We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anticommuting 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 $\alpha \ge 2D$, correlations between such operators decay at least algebraically to 0 with an exponent arbitrarily close to $\alpha$ at any nonzero temperature. Our bound is asymptotically tight, which we demonstrate by a high temperature expansion and by numerically analyzing density-density correlations in the one-dimensional quadratic (free, exactly solvable) Kitaev chain with long-range pairing.

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非零温度下具有幂律相互作用的费米离子晶格系统的相关衰减

我们研究在热平衡中具有长距离相互作用的费米离子晶格系统中的相关性。我们证明了反换向算子之间的相关性衰减的界，并推广了一个长距离的李布-罗宾逊型界。我们的结果表明，在这些空间维数系统中$d$ 具有但不一定是平移不变的两点相互作用，且随着距离的增加而呈指数递减 $\alpha \ge \mathrm{2个}d$，这样的算子之间的相关性至少在代数上衰减为0，并且指数任意接近 $\alpha$在任何非零温度下。我们的边界是渐近紧密的，这可以通过高温扩展和对具有长距离配对的一维二次（自由，可精确求解）Kitaev链中的密度-密度相关性进行数值分析来证明。