Publications

Uniaxial strain experiments have become a powerful tool to unveil the character of unconventional phases of electronic matter. Here we propose a combination of the superconducting fitness analysis and density functional theory (DFT) calculations in order to dissect the effects of strain in complex multi-orbital quantum materials from a microscopic perspective. We apply this framework to the superconducting state of Sr

The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and the emerging hybrid quantum-classical computational paradigm of variational quantum algorithms. VQMC overcomes the curse of dimensionality by performing alternating steps of Monte Carlo sampling from a parametrized quantum state followed by gradient-based optimization. While VQMC has been applied to solve high-dimensional problems, it is known to be difficult to parallelize, primarily owing to the Markov Chain Monte Carlo (MCMC) sampling step. In this work, we explore the scalability of VQMC when autoregressive models, with exact sampling, are used in place of MCMC. This approach can exploit distributed-memory, shared-memory and/or GPU parallelism in the sampling task without any bottlenecks. In particular, we demonstrate the GPU-scalability of VQMC for solving up to ten-thousand dimensional combinatorial optimization problems.

We initiate the study of neural-network quantum state algorithms for analyzing continuous-variable lattice quantum systems in first quantization. A simple family of continuous-variable trial wavefunctons is introduced which naturally generalizes the restricted Boltzmann machine (RBM) wavefunction introduced for analyzing quantum spin systems. By virtue of its simplicity, the same variational Monte Carlo training algorithms that have been developed for ground state determination and time evolution of spin systems have natural analogues in the continuum. We offer a proof of principle demonstration in the context of ground state determination of a stoquastic quantum rotor Hamiltonian. Results are compared against those obtained from partial differential equation (PDE) based scalable eigensolvers. This study serves as a benchmark against which future investigation of continuous-variable neural quantum states can be compared, and points to the need to consider deep network architectures and more sophisticated training algorithms.

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