量子链模型中Gauss定律与费米符号问题的相互作用
Interplay of Gauss Law and the fermion sign problem in quantum link models with dynamical matter
AI总结：
研究揭示了量子链模型中Gauss定律与费米符号问题的相互作用，证明特定sector无符号问题并提出meron簇算法采样基态。
摘要：
具有动态物质耦合到自旋-1/2 U(1)规范场的量子链模型在d=2+1和3+1维中可能产生量子电动力学(QED)中预期的库仑相以及其他束缚相。利用精确对角化技术，我们证明在没有磁场的一类模型中，基态总处于满足(G_e,G_o)=(d, -d)的sector中，其中d是空间维度，e和o是偶数和奇数位点。可以严格证明该sector不存在费米符号问题。我们还展示了一个meron簇算法自然采样Hamiltonian在上述Gauss定律sector中的基态。
英文摘要：
Quantum Link Models with dynamical matter coupled to spin-$\frac{1}{2} \ \rm U(1)$ gauge fields in $d=2+1 $ and $3+1$ can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies $(G_e,G_o) = (d,\ -d)$, where $d$ is the spatial dimension and $e$ and $o$ are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.
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