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arXiv:2403.08184 · Physical review. B./Physical review. B

Quantum skyrmion dynamics studied by neural network quantum states

Ashish Joshi, Robert Peters, Thore Posske

Published Sep 5, 2024• 11 citations
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Abstract

We study the dynamics of quantum skyrmions under a magnetic field gradient using neural network quantum states. First, we obtain a quantum skyrmion lattice ground state using variational Monte Carlo with a restricted Boltzmann machine as the variational ansatz for a quantum Heisenberg model with a Dzyaloshinskii-Moriya interaction. Then, using the time-dependent variational principle, we study the real-time evolution of quantum skyrmions after a Hamiltonian quench with an inhomogeneous external magnetic field. We show that field gradients are an effective way of manipulating and moving quantum skyrmions. Furthermore, we demonstrate that quantum skyrmions can decay when interacting with each other. This work shows that neural network quantum states offer a promising way of studying the real-time evolution of quantum magnetic systems that are outside the realm of exact diagonalization. Published by the American Physical Society 2024

DOI
10.1103/physrevb.110.104411

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Study of nanostructures coupled with a superconducting lead via the neural-network quantum states methods.\n

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The Neural-Network Quantum States (NNQS) method is rapidly emerging as a powerful tool for investigating \nquantum many-body physics. By combining variational Monte Carlo techniques with neural network-based \nvariational functions, this approach leverages the remarkable advancements in deep learning achieved in \nrecent years. While substantial progress has been made in simulating magnetic systems on lattices, simple \nmolecules, and even continuous systems, the ab initio simulation of complex strongly correlated electron \nsystems continues to pose significant challenges. With the help of the generalized atomic limit (GAL) – a \nrecently developed model describing a system of quantum dots coupled to a superconducting lead – we \nattempt to show the efficiency and accuracy of NNQS, mainly the Restricted Boltzmann Machine, by comparing \nthe acquired results to other available methods such as exact diagonalization. The simultaneous study of the \nsystem’s properties such as the energy spectrum and quantum phase transitions could bring advancements \nin electronics, sensors or the design of high-quality qubits used in quantum computers.

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We study the dynamics of quantum skyrmions under a magnetic field gradient using neural network quantum states. First, we obtain a quantum skyrmion lattice ground state using variational Monte Carlo with a restricted Boltzmann machine as the variational ansatz for a quantum Heisenberg model with a Dzyaloshinskii-Moriya interaction. Then, using the time-dependent variational principle, we study the real-time evolution of quantum skyrmions after a Hamiltonian quench with an inhomogeneous external magnetic field. We show that field gradients are an effective way of manipulating and moving quantum skyrmions. Furthermore, we demonstrate that quantum skyrmions can decay when interacting with each other. This work shows that neural network quantum states offer a promising way of studying the real-time evolution of quantum magnetic systems that are outside the realm of exact diagonalization. Published by the American Physical Society 2024
We investigate the ground state properties of quantum skyrmions in a ferromagnet using variational Monte Carlo with the neural network quantum state as variational ansatz. We study the ground states of a two-dimensional quantum Heisenberg model in the presence of the Dzyaloshinskii-Moriya interaction (DMI) and show that the ground state accommodates a quantum skyrmion for a large range of parameters, especially at large DMI. The spins in these quantum skyrmions are weakly entangled, and the entanglement increases with decreasing DMI. We also find that the central spin is completely disentangled from the rest of the lattice, establishing a non-destructive way of detecting this type of skyrmion by local magnetization measurements. While neural networks are well suited to detect weakly entangled skyrmions with large DMI, they struggle to describe skyrmions in the small DMI regime due to nearly degenerate ground states and strong entanglement. In this paper, we propose a method to identify this regime and a technique to alleviate the problem. Finally, we analyze the workings of the neural network and explore its limits by pruning. Our work shows that neural network quantum states can be efficiently used to describe the quantum magnetism of large systems exceeding the size manageable in exact diagonalization by far.
We utilize neural network quantum states (NQS) to investigate the ground state properties of the Heisenberg model on a Shastry-Sutherland lattice using the variational Monte Carlo method. We show that already relatively simple NQSs can be used to approximate the ground state of this model in its different phases and regimes. We first compare several types of NQSs with each other on small lattices and benchmark their variational energies against the exact diagonalization results. We argue that when precision, generality, and computational costs are taken into account, a good choice for addressing larger systems is a shallow restricted Boltzmann machine NQS. We then show that such NQS can describe the main phases of the model in zero magnetic field. Moreover, NQS based on a restricted Boltzmann machine correctly describes the intriguing plateaus forming in magnetization of the model as a function of increasing magnetic field.
We investigate the Shastry-Sutherland model (SSM), i.e., spin-1/2 quantum Heisen- berg model on a Shastry-Sutherland lattice, using a newly emerging approach exploiting well-developed machine learning techniques. We utilize neural networks as variational quantum states in quantum Monte Carlo investigations of the ground state properties. We first focus on SSM without an external magnetic field. For small lattices accessible via exact diagonalization, we compare the precision of various architectures based on re- stricted Boltzmann machines (RBM) or group-convolutional neural networks. The most versatile and precise architecture, namely complex-valued RBM, is then applied for larger lattices. Here we investigate the frustrated regime. We show that the RBM is able to represent all three of the major and fundamentally different phases of SSM. Finally, we apply the complex-valued RBM for SSM in a finite external magnetic field. We find that it cannot capture the intriguing steps in magnetization typical for SSM correctly due to its tendency to prefer more ordered states with higher magnetization. 1
The Neural-Network Quantum States (NNQS) method is rapidly emerging as a powerful tool for investigating quantum many-body physics.By combining variational Monte Carlo techniques with neural network-based variational functions, this approach leverages the remarkable advancements in deep learning achieved in recent years.While substantial progress has been made in simulating magnetic systems on lattices, simple molecules, and even continuous systems, the ab initio simulation of complex strongly correlated electron systems continues to pose significant challenges.With the help of the generalized atomic limit (GAL) -a recently developed model describing a system of quantum dots coupled to a superconducting lead -we attempt to show the efficiency and accuracy of NNQS, mainly the Restricted Boltzmann Machine, by comparing the acquired results to other available methods such as exact diagonalization.The simultaneous study of the system's properties such as the energy spectrum and quantum phase transitions could bring advancements in electronics, sensors or the design of high-quality qubits used in quantum computers.
In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine-learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.
The Neural-Network Quantum States (NNQS) method is rapidly emerging as a powerful tool for investigating \nquantum many-body physics. By combining variational Monte Carlo techniques with neural network-based \nvariational functions, this approach leverages the remarkable advancements in deep learning achieved in \nrecent years. While substantial progress has been made in simulating magnetic systems on lattices, simple \nmolecules, and even continuous systems, the ab initio simulation of complex strongly correlated electron \nsystems continues to pose significant challenges. With the help of the generalized atomic limit (GAL) – a \nrecently developed model describing a system of quantum dots coupled to a superconducting lead – we \nattempt to show the efficiency and accuracy of NNQS, mainly the Restricted Boltzmann Machine, by comparing \nthe acquired results to other available methods such as exact diagonalization. The simultaneous study of the \nsystem’s properties such as the energy spectrum and quantum phase transitions could bring advancements \nin electronics, sensors or the design of high-quality qubits used in quantum computers.