Chebyshev expansion of spectral functions using restricted Boltzmann machines

Abstract

Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional systems present insurmountable hurdles, ranging from the sign problem in quantum Monte Carlo (MC), to the entanglement area law in tensor network based methods. We hereby present a variational approach based on a Chebyshev expansion of the spectral function and a neural network representation for the wave functions. The Chebyshev moments are obtained by recursively applying the Hamiltonian and projecting on the space of variational states using a modified natural gradient descent method. We compare this approach with a modified approximation of the spectral function which uses a Krylov subspace constructed from the "Chebyshev wave-functions". We present results for the one-dimensional and two-dimensional Heisenberg model on the square lattice, and compare to those obtained by other methods in the literature.

8 pages, 5 figs

References in corpus (14)

• Real time evolution using the density matrix renormalization group
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Time-evolving a matrix product state with long-ranged interactions
• Fractional excitations in the square-lattice quantum antiferromagnet
• Time-step targetting methods for real-time dynamics using DMRG
• 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
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• Chebyshev expansion for Impurity Models using Matrix Product States
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Spectral functions and time evolution from the Chebyshev recursion
• Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group

Cited by in corpus (10)

• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Designing quantum many-body matter with conditional generative adversarial networks
• Highly resolved spectral functions of two-dimensional systems with neural quantum states
• Neural network approach to quasiparticle dispersions in doped antiferromagnets
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• Is attention all you need to solve the correlated electron problem?
• Capturing dynamical correlations using implicit neural representations
• Sample generation for the spin-fermion model using neural networks
• A circuit-differentiation framework for Green's functions on quantum computers
• Physically interpretable approximations of many-body spectral functions