Many-body quantum sign structures as non-glassy Ising models

Abstract

The non-trivial phase structure of the eigenstates of many-body quantum systems severely limits the applicability of quantum Monte Carlo, variational, and machine learning methods. Here, we study real-valued signful ground-state wave functions of frustrated quantum spin systems and, assuming that the tasks of finding wave function amplitudes and signs can be separated, show that the signs can be easily bootstrapped from the amplitudes. We map the problem of finding the sign structure to an auxiliary classical Ising model defined on a subset of the Hilbert space basis. We show that the Ising model does not exhibit significant frustrations even for highly frustrated parental quantum systems, and is solvable with a fully deterministic $O(K\log K)$-time combinatorial algorithm (where $K$ is the Ising model size). Given the ground state amplitudes, we reconstruct the signs of the ground states of several frustrated quantum models, thereby revealing the hidden simplicity of many-body sign structures.

arXiv comment11 pages, 9 figures in the main text; 9 pages, 4 figures in the supplemental information

References in corpus (32)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum Coherence as a Resource
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Time-dependent variational principle for quantum lattices
• Many-body quantum state tomography with neural networks
• Perspectives of quantum annealing: Methods and implementations
• Machine learning quantum phases of matter beyond the fermion sign problem
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Subspace-search variational quantum eigensolver for excited states
• Optimization of quantum Monte Carlo wave functions by energy minimization
• Wave function optimization in the variational Monte Carlo method
• Quantum versus Classical Annealing of Ising Spin Glasses
• Neural Quantum States of frustrated magnets: generalization and sign structure
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• Ruling out real-valued standard formalism of quantum theory
• Neural Gutzwiller-projected variational wave functions
• Neural network wave functions and the sign problem
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Non-Fermi-liquid d-wave metal phase of strongly interacting electrons
• Structure of fermion nodes and nodal cells
• Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
• Hybrid quantum annealing for larger-than-QPU lattice-structured problems
• Entanglement and the Sign Structure of Quantum States
• Expressive power of complex-valued restricted Boltzmann machines for solving non-stoquastic Hamiltonians
• Topological Origin of the Fermion Sign Problem
• Frustration - how it can be measured
• Neural Network Evolution Strategy for Solving Quantum Sign Structures
• lattice-symmetries: A package for working with quantum many-body bases
• Fermionic quantum criticality and the fractal nodal surface
• Entanglement entropies and fermion signs of critical metals
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

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