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This research introduces non-Euclidean neural quantum states utilizing hyperbolic Lorentz recurrent architectures, demonstrating superior efficiency in modeling ground state wavefunctions compared to traditional Euclidean counterparts. By achieving better representations with significantly fewer parameters on Heisenberg spin models, the study validates a more resource-efficient approach for variational Monte Carlo simulations of complex quantum many-body systems.
New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures
arXiv:2604.24337v3 Announce Type: replace Abstract: In this work, we construct new non-Euclidean neural quantum states (NQS) based on hyperbolic Lorentz recurrent architectures (RNN/GRU). These constructions, together with the Poincare RNN NQS also newly constructed here, extend the class of previously introduced non-Eucllidean NQS which consists only of Poincare hyperbolic GRU. Using the Heisenberg J1J2 and J1J2J3 models consisting of 100 spins in the Variational Monte Carlo (VMC) setting, we show that the four hyperbolic RNN/GRU NQS variants are always able to furnish better representations of the ground state wavefunctions of the quantum systems than their respective Euclidean counterparts with the same architecture. In our experiments, among the four hyperbolic NQS, Lorentz RNN stands out in particular because despite having almost three times fewer parameters, it is capable of surpassing the more complex Poincare GRU and Lorentz GRU to emerge as the best overall hyperbolic NQS ansatz on many instances involving different J2 and (J2,J3) couplings. Given the findings from this work showing that the four newly constructed hyperbolic RNN/GRU NQS ansatze are able to outperform the well-established Euclidean RNN/GRU NQS in Heisenberg spin models, we establish the utility and efficiency of the hyperbolic Lorentz RNN/GRU NQS as well as the Poincare RNN/GRU NQS for future variational studies of quantum many-body systems, especially those exhibiting a hierarchical structure in the form of the different degrees of nearest-neighbor interactions.
Abstract:In this work, we construct new non-Euclidean neural quantum states (NQS) based on hyperbolic Lorentz recurrent architectures (RNN/GRU). These constructions, together with the Poincare RNN NQS also newly constructed here, extend the class of previously introduced non-Eucllidean NQS which consists only of Poincare hyperbolic GRU. Using the Heisenberg J1J2 and J1J2J3 models consisting of 100 spins in the Variational Monte Carlo (VMC) setting, we show that the four hyperbolic RNN/GRU NQS variants are always able to furnish better representations of the ground state wavefunctions of the quantum systems than their respective Euclidean counterparts with the same architecture. In our experiments, among the four hyperbolic NQS, Lorentz RNN stands out in particular because despite having almost three times fewer parameters, it is capable of surpassing the more complex Poincare GRU and Lorentz GRU to emerge as the best overall hyperbolic NQS ansatz on many instances involving different J2 and (J2,J3) couplings. Given the findings from this work showing that the four newly constructed hyperbolic RNN/GRU NQS ansatze are able to outperform the well-established Euclidean RNN/GRU NQS in Heisenberg spin models, we establish the utility and efficiency of the hyperbolic Lorentz RNN/GRU NQS as well as the Poincare RNN/GRU NQS for future variational studies of quantum many-body systems, especially those exhibiting a hierarchical structure in the form of the different degrees of nearest-neighbor interactions.
v2: additional improved results added, new discussions added, main conclusions remain unchanged. v3: title changed to reflect the main findings involving Lorentz hyperbolic recurrent architectures, minor descriptions added, abstract slightly modified to enhance clarity
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG)
arXiv:2604.24337 [quant-ph]
(or arXiv:2604.24337v3 [quant-ph] for this version)
From: H. L. Dao [view email] [v1] Mon, 27 Apr 2026 11:27:32 UTC (1,297 KB) [v2] Thu, 16 Jul 2026 16:03:32 UTC (634 KB) [v3] Mon, 3 Aug 2026 09:44:05 UTC (635 KB)
Full text under the publisher's open licence · 309 words
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