TY - JOUR
T1 - Dirac-Type Nodal Spin Liquid Revealed by Refined Quantum Many-Body Solver Using Neural-Network Wave Function, Correlation Ratio, and Level Spectroscopy
AU - Nomura, Yusuke
AU - Imada, Masatoshi
N1 - Funding Information:
We acknowledge useful discussions with Satoshi Morita, Anders W. Sandvik, and Zi Yang Meng. We also thank Satoshi Morita for providing us with the raw data in Ref. . Y. N. is grateful for fruitful discussions with Ribhu Kaul, Hidemaro Suwa, Yoshitomo Kamiya, Kenji Harada, Zheng-Cheng Gu, Giuseppe Carleo, and Ryui Kaneko. The implementation of the scheme is done based on the m vmc package . The computation was mainly done at Supercomputer Center, Institute for Solid State Physics, University of Tokyo, and RIKEN supercomputers K and Fugaku. The authors are grateful for the financial support by a Grant-in-Aid for Scientific Research (Grant No. 16H06345) from Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. Y. N. was supported by Grant-in-Aids for Scientific Research (JSPS KAKENHI) (Grants No. 17K14336 and No. 18H01158). This work is financially supported by the MEXT HPCI Strategic Programs, and the Creation of New Functional Devices and High-Performance Materials to Support Next Generation Industries (CDMSI), as well as by “Program for Promoting Researches on the Supercomputer Fugaku” (Basic Science for Emergence and Functionality in Quantum Matter—Innovative Strongly-Correlated Electron Science by Integration of “Fugaku” and Frontier Experiments) (Grants No. hp200132 and No. hp210163). We also acknowledge the support provided by the RIKEN Advanced Institute for Computational Science under the HPCI System Research project (Grants No. hp170263, No. hp180170, and No. hp190145).
Publisher Copyright:
© 2021 authors. Published by the American Physical Society.
PY - 2021/9
Y1 - 2021/9
N2 - Pursuing fractionalized particles that do not bear properties of conventional measurable objects, exemplified by bare particles in the vacuum such as electrons and elementary excitations such as magnons, is a challenge in physics. Here we show that a machine-learning method for quantum many-body systems that has achieved state-of-the-art accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region 0.49≲J2/J1≲0.54 convincingly in spin-1/2 frustrated Heisenberg model with the nearest and next-nearest-neighbor exchanges, J1 and J2, respectively, on the square lattice. This is achieved by combining with the cutting-edge computational schemes known as the correlation ratio and level spectroscopy methods to mitigate the finite-size effects. The quantitative one-to-one correspondence between the correlations in the ground state and the excitation spectra found in the present analyses enables the reliable identification and estimation of the QSL and its nature. The spin excitation spectra containing both singlet and triplet gapless Dirac-like dispersions signal the emergence of gapless fractionalized spin-1/2 Dirac-type spinons in the distinctive QSL phase. Unexplored critical behavior with coexisting and dual power-law decays of Néel antiferromagnetic and dimer correlations is revealed. The power-law decay exponents of the two correlations differently vary with J2/J1 in the QSL phase and thus have different values except for a single point satisfying the symmetry of the two correlations. The isomorph of excitations with the cuprate d-wave superconductors revealed here implies a tight connection between the present QSL and superconductivity. This achievement demonstrates that the quantum-state representation using machine-learning techniques, which had mostly been limited to benchmarks, is a promising tool for investigating grand challenges in quantum many-body physics.
AB - Pursuing fractionalized particles that do not bear properties of conventional measurable objects, exemplified by bare particles in the vacuum such as electrons and elementary excitations such as magnons, is a challenge in physics. Here we show that a machine-learning method for quantum many-body systems that has achieved state-of-the-art accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region 0.49≲J2/J1≲0.54 convincingly in spin-1/2 frustrated Heisenberg model with the nearest and next-nearest-neighbor exchanges, J1 and J2, respectively, on the square lattice. This is achieved by combining with the cutting-edge computational schemes known as the correlation ratio and level spectroscopy methods to mitigate the finite-size effects. The quantitative one-to-one correspondence between the correlations in the ground state and the excitation spectra found in the present analyses enables the reliable identification and estimation of the QSL and its nature. The spin excitation spectra containing both singlet and triplet gapless Dirac-like dispersions signal the emergence of gapless fractionalized spin-1/2 Dirac-type spinons in the distinctive QSL phase. Unexplored critical behavior with coexisting and dual power-law decays of Néel antiferromagnetic and dimer correlations is revealed. The power-law decay exponents of the two correlations differently vary with J2/J1 in the QSL phase and thus have different values except for a single point satisfying the symmetry of the two correlations. The isomorph of excitations with the cuprate d-wave superconductors revealed here implies a tight connection between the present QSL and superconductivity. This achievement demonstrates that the quantum-state representation using machine-learning techniques, which had mostly been limited to benchmarks, is a promising tool for investigating grand challenges in quantum many-body physics.
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U2 - 10.1103/PhysRevX.11.031034
DO - 10.1103/PhysRevX.11.031034
M3 - Article
AN - SCOPUS:85113144069
SN - 2160-3308
VL - 11
JO - Physical Review X
JF - Physical Review X
IS - 3
M1 - 031034
ER -