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2021

Bootstrapping Lattice Vacua

Lawrence, Scott

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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.

Bootstrapping Lattice Vacua · Around

Built on

G.F. Chew, The S-matrix theory of strong interactions (1961)
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X. Han, S.A. Hartnoll and J. Kruthoff, Bootstrapping Matrix Quantum Mechanics , Phys. Rev. Lett. 125
Original
2004
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M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum monte carlo simulations , Physical review letters 94
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R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12
Original
2008
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S. Caron-Huot and V. Van Duong, Extremal Effective Field Theories , JHEP 05
Original
2011
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