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arXiv 2302.11267quant-phcond-mat.stat-mech
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海森堡耦合量子比特的自旋-能量算符不等式

A spin-energy operator inequality for Heisenberg-coupled qubits

Daniel Ranard, C. Jess Riedel

摘要:

我们稍微加强了Correggi等人提出的一个算子不等式,该不等式利用总自旋下界了$s=1/2$自旋的海森堡耦合图的能量。特别是,$ΔH \ge C Δ\vec{S}^2$对于依赖于图形的常数$C$,其中$ΔH$是基态以上的能量,$Δ\vec{S}^2$是总自旋的平方$\vec{S} = \sum_i \vecσ_i/2$低于其最大可能值的量。我们得到明确的常数在特殊情况下的立方晶格。我们简要地讨论了这个约束的解释,在低能量,近似非相互作用的自旋波理论的磁振子,并将其与另一个不等式发现的Bärwinkel等人。

英文摘要:

We slightly strengthen an operator inequality identified by Correggi et al. that lower bounds the energy of a Heisenberg-coupled graph of $s=1/2$ spins using the total spin. In particular, $ΔH \ge C Δ\vec{S}^2$ for a graph-dependent constant $C$, where $ΔH$ is the energy above the ground state and $Δ\vec{S}^2$ is the amount by which the square of the total spin $\vec{S} = \sum_i \vecσ_i/2$ falls below its maximum possible value. We obtain explicit constants in the special case of a cubic lattice. We briefly discuss the interpretation of this bound in terms of low-energy, approximately non-interacting magnons in spin wave theory and contrast it with another inequality found by Bärwinkel et al.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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