group actively develops and applies numerical methods to study strongly correlated quantum systems, going beyond mean-field descriptions to obtain unbiased results for challenging many-body problems.

• Density matrix renormalization group (DMRG) — We use DMRG to study quantum criticality and exotic phases in one-dimensional and quasi-one-dimensional models, providing benchmarks for our analytical theories.
• Variational Monte Carlo (VMC) — We develop new classes of variational wavefunctions in two dimensions to capture Mott physics, Fermi surface reconstruction, and fractionalization.
• Dynamical mean-field theory (DMFT) — We use DMFT to study correlated physics including pseudogap, non-Fermi liquid behavior, and superconductivity. One recent application is on bilayer nickelate.
• Neural network quantum states — We explore neural network ansatze as expressive variational wavefunctions for strongly correlated systems.