Research statement

My research centers on the design of strongly correlated lattice models and their unbiased simulation using determinant Quantum Monte Carlo (DQMC) methods. A unifying theme of my work is the development of sign-problem-free models that enable controlled numerical studies of quantum criticality, non–Fermi-liquid (nFL) behavior, and the rich correlated phenomena in moiré and kagome materials. I also work on algorithmic advances—including entanglement-entropy algorithms and theoretical understanding of the fermion sign problem—that broaden the reach of QMC for strongly interacting fermionic systems.

My research program is organized around four interconnected directions:

1. QMC algorithms, entanglement, and the fermion sign problem

A major part of my research involves expanding the algorithmic capacity of QMC and understanding the origin and structure of the fermion sign problem.

Algorithms for entanglement entropy and exponential observables. We analyzed the numerical structure of existing Rényi entropy methods 1 and developed a significantly more stable integral algorithm for evaluating exponential observables, including entanglement entropy and free energy 2, 3. An annealing-inspired extension further improves efficiency for extracting entanglement entropy as a continuous function of parameters 4.

Momentum-space QMC for twisted systems. Starting from the Bistritzer–MacDonald continuum model with long-range Coulomb interactions, we constructed a projected momentum-space Hamiltonian that contain both interaction effects and form factor. The resulting QMC method is free of the sign problem at the charge-neutrality point (CNP) due to \(C_2P\) and \(C_2T\) symmetries 5. For generic integer fillings, sign problems arise, and we investigated their computational implications 6.

Sign problem and phase transitions. We examined the relationship between Monte Carlo signs and phase transitions, showing that extrema of the sign or its derivatives do not in general coincide with true critical points. We proposed a modified sign that correctly tracks the transition 7.

Sign Bound Theory. In systems with sign problems, the average sign is typically expected to decay exponentially with inverse temperature \(\beta\) and system size \(L\). We identified a class of systems where, in the zero-temperature limit, the sign instead decays algebraically with \(L\). The mean sign is controlled by the ground-state degeneracies of the original and reference systems; with appropriate reference choices, the degeneracies match, yielding a polynomial lower bound. Our Sign Bound Theory 8, 6 gives general criteria for when such behavior occurs and enables controlled QMC simulations of twisted moiré systems previously believed to be inaccessible 6, 9.

2. Kondo physics and Kondo models coupled to a compact \(U(1)\) gauge field

Heavy-fermion systems often require theoretical frameworks in which Kondo hybridization coexists with emergent gauge structures. To capture this physics in a numerically controlled setting, we developed a Kondo model coupled to a compact \(U(1)\) gauge field 10. In contrast to traditional Kondo–Heisenberg models—where hybridization introduces complicated composite operators that make Wick expansions and unbiased QMC simulations intractable—our formulation introduces conduction electrons \(c\), localized fermions \(f\), and a compact \(U(1)\) gauge link, together with a matter field carrrying gauge charge that mediates the hybridization between \(c\) and \(f\).

This matter field \(z\), carrying a nontrivial gauge charge, binds to the \(f\) fermion to form a composite fermion \(d = z f\), ensuring that the Kondo hybridization channel is fully gauge-invariant. The model naturally realizes a \(\pi\)-flux Dirac dispersion and, crucially, admits sign-problem-free QMC simulations due to its gauge structure.

Using this gauge-field–coupled Kondo model, I computed composite-fermion spectral functions and optical conductivity across the Kondo–to–Kondo-breakdown transition. The emergence and collapse of heavy hybridized bands provide a clear numerical signature of Kondo breakdown. Moreover, the evolution of optical conductivity reveals behavior consistent with an orbital-selective Mott transition. This construction establishes a new, unbiased QMC platform for studying Kondo breakdown, heavy-fermion criticality, and gauge-fluctuation–driven phenomena in strongly correlated electron systems.

3. Correlated and topological phases in moiré and kagome materials

Moiré superlattices and kagome metals are ideal platforms for exploring flat-band physics, unconventional ordering, and topological phenomena. My contributions span both methodological advances and microscopic understanding of experimentally relevant phases.

Quasiparticle spectroscopy of chiral charge order. Building on our previous modeling of chiral charge order in \(CsV_3Sb_5\), we combined numerical simulations with STM quasiparticle spectroscopy to investigate how a magnetic impurity couples to the loop-current sector of the chiral flux phase 11. We find that a Co impurity locally reverses the circulating current on a kagome plaquette, creating a topological in-gap excitation inside the CDW pseudogap—fully consistent with STM observations. This provides microscopic evidence for time-reversal–breaking loop-current order and a paradigm for probing flux-sector excitations.

Collective modes and correlation effects in TBG and TMD moiré systems. Using the momentum-space QMC framework, we computed single-particle and particle–hole spectra. At CNP, we found that the intervalley coherent (IVC) state is the leading instability, competing closely with valley polarization(VP) 12, and identified long-lived valley-wave modes analogous to Heisenberg spin waves. In the chiral and flat-band limits at filling \(\nu=1\), we leveraged polynomially decaying signs to simulate the system at low temperatures 9. The simulations reveal an Ising thermal transition, a QAH–TMI state, and an unusual suppression of \(T_c\) driven by particle–hole excitons. We also uncovered doping-independent gaps and enhanced compressibility in twisted TMDs 13.

4. Quantum criticality and non–Fermi-liquid behavior

Understanding universal features of nFL regimes is central to correlated-electron physics. My work explores such behavior in both itinerant lattice model and disorder SYK-like model.

Spin–fermion model and itinerant quantum criticality. We designed a spin–fermion coupled model on the square lattice hosting an itinerant antiferromagnetic QCP with fermion pockets and hot spots 14, 15. QMC simulations reveal clear nFL behavior: the Matsubara-frequency dependence of \(\mathrm{Im}\,\Sigma(k,\omega_n)\) saturates to a finite constant at low \(\omega_n\), contradicting Hertz–Millis predictions. The extracted anomalous dimension \(\eta \approx 0.25\) highlights strong deviations from Fermi-liquid behavior.

Self-tuned Yukawa–SYK model. To overcome challenges of fine-tuning toward quantum criticality, we studied the Yukawa–SYK model 16, 17, which “self-tunes” to a critical point independent of bare parameters like the boson mass \(m_0\). Our sign-problem-free QMC simulations provide direct evidence of self-tuned quantum-criticality and nFL scaling in both fermionic and bosonic Green’s functions.

References