Condensed Matter

Dense hydrogen, the most abundant matter in the visible universe, exhibits a range of fascinating physical phenomena such as metallization and high-temperature superconductivity, with significant implications for planetary physics and nuclear fusion research. Accurate prediction of the equations of state and phase diagram of dense hydrogen has long been a challenge for computational methods. In this talk, we present a deep generative model-based variational free energy approach to tackle the problem of dense hydrogen, overcoming the limitations of traditional computational methods. Our approach employs a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wavefunction at given proton positions. The joint optimization of these two neural networks leads to a comparable variational free energy to previous coupled electron-ion Monte Carlo calculations. Our results suggest that hydrogen in planetary conditions is even denser than previously estimated using Monte Carlo and ab initio molecular dynamics methods. Having reliable computation of the equation of state for dense hydrogen, and in particular, direct access to its entropy and free energy, opens new opportunities in planetary modeling and high-pressure physics research.

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09 We introduce a novel neural quantum state architecture for the accurate simulation of extended, strongly interacting fermions in continuous space. The variational state is parameterized via permutation equivariant message passing neural networks to transform single-particle coordinates to highly correlated quasi-particle coordinates. We show the versatility and accuracy of this Ansatz by simulating the ground-state of the 3D homogeneous electron gas at different densities and system sizes. Our model respects basic symmetries of the Hamiltonian, such as continuous translation symmetries. We compare our ground-state energies to results obtained by different state-of-the-art NQS Ansaetze for continuous space, as well as to different quantum chemistry methods. We obtain better or comparable ground-state energies, while using orders of magnitudes less variational parameters and optimization steps. We investigate its capability of identifying and representing different phases of matter without imposing any structural bias toward a given phase. We scale up to system sizes of N=128 particles, opening the door for future work on finite-size extrapolations to the thermodynamic limit.

ZOOM: https://pitp.zoom.us/j/94595394881?pwd=OUZSSXpzYlhFcGlIRm81Y3VaYVpCQT09 In this work, we use data-driven methods to reduce the dimensionality of the vertex function for the Hubbard model and spin liquid model. By employing a deep learning architecture based on the autoencoder, we show that the functional renormalization group (FRG) dynamics can be efficiently learned. Our approach is compared with other methods, including principal component analysis and dynamic mode decomposition. Our results demonstrate the effectiveness of our proposed approach for understanding the FRG flow in these models.

Macroscopic physics of a quantum many-body systems on a lattice is commonly captured by a continuum field theory. We will discuss the interplay between lattice effects and continuum theory from the perspective of symmetry and ’t Hooft anomalies. In the first part of the talk, using the example of a spin-1/2 XXZ chain, we will show how the continuum limit of a lattice model is properly described in terms of a field theory with topological defects. In particular, anomaly explains a curious size dependence of the ground state momentum in the XXZ chain. In the second part, we will examine U(1) filling anomaly for subsystem symmetries. With a generalized flux-insertion argument, we derive nontrivial constraints on the mobility of excitations in a symmetry-preserving gapped phase.

Zoom link:  https://pitp.zoom.us/j/96117447396?pwd=QVNaSHdHeDh1RENvenRjamVlVGNudz09