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Quantum Simulation

Correlation Length versus Gap in Frustration-Free Systems

arXiv

Authors: David Gosset, Yichen Huang

Year

2015

Paper ID

27124

Status

Preprint

Abstract Read

~2 min

Abstract Words

104

Citations

N/A

Abstract

Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap ε has correlation length ξ upper bounded as ξ=O(1/ε). In general this bound cannot be improved. Here we study the scaling of the correlation length as a function of the spectral gap in frustration-free local Hamiltonians, and we prove a tight bound ξ=O\(1/sqrtε\) in this setting. This highlights a fundamental difference between frustration-free and frustrated systems near criticality. The result is obtained using an improved version of the combinatorial proof of correlation decay due to Aharonov, Arad, Vazirani, and Landau.

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This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1509.06360 [2] arXiv https://arxiv.org/abs/1509.06360 [3] Publisher https://arxiv.org/abs/1509.06360

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