Network-Initialized Monte Carlo Based on Generative Neural Networks

@article{Lu2022NetworkInitializedMC,
  title={Network-Initialized Monte Carlo Based on Generative Neural Networks},
  author={Hongyu Lu and Chuhao Li and Bin-Bin Chen and Wei Li and Yang Qi and Zi Yang Meng},
  journal={Chinese Physics Letters},
  year={2022}
}
We design generative neural networks that generate Monte Carlo configurations with complete absence of autocorrelation from which only short Markov chains are needed before making measurements for physical observables, irrespective of the system locating at the classical critical point, fermionic Mott insulator, Dirac semimetal, or quantum critical point. We further propose a network-initialized Monte Carlo scheme based on such neural networks, which provides independent samplings and can… 

References

SHOWING 1-10 OF 67 REFERENCES
Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits
TLDR
An efficient variational algorithm is devised to jointly optimize the classical neural network and the quantum circuit to solve quantum statistical mechanics problems and obtain thermal observables such as the variational free energy, entropy, and specific heat.
Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
TLDR
The variational density matrix approach to the thermal properties of interacting fermions in the continuum is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model and holds the promise to deliver new physical results on strongly correlated fermIONS in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.
Machine learning quantum phases of matter beyond the fermion sign problem
TLDR
It is demonstrated that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems.
Constructing exact representations of quantum many-body systems with deep neural networks
TLDR
A technique to construct classical representations of many-body quantum systems based on artificial neural networks based on the deep Boltzmann machine architecture, based on which two layers of hidden neurons mediate quantum correlations are constructed.
Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems
TLDR
The principles found for the update in continuous time generalize to any continuous variables in the space of discrete virtual transitions, and in principle make it possible to simulate continuous systems exactly.
World-line and Determinantal Quantum Monte Carlo Methods for Spins, Phonons and Electrons
In this chapter we will concentrate primarily on world-line methods with loop updates, for spins and also for spin-phonon systems, as well as on the auxiliary field quantum Monte Carlo (QMC) method.
Solving the quantum many-body problem with artificial neural networks
TLDR
A variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons and a reinforcement-learning scheme that is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems.
Machine learning for quantum matter
ABSTRACT Quantum matter, the research field studying phases of matter whose properties are intrinsically quantum mechanical, draws from areas as diverse as hard condensed matter physics, materials
Itinerant quantum critical point with fermion pockets and hotspots
TLDR
A state-of-the-art large-scale quantum Monte Carlo simulation technique is developed and systematically investigated the itinerant quantum critical point on a 2D square lattice with antiferromagnetic spin fluctuations at wavevector Q=(π,π)—a problem that resembles the Fermi surface setup and low-energy antiferromeagnetic fluctuations in high-Tc cuprates and other critical metals, which might be relevant to their non–Fermi-liquid behaviors.
Quantum spin liquid emerging in two-dimensional correlated Dirac fermions
TLDR
It is shown, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermion and an antiferromagnetically ordered Mott insulator.
...
...