Natural Quantum Monte Carlo Computation of Excited States

We present a variational Monte Carlo algorithm for estimating the lowest excited states of a quantum system which is a natural generalization of the estimation of ground states. The method has no free parameters and requires no explicit orthogonalization of the different states, instead transforming the problem of finding excited states of a given system into that of finding the ground state of an expanded system. Expected values of arbitrary observables can be calculated, including off-diagonal expectations between different states such as the transition dipole moment. Although the method is entirely general, it works particularly well in conjunction with recent work on using neural networks as variational Ansatze for many-electron systems, and we show that by combining this method with the FermiNet and Psiformer Ansatze we can accurately recover vertical excitation energies and oscillator strengths on molecules as large as benzene. Beyond the examples on molecules presented here, we expect this technique will be of great interest for applications of variational quantum Monte Carlo to atomic, nuclear and condensed matter physics

Discovering quantum phase transitions with fermionic neural networks

Deep neural networks have been very successful as highly accurate wave function Ansätze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such Ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density, despite being given no a priori knowledge that a phase transition exists

Quantum Dynamics, Many-body methods and basis sets

Accurate descriptions of many-particle quantum systems subject to laser interactions can be found using real-time ab initio methods. Of these the arguably most popular and exact is the multi-configuration time-dependent Hartree-Fock (MCTDHF) method. However, MCTDHF suffers from computational limitations in that it quickly becomes too time consuming. The orbital-adaptive time-dependent coupled-cluster (OATDCC) method represents a hierarchy of approximations to MCTDHF that are less computationally expensive while retaining as much accuracy as possible. Building on an existing codebase we have in this thesis generalized the OATDCC method to include Q-space orbital equations. A novel ground state solver is implemented, employing adiabatic switching, since imaginary time propagation is not feasible "out of the box". Furthermore, we implement a sinc-discrete variable representation basis for one-dimensional model systems. We demonstrate that ionization and high-harmonic processes can be described using the OATDCCD method. Comparison with the more accurate, yet more expensive, multiconfigurational time-dependent Hartree-Fock method indicates that the OATDCCD method is an excellent approximation

Neural Wave Functions for Superfluids

Understanding superfluidity remains a major goal of condensed matter physics. Here we tackle this challenge utilizing the recently developed Fermionic neural network (FermiNet) wave function Ansatz for variational Monte Carlo calculations. We study the unitary Fermi gas, a system with strong, short-range, two-body interactions known to possess a superfluid ground state but difficult to describe quantitively. We demonstrate key limitations of the FermiNet Ansatz in studying the unitary Fermi gas and propose a simple modification that outperforms the original FermiNet significantly, giving highly accurate results. We prove mathematically that the new Ansatz is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters. Our approach shares several advantanges with the FermiNet: the use of a neural network removes the need for an underlying basis set; and the flexiblity of the network yields extremely accurate results within a variational quantum Monte Carlo framework that provides access to unbiased estimates of arbitrary ground-state expectation values. We discuss how the method can be extended to study other superfluids.Comment: 14 pages, 5 figures. Talk presented at the 2023 APS March Meeting, March 5-10, 2023, Las Vegas, Nevada, United State