Investigating ultrafast quantum magnetism with machine learning

Abstract

We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum spin dynamics in the two-dimensional Heisenberg model on a square lattice. For static properties we find close agreement with numerically exact Quantum Monte Carlo results in the thermodynamical limit. For dynamics and small systems, we find excellent agreement with exact diagonalization, while for systems up to N=256 spins close consistency with interacting spin-wave theory is obtained. In all cases the accuracy converges fast with the number of network parameters, giving access to much bigger systems than feasible before. This suggests great potential to investigate the quantum many-body dynamics of large scale spin systems relevant for the description of magnetic materials strongly out of equilibrium.

Fermionic neural-network states for ab-initio electronic structure

“…(4). One conceptual interest of NQS is that, because of the flexibility of the underlying non-linear parameterization, they can be adopted to study both equilibrium 24,25 and out-ofequilibrium [26][27][28][29][30][31] properties of diverse many-body quantum systems. In this work, we adopt a simple neural-network parameterization in terms of a complex-valued, shallow restricted Boltzmann machine (RBM) 10,32 .…”

Quantum walk versus classical wave: Distinguishing ground states of quantum magnets by spacetime dynamics

“…In particular, the subtle magnetic ground states in recently discovered two-dimensional van der Waals materials with CrI 3 [40] as a truly atomically thin ferromagnet would make for interesting test objects of our predictions, provided that real-space and real-time imaging techniques can be pushed accordingly. Similarly, there are some well-known realizations of quasi-two-dimensional Heisenberg antiferromagnets [41], and light-cone spreading has only recently been simulated in such systems [42]. A potential experimental probe is timeresolved resonant inelastic x-ray scattering, as proposed, for instance, in [43] and demonstrated in [44].…”

QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

“…The reason for this often times relies on the fact that the underlying physics of these problems cannot be explained without taking into consideration the contribution from high-energy states excited during the nonequilibrium process. Some prominent examples of such problems include the study of the many-body localisation (MBL) transition [24,25,26,27,28], the Eigenstate Thermalisation hypothesis [29], ergodicity breaking, thermalization and scrambling [30,31,32], quantum quench dynamics [33], periodically-driven systems [34,35,36,37,38,39,40,41,42], non-demolition measurements in many-body systems [43], long-range quantum coherence [44], dynamics-induced instabilities [45,46,47,48,49,50,51,52], adiabatic and counter-diabatic state preparation [53,54,55,56,57], dynamical [58,59] and topological [60] phase transitions applications of Machine Learning to (non-equilibrium) physics [61,49,62,63,64,65,66], optimal control [67,<...>…”

“…As we can we below, the generator function allows us to get away with a single loop. 66 # user-defined generator for stroboscopic dynamics 67 def evolve_gen(psi 0,nT,*U_list): Finally, we are ready to compute the time-dependent quantities of interest. In order to calculate the expectation ψ(t)|H zz |ψ(t) QuSpin has a routine called obs_vs_time().…”