Christoper Roth, UT-Austin

"Learning the Wavefunction of Periodic Systems Using Recurrent Neural Networks"

Abstract: Modeling quantum many-body systems is enormously challenging due to the exponential scaling of Hilbert space with system size. Finding an Ansatz that efficiently compresses the wavefunction is key to simulating large systems. Here, we present an approach for simulating periodic quantum systems using long short term memory networks (LSTMs) whose recurrent structure is able to efficiently capture invariance to discrete translations in the bulk.

We do Variational Monte Carlo using an autoregressive Ansatz, where the probability amplitude and phase associated with an electron having a particular quantum number is conditioned on the quantum numbers of the electrons behind it. These amplitudes and phases are iteratively generated by an LSTM, which is trained to minimize the energy using stochastic gradient descent.

We show that such a formulation can be used to find the ground state of the 1D Hubbard and J1-J2 Heisenberg model for several hundred electrons. Furthermore, we show that we can learn about the bulk by "growing" the sample; iteratively training the solution on larger and larger systems until the edge effects become negligible. We argue that such a scheme can be generalized more naturally to higher dimensions than Density Matrix Renormalization Group.