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Bootstrapping Lattice Vacua
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This paper demonstrates the application of semidefinite programming to lattice field theories, showcasing spin chains and lattice scalar field theory. Requiring expectation values of manifestly positive semi-definite operators to be non-negative results in a lower bound on the ground-state energy of any quantum mechanical system, which can be made arbitrarily tight for systems described by finite-dimensional Hilbert spaces. Such bounds can be obtained directly in the infinite-volume limit. The process of optimizing these lower bounds also yields estimates for a chosen set of expectation values in the ground state.
Forward citations
Cited by 2 Pith papers
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Bootstrapping periodic quantum systems
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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Real-time dynamics from convex geometry
The paper derives model-independent, tight bounds on smeared real-time correlators from Euclidean lattice data by solving a finite-dimensional convex program.
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