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Quantum Many-body Bootstrap

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arxiv 2006.06002 v2 pith:35XTUWZF submitted 2020-06-10 cond-mat.str-el cond-mat.stat-mech

Xizhi Han This is my paper · ORCID
classification cond-mat.str-elcond-mat.stat-mech
keywords boundsgroundstatebootstrapmany-bodymethodquantumsystems
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A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing positivity constraints on certain operator expectation values. Complemented with variational upper bounds, ground state observables are constrained to be within a narrow range. The method is demonstrated with the Hubbard model in one and two dimensions, and bounds on ground state double occupancy and magnetization are discussed.

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  1. Bootstrapping periodic quantum systems

    hep-th 2025-07 conditional novelty 7.0 of 10

    A bootstrap method that includes the translation operator and uses reality conditions computes accurate Bloch-band dispersion relations for the cosine potential without positivity constraints.

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