Condensed Matter

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

Fermi liquids are gapless quantum many-body states of fermions, which describes electrons in the normal state of most metals at low temperature. Despite its long history of study, there has been renewed interest in understanding the stability of Fermi liquid from the perspectives of emergent symmetry and quantum anomaly. In this talk, I will introduce the concept of Fermi surface anomaly and propose a possible scheme to classify it. The classification scheme is based on viewing the Fermi surface as the boundary of a Chern insulator in the phase space, with an unusual dimension counting arising from the non-commutative phase space geometry. This enables us to extend the notion of Fermi surface anomaly to the non-perturbative cases and discuss symmetric mass generation on the Fermi surface when the anomaly is canceled. I will provide examples of lattice models that demonstrate Fermi surface symmetric mass generation and make connections to the recent progress in understanding the pseudo-gap transition in cuprate materials.

Zoom link: https://pitp.zoom.us/j/97223165997?pwd=SkhJZEt1ejhQRm0yK2tKS3NhM2o2Zz09