Publications

We study four-dimensional fractional quantum Hall states on CP2 geometry from microscopic approaches. While in 2d the standard Laughlin wave function, given by a power of Vandermonde determinant, admits a product representation in terms of the Jastrow factor, this is no longer true in higher dimensions. In 4d we can define two different types of Laughlin wavefunctions, the Determinant-Laughlin (Det-Laughlin) and Jastrow-Laughlin (Jas-Laughlin) states. We find that they are exactly annihilated by, respectively, two-particle and three-particle short ranged interacting Hamiltonians. We then mainly focus on the ground state, low energy excitations and the quasi-hole degeneracy of Det-Laughlin state. The quasi-hole degeneracy exhibits an anomalous counting, indicating the existence of multiple forms of quasi-hole wavefunctions. We argue that these are captured by the mathematical framework of the "commutative algebra of N-points in the plane". We also generalize the pseudopotential formalism to dimensions higher than two, by considering coherent state wavefunction of bound states. The microscopic wavefunctions and Hamiltonians studied in this work pave the way for systematic study of high dimensional topological phase of matter that is potentially realizable in cold atom and optical experiments.

We propose models of twisted multilayer graphene that exhibit exactly flat Bloch bands with arbitrary Chern numbers and ideal band geometries. The models are constructed by twisting two sheets of Bernal-stacked multiple graphene layers with only inter-sublattice couplings. Analytically we show that flatband wavefunctions in these models exhibit a momentum space holomorphic character, leading to ideal band geometries. We also explicitly demonstrate a generic "wavefunction exchange" mechanism that generates the high Chern number of these ideal flatbands. The ideal band geometries and high Chern numbers of the flatbands imply the possibility of hosting exotic fractional Chern insulators which do not have analogues in continuum Landau levels. We numerically verify that these exotic fractional Chern insulators are model states for short-range interactions, characterized by exact ground-state degeneracies at zero energy and infinite particle-cut entanglement gaps.

From first-principles calculations, we investigate the structural and electronic properties of the kagome metals AV3Sb5 (A = Cs, K, Rb) under isotropic and anisotropic pressure. Charge ordering patterns are found to be unanimously suppressed, while there is a significant rearrangement of p-type and m-type van Hove point energies with respect to the Fermi level. Already for moderate tensile strain along the V plane and compressive strain normal to the V layer, we find that a van Hove point can be shifted to the Fermi energy. Such a mechanism provides an invaluable tuning knob to alter the correlation profile in the kagome metal, and suggests itself for further experimental investigation. It might allow to reconcile possible multi-dome superconductivity in kagome metals not only from phonons, but also from the viewpoint of unconventional pairing.

Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the onsite term is paramount. Recently, the onset of superconductivity at 4.7K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.

Inspired by Grimme's simplified Tamm-Dancoff density functional theory approach [S. Grimme, J. Chem. Phys.

We present a vibrational dynamical mean-field theory (VDMFT) of the dynamics of atoms in solids with anharmonic interactions. Like other flavors of DMFT, VDMFT maps the dynamics of a periodic anharmonic lattice of atoms onto those of a self-consistently defined impurity problem with local anharmonicity and coupling to a bath of harmonic oscillators. VDMFT is exact in the harmonic and molecular limits, nonperturbative, systematically improvable through its clusters extensions, and usable with classical or quantum impurity solvers, depending on the importance of nuclear quantum effects. When tested on models of anharmonic optical and acoustic phonons, we find that classical VDMFT gives good agreement with classical molecular dynamics, including the temperature dependence of phonon frequencies and lifetimes. Using a quantum impurity solver, signatures of nuclear quantum effects are observed at low temperatures.

Efficient computer implementations of the GW approximation must approximate a numerically challenging frequency integral; the integral can be performed analytically, but doing so leads to an expensive implementation whose computational cost scales as O(N

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by leveraging repeated random sampling and averaging. We present a general approach to extending such methods for the estimation of multiple eigenvalues and demonstrate its performance for several benchmark problems in quantum chemistry.

The inherent atomistic precision of synthetic chemistry enables bottom-up structural control over quantum bits, or qubits, for quantum technologies. Tuning paramagnetic molecular qubits that feature optical-spin initialization and readout is a crucial step toward designing bespoke qubits for applications in quantum sensing, networking, and computing. Here, we demonstrate that the electronic structure that enables optical-spin initialization and readout for S = 1, Cr(aryl)4, where aryl = 2,4-dimethylphenyl (1), o-tolyl (2), and 2,3-dimethylphenyl (3), is readily translated into Cr(alkyl)4 compounds, where alkyl = 2,2,2-triphenylethyl (4), (trimethylsilyl)methyl (5), and cyclohexyl (6). The small ground state zero field splitting values (<5 GHz) for 1–6 allowed for coherent spin manipulation at X-band microwave frequency, enabling temperature-, concentration-, and orientation-dependent investigations of the spin dynamics. Electronic absorption and emission spectroscopy confirmed the desired electronic structures for 4–6, which exhibit photoluminescence from 897 to 923 nm, while theoretical calculations elucidated the varied bonding interactions of the aryl and alkyl Cr4+ compounds. The combined experimental and theoretical comparison of Cr(aryl)4 and Cr(alkyl)4 systems illustrates the impact of the ligand field on both the ground state spin structure and excited state manifold, laying the groundwork for the design of structurally precise optically addressable molecular qubits.

The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis sets commonly used in molecular simulation show significant linear dependencies when used in close-packed solids, leading to severe numerical issues that hamper the convergence to the complete basis set (CBS) limit, especially in correlated calculations. In this work, we revisit Dunning's strategy for construction of correlation-consistent basis sets and examine the relationship between accuracy and numerical stability in periodic settings. Specifically, we find that limiting the number of primitive functions avoids the appearance of problematic small exponents while still providing smooth convergence to the CBS limit. As an example, we generate double-, triple-, and quadruple-zeta correlation-consistent Gaussian basis sets for periodic calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets cover the main-group elements from the first three rows of the periodic table. Especially for atoms on the left side of the periodic table, our basis sets are less diffuse than those used in molecular calculations. We verify the fast and reliable convergence to the CBS limit in both Hartree-Fock and post-Hartree-Fock (MP2) calculations, using a diverse test set of 19 semiconductors and insulators.