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arXiv · 1702.00371

Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature

Senaida Hernández-Santana·Christian Gogolin·J. Ignacio Cirac·Antonio Acín
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Abstract

We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anti-commuting operators and generalize a long-range Lieb-Robinson type bound. Our results show that in these systems of spatial dimension $D$ with, not necessarily translation invariant, two-site interactions decaying algebraically with the distance with an exponent $α\geq 2\,D$, correlations between such operators decay at least algebraically with an exponent arbitrarily close to $α$ at any non-zero temperature. Our bound is asymptotically tight, which we demonstrate by a high temperature expansion and by numerically analyzing density-density correlations in the 1D quadratic (free, exactly solvable) Kitaev chain with long-range pairing.

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Senaida Hernández-Santana, Christian Gogolin, J. Ignacio Cirac, Antonio Acín. 2017-03-23. Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature. https://doi.org/10.1103/physrevlett.119.110601

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