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We present an algorithm to estimate the excited states of a quantum system by variational Monte Carlo, which has no free parameters and requires no orthogonalization of the states, instead transforming the problem into that of finding the ground state of an expanded system. Arbitrary observables can be calculated, including off-diagonal expectations, such as the transition dipole moment. The method works particularly well with neural network ansätze, and by combining this method with the FermiNet and Psiformer ansätze, we can accurately recover excitation energies and oscillator strengths on a range of molecules. We achieve accurate vertical excitation energies on benzene-scale molecules, including challenging double excitations. Beyond the examples presented in this work, we expect that this technique will be of interest for atomic, nuclear, and condensed matter physics.

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.

Grid cells are part of a widespread network which supports navigation and spatial memory. Stable grid patterns appear late in development, in concert with extracellular matrix aggregates termed perineuronal nets (PNNs) that condense around inhibitory neurons. It has been suggested that PNNs stabilize synaptic connections and long-term memories, but their role in the grid cell network remains elusive. We show that removal of PNNs leads to lower inhibitory spiking activity, and reduces grid cells' ability to create stable representations of a novel environment. Furthermore, in animals with disrupted PNNs, exposure to a novel arena corrupted the spatiotemporal relationships within grid cell modules, and the stored representations of a familiar arena. Finally, we show that PNN removal in entorhinal cortex distorted spatial representations in downstream hippocampal neurons. Together this work suggests that PNNs provide a key stabilizing element for the grid cell network.