An Anderson Impurity Interacting with the Helical Edge States in a Quantum Spin Hall Insulator

Using the natural orbitals renormalization group(NORG)method,we investigate the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator.It is found that there is a local spin formed at the impurity site and the local spin is completel.y screened by electrons in the quantum spin Hall insulator.Meanwhile,the local spin is screened dominantly by a single active natural orbital.We then show that the Kondo screening mechanism becomes transparent and simple in the framework of the natural orbitals formalism.We project the active natural orbital respectively into real space and momentum space to characterize its structure.We conilrm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state on the edge to which the impurity couples.Furthermore,we study the dynamical property of the active natural orbital represented by the local density of states,from which we observe the Kondo resonance peak.     

Interaction-Induced Characteristic Length in Strongly Many-Body Localized Systems

A complete set of local integrals of motion(LIOM) is a key concept for describing many-body localization(MBL),which explains a variety of intriguing phenomena in MBL systems.For example,LIOM constrain the dynamics and result in ergodicity violation and breakdown of the eigenstate thermalization hypothesis.However,it is difficult to find a complete set of LIOM explicitly and accurately in practice,which impedes some quantitative structural characterizations of MBL systems.Here we propose an accurate numerical method for constructing LIOM,discover through the LIOM an interaction-induced characteristic length +,and prove a ‘quasi-productstate' structure of the eigenstates with that characteristic length + for MBL systems.More specifically,we find that there are two characteristic lengths in the LIOM.The first one is governed by disorder and is of Andersonlocalization nature.The second one is induced by interaction but shows a discontinuity at zero interaction,showing a nonperturbative nature.We prove that the entanglement and correlation in any eigenstate extend not longer than twice the second length and thus the eigenstates of the system are the quasi-product states with such a localization length.     

Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J1-J2 Heisenberg model

Restricted Boltzmann machine (RBM) has been proposed as a powerful variational ansatz to represent the ground state of a given quantum many-body system. On the other hand, as a shallow neural network, it is found that the RBM is still hardly able to capture the characteristics of systems with large sizes or complicated interactions. In order to find a way out of the dilemma, here, we propose to adopt the Green's function Monte Carlo (GFMC) method for which the RBM is used as a guiding wave function. To demonstrate the implementation and effectiveness of the proposal, we have applied the proposal to study the frustrated J₁-J₂ Heisenberg model on a square lattice, which is considered as a typical model with sign problem for quantum Monte Carlo simulations. The calculation results demonstrate that the GFMC method can significantly further reduce the relative error of the ground-state energy on the basis of the RBM variational results. This encourages to combine the GFMC method with other neural networks like convolutional neural networks for dealing with more models with sign problem in the future.