A machine learning approach to dynamical properties of quantum many-body systems

Abstract

Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional quantum Hall states, for instance), and others operate as a black box that may contain information about the underlying structure of entanglement and correlations (tensor networks, neural networks) and offer the advantage of a large set of variational parameters that can be efficiently optimized. However, using variational approaches to study excited states and, in particular, calculating the excitation spectrum, remains a challenge. We present a variational method to calculate the dynamical properties and spectral functions of quantum many-body systems in the frequency domain, where the Green's function of the problem is encoded in the form of a restricted Boltzmann machine (RBM). We introduce a natural gradient descent approach to solve linear systems of equations and use Monte Carlo to obtain the dynamical correlation function. In addition, we propose a strategy to regularize the results that improves the accuracy dramatically. As an illustration, we study the dynamical spin structure factor of the one dimensional $J_1-J_2$ Heisenberg model. The method is general and can be extended to other variational forms.

References in corpus (36)

• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Correlated Electrons in High Temperature Superconductors
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Geometric Quantum Mechanics
• Dynamical density-matrix renormalization-group method
• Dynamical Correlation Functions using the Density Matrix Renormalization Group
• Wave function optimization in the variational Monte Carlo method
• Fractional excitations in the square-lattice quantum antiferromagnet
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Energy and variance optimization of many body wave functions
• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• Time-step targetting methods for real-time dynamics using DMRG
• Ground State and Finite Temperature Lanczos Methods
• Chebyshev matrix product state approach for spectral functions
• Solving the Bose-Hubbard model with machine learning
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Optimizing large parameter sets in variational quantum Monte Carlo
• Green Function Monte Carlo with Stochastic Reconfiguration: an effective remedy for the sign problem disease
• Constrained sampling method for analytic continuation
• Algorithmic differentiation and the calculation of forces by quantum Monte Carlo
• Excitations and the tangent space of projected entangled-pair states
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Spectral functions and time evolution from the Chebyshev recursion
• Dynamical structure factor of the $J_1-J_2$ Heisenberg model in one dimension: the variational Monte Carlo approach
• Variational study of the neutron resonance mode in the cuprate superconductors
• Scattering particles in quantum spin chains
• Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions
• The Nonequilibrium Many-Body Problem as a paradigm for extreme data science

Cited by in corpus (22)

• Geometry of variational methods: dynamics of closed quantum systems
• Neural network wave functions and the sign problem
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• A variational quantum eigensolver for dynamic correlation functions
• Role of stochastic noise and generalization error in the time propagation of neural-network quantum states
• Predicting impurity spectral functions using machine learning
• Neural network approach to quasiparticle dispersions in doped antiferromagnets
• Highly resolved spectral functions of two-dimensional systems with neural quantum states
• Chebyshev expansion of spectral functions using restricted Boltzmann machines
• A Bayesian Inference Framework for Compression and Prediction of Quantum States
• Beyond perturbation theory: A time-dependent approach to inelastic scattering spectroscopies in- and away from equilibrium
• Momentum-resolved time evolution with matrix product states
• Neural network enhanced hybrid quantum many-body dynamical distributions
• Spectral features of polaronic excitations in a superconducting analog simulator
• Investigating Network Parameters in Neural-Network Quantum States
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Boltzmann machines and quantum many-body problems
• Investigation of bi-particle states in gate-array-controlled quantum-dot systems aided by machine learning techniques
• Sample generation for the spin-fermion model using neural networks
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• Experimental kernel-based quantum machine learning in finite feature space
• Machine Learning Green's Functions of Strongly Correlated Hubbard Models