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arXiv:2303.14108 · SciPost Physics Core

Neural network quantum states analysis of the Shastry-Sutherland model

Matěj Mezera, Jana Menšíková, Pavel Baláž, Martin Žonda

Published Dec 22, 2023• 5 citations
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Abstract

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.

DOI
10.21468/scipostphyscore.6.4.088

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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.
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
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.
Variational Monte Carlo with neural network quantum states has proven to be a promising avenue for evaluating the ground state energy of spin Hamiltonians. Based on anecdotal evidence, it has been claimed repeatedly in the literature that neural network quantum state simulations are insensitive to the sign problem. We present a detailed and systematic study of restricted Boltzmann machine (RBM) based variational Monte Carlo for quantum spin chains, resolving exactly how relevant stoquasticity is in this setting. We show that in most cases, when the Hamiltonian is phase connected with a stoquastic point, the complex RBM state can faithfully represent the ground state, and local quantities can be evaluated efficiently by sampling. On the other hand, we identify a number of new phases that are challenging for the RBM Ansatz, including non-topological robust non-stoquastic phases as well as stoquastic phases where sampling is nevertheless inefficient. Our results suggest that great care needs to be taken with neural network quantum state based variational Monte Carlo when the system under study is highly frustrated.
Artificial neural networks have been recently introduced as a general ansatz to represent many-body wave functions. In conjunction with variational Monte Carlo calculations, this ansatz has been applied to find Hamiltonian ground states and their energies. Here, we provide extensions of this method to study excited states, a central task in several many-body quantum calculations. First, we give a prescription that allows us to target eigenstates of a (nonlocal) symmetry of the Hamiltonian. Second, we give an algorithm to compute low-lying excited states without symmetries. We demonstrate our approach with both restricted Boltzmann machines and feed-forward neural networks. Results are shown for the one-dimensional spin-1/2 Heisenberg model, and for the one-dimensional Bose-Hubbard model. When comparing to exact results, we obtain good agreement for a large range of excited-states energies. Interestingly, we find that deep networks typically outperform shallow architectures for high-energy states.