Bootstrap certification of string order in quantum spin chains

arXiv:2609.22420 · cond-mat.str-el, quant-ph · Submitted 2026-09-18 · Read on arXiv

cond-mat.str-el, quant-ph

Submitted: 2026-09-18

Updated: 2026-09-18

Terminology

• Benchmark — 4× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Symmetry Breaking — 2× in this paper · explained in 3 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Noncommutative Polynomial Optimization — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes

Sources

• Bootstrapping Simple QM Systems
• Bootstrapping More QM Systems
• Lower Bounds for Ground States of Condensed Matter Systems
• Quantum Many-body Bootstrap
• Variational-Correlations Approach to Quantum Many-body Problems
• Numerical exploration of the bootstrap in spin chain models
• Bootstrapping the Ising Model on the Lattice
• Defect Bootstrap: Tight Ground State Bounds in Spontaneous Symmetry Breaking Phases
• Bootstrap bounds for Quantum Spin Systems using String Operators
• Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization
• Exact Models for Symmetry-Protected Topological Phases in One Dimension

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