Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network 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 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 $0.49\lesssim J_2/J_1\lesssim 0.54$ convincingly in spin-1/2 frustrated Heisenberg model with the nearest and next-nearest neighbor exchanges, $J_1$ and $J_2$, 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 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 $J_2/J_1$ 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 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.

18 pages, 17 figures, 2 tables, accepted for publication in Phys. Rev. X

References in corpus (14)

• U(1) Gauge Theory of the Hubbard Model : Spin Liquid States and Possible Application to k-(BEDT-TTF)_2 Cu_2 (CN)_3
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Algebraic spin liquid as the mother of many competing orders
• Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Gapless quantum spin liquid, stripe and antiferromagnetic phases in frustrated Hubbard models in two dimensions
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Neural network wave functions and the sign problem
• Quantum-number projection in the path-integral renormalization group method
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Kernel method for corrections to scaling

Cited by in corpus (103)

• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Variational Benchmarks for Quantum Many-Body Problems
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• Optimizing Design Choices for Neural Quantum States
• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas
• Rise and fall of plaquette order in Shastry-Sutherland magnet revealed by pseudo-fermion functional renormalization group
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Pinch-points to half-moons and up in the stars: the kagome skymap
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics
• Quantum spin liquid phase in the Shastry-Sutherland model detected by an improved level spectroscopic method
• Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Neural Network Evolution Strategy for Solving Quantum Sign Structures
• Candidate quantum disordered intermediate phase in the Heisenberg antiferromagnet on the maple-leaf lattice
• Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group
• Electronic spectra with paramagnon fractionalization in the single band Hubbard model
• Superconductivity studied by solving ab initio low-energy effective Hamiltonians for carrier doped CaCuO${}_2$, Bi${}_2$Sr${}_2$CuO${}_6$, Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$, and HgBa${}_2$CuO${}_4$
• Highly resolved spectral functions of two-dimensional systems with neural quantum states
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• $2^{1296}$ Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method
• Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transition and the second-order phase transition in the XXZ models
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Benchmarking energy consumption and latency for neuromorphic computing in condensed matter and particle physics
• Variational optimization of the amplitude of neural-network quantum many-body ground states
• Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
• The quantum Gaussian process state: A kernel-inspired state with quantum support data
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• Certifying ground-state properties of quantum many-body systems
• Symmetry-projected cluster mean-field theory applied to spin systems
• Neural-network quantum states for a two-leg Bose-Hubbard ladder under magnetic flux
• Majorana chiral spin liquid in Mott insulating cuprates
• A framework for efficient ab initio electronic structure with Gaussian Process States
• Learning ground states of gapped quantum Hamiltonians with Kernel Methods
• Investigating Berezinskii-Kosterlitz-Thouless phase transitions in Kagome spin ice by quantifying Monte Carlo process: Distribution of Hamming distances
• Fine-tuning Neural Network Quantum States
• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• Spin dynamics and continuum spectra of the honeycomb J1-J2 antiferromagnetic Heisenberg model
• Scalable Imaginary Time Evolution with Neural Network Quantum States
• Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice
• Variational Quantum Eigensolver Ansatz for the $J_1$-$J_2$-model
• Impact of conditional modelling for a universal autoregressive quantum state
• Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling
• Accurate neural quantum states for interacting lattice bosons
• Are queries and keys always relevant? A case study on Transformer wave functions
• Equivariant Variational Quantum Eigensolver to detect Phase Transitions through Energy Level Crossings
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Free Energy Evaluation Using Marginalized Annealed Importance Sampling
• Investigating Network Parameters in Neural-Network Quantum States
• Tunable $t-t^{\prime }-U$ Hubbard models in twisted square homobilayers
• Neural Network Quantum States analysis of the Shastry-Sutherland model
• Linear combinations of cluster mean-field states applied to spin systems
• Defining a universal sign to strictly probe a phase transition
• Beyond single-reference fixed-node approximation in ab initio Diffusion Monte Carlo using antisymmetrized geminal power applied to systems with hundreds of electrons
• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• 2D excitation information by MPS method on infinite helixes
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Boltzmann machines and quantum many-body problems
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Non-stabilizerness of Neural Quantum States
• Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states
• Neural Network Approach to Scaling Analysis of Critical Phenomena
• Quantum criticality of bandwidth-controlled Mott transition
• Probing a quantum spin liquid with equilibrium and nonequilibrium hole dynamics
• Exploring explicit coarse-grained structure in artificial neural networks
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• Variational Neural and Tensor Network Approximations of Thermal States
• Fractionalized Fermi liquids and the cuprate phase diagram
• Understanding Symmetry Breaking in Twisted Bilayer Graphene from Cluster Constraints
• Design principles of deep translationally-symmetric neural quantum states for frustrated magnets
• General Formula for the Green's Function Approach to the Spin-1/2 Antiferromagnetic Heisenberg Model
• Noncoplanar and chiral spin states on the way towards Néel ordering in fullerene Heisenberg models
• From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
• Improving neural network performance for solving quantum sign structure
• Emergence of global receptive fields capturing multipartite quantum correlations
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Exact diagonalization study of triangular Heisenberg model with four-spin ring-exchange interaction
• Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Composite Spatial Monte Carlo Integration Based on Generalized Least Squares
• Kinetic samplers for neural quantum states
• Accuracy of Restricted Boltzmann Machines for the one-dimensional $J_1-J_2$ Heisenberg model
• Spiral Phase and Phase Diagram of the $S$=1/2 XXZ Model on the Shastry-Sutherland Lattice
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice
• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
• Neural-Network Quantum States for Periodic Systems in Continuous Space
• Learning a compass spin model with neural network quantum states
• Optimizing Temperature Distributions for Training Neural Quantum States using Parallel Tempering
• Bridging the Gap between Deep Learning and Frustrated Quantum Spin System for Extreme-scale Simulations on New Generation of Sunway Supercomputer
• Predicting sampling advantage of stochastic Ising Machines for Quantum Simulations
• The toric code under antiferromagnetic isotropic Heisenberg interactions
• Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets