DiracType Nodal Spin Liquid Revealed by Refined Quantum ManyBody Solver Using NeuralNetwork Wave Function, Correlation Ratio, and Level Spectroscopy
Abstract
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 machinelearning method for quantum manybody systems that has achieved stateoftheart accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region 0.49 ≲J_{2}/J_{1}≲0.54 convincingly in spin1 /2 frustrated Heisenberg model with the nearest and nextnearestneighbor exchanges, J_{1} and J_{2}, respectively, on the square lattice. This is achieved by combining with the cuttingedge computational schemes known as the correlation ratio and level spectroscopy methods to mitigate the finitesize effects. The quantitative onetoone 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 Diraclike dispersions signal the emergence of gapless fractionalized spin1 /2 Diractype spinons in the distinctive QSL phase. Unexplored critical behavior with coexisting and dual powerlaw decays of Néel antiferromagnetic and dimer correlations is revealed. The powerlaw decay exponents of the two correlations differently vary with J_{2}/J_{1} 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 quantumstate representation using machinelearning techniques, which had mostly been limited to benchmarks, is a promising tool for investigating grand challenges in quantum manybody physics.
 Publication:

Physical Review X
 Pub Date:
 July 2021
 DOI:
 10.1103/PhysRevX.11.031034
 arXiv:
 arXiv:2005.14142
 Bibcode:
 2021PhRvX..11c1034N
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Superconductivity;
 Quantum Physics
 EPrint:
 18 pages, 17 figures, 2 tables, accepted for publication in Phys. Rev. X