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Finite-size criteria for spectral gaps in D-dimensional quantum spin systems
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Finite-size criteria for spectral gaps in D-dimensional quantum spin systems
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We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems to $D>2$ dimensions. We obtain a local gap threshold of $\frac{3}{n}$, independent of $D$, for nearest-neighbor interactions. The $\frac{1}{n}$ scaling persists for arbitrary finite-range interactions in $\mathbb Z^3$. The key observation is that there is more flexibility in Knabe's combinatorial approach if one employs the operator Cauchy-Schwarz inequality.
Forward citations
Cited by 2 Pith papers
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The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds
A family of SDP-derived certified upper bounds converges to the bulk spectral gap, proving it semi-decidable for quantum lattice systems.
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The bulk spectral gap is semi-decidable: a convergent family of certified upper bounds
A convergent SDP hierarchy certifies upper bounds on the thermodynamic-limit bulk spectral gap, making the bulk gap semi-decidable and producing the first certified bounds for the kagome Heisenberg model.
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