Chen, A.; Heyl, M. Empowering deep neural quantum states through efficient optimization Journal Article Nat. Phys. 20, 1476, 2024. @article{chen_empowering_2024,
title = {Empowering deep neural quantum states through efficient optimization},
author = {A. Chen and M. Heyl},
doi = {10.1038/s41567-024-02566-1},
year = {2024},
date = {2024-07-01},
urldate = {2024-07-01},
journal = {Nat. Phys.},
volume = {20},
number = {9},
pages = {1476},
abstract = {Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum many-body problem by encoding the many-body wavefunction into artificial neural networks. However, this method has faced the critical limitation that existing optimization algorithms are not suitable for training modern large-scale deep network architectures. Here, we introduce a minimum-step stochastic-reconfiguration optimization algorithm, which allows us to train deep neural quantum states with up to 106 parameters. We demonstrate our method for paradigmatic frustrated spin-1/2 models on square and triangular lattices, for which our trained deep networks approach machine precision and yield improved variational energies compared to existing results. Equipped with our optimization algorithm, we find numerical evidence for gapless quantum-spin-liquid phases in the considered models, an open question to date. We present a method that captures the emergent complexity in quantum many-body problems through the expressive power of large-scale artificial neural networks.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum many-body problem by encoding the many-body wavefunction into artificial neural networks. However, this method has faced the critical limitation that existing optimization algorithms are not suitable for training modern large-scale deep network architectures. Here, we introduce a minimum-step stochastic-reconfiguration optimization algorithm, which allows us to train deep neural quantum states with up to 106 parameters. We demonstrate our method for paradigmatic frustrated spin-1/2 models on square and triangular lattices, for which our trained deep networks approach machine precision and yield improved variational energies compared to existing results. Equipped with our optimization algorithm, we find numerical evidence for gapless quantum-spin-liquid phases in the considered models, an open question to date. We present a method that captures the emergent complexity in quantum many-body problems through the expressive power of large-scale artificial neural networks. |  |
Kosior, A.; Heyl, M. Vortex loop dynamics and dynamical quantum phase transitions in three-dimensional fermion matter Journal Article Phys. Rev. B 109, L140303, 2024. @article{kosior_vortex_2024,
title = {Vortex loop dynamics and dynamical quantum phase transitions in three-dimensional fermion matter},
author = {A. Kosior and M. Heyl},
doi = {10.1103/physrevb.109.l140303},
year = {2024},
date = {2024-04-15},
urldate = {2024-01-01},
journal = {Phys. Rev. B},
volume = {109},
number = {14},
pages = {L140303},
abstract = {Over the past decade, dynamical quantum phase transitions (DQPTs) have emerged as a paradigm shift in understanding nonequilibrium quantum many-body systems. However, the challenge lies in identifying order parameters that effectively characterize the associated dynamic phases. In this study we investigate the behavior of vortex singularities in the phase of the Green's function for a broad class of fermion lattice models in three dimensions after an instantaneous quench in both interacting and noninteracting systems. We find that the full set of vortices form one-dimensional dynamical objects, which we call vortex loops. We propose that the number of such vortex loops can be interpreted as a quantized order parameter that distinguishes between different nonequilibrium phases. Our results establish an explicit link between variations in the order parameter and DQPTs in the noninteracting scenario. Moreover, we show that the vortex loops are robust in the weakly interacting case, even though there is no direct relation between the Loschmidt amplitude and the Green's function. Finally, we observe that vortex loops can form complex dynamical patterns in momentum space. Our findings provide valuable insights for developing definitions of dynamical order parameters in nonequilibrium systems.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Over the past decade, dynamical quantum phase transitions (DQPTs) have emerged as a paradigm shift in understanding nonequilibrium quantum many-body systems. However, the challenge lies in identifying order parameters that effectively characterize the associated dynamic phases. In this study we investigate the behavior of vortex singularities in the phase of the Green's function for a broad class of fermion lattice models in three dimensions after an instantaneous quench in both interacting and noninteracting systems. We find that the full set of vortices form one-dimensional dynamical objects, which we call vortex loops. We propose that the number of such vortex loops can be interpreted as a quantized order parameter that distinguishes between different nonequilibrium phases. Our results establish an explicit link between variations in the order parameter and DQPTs in the noninteracting scenario. Moreover, we show that the vortex loops are robust in the weakly interacting case, even though there is no direct relation between the Loschmidt amplitude and the Green's function. Finally, we observe that vortex loops can form complex dynamical patterns in momentum space. Our findings provide valuable insights for developing definitions of dynamical order parameters in nonequilibrium systems. | |
