AI 中文总结
本文证明了一类广泛相互作用费米子模型的Lee-Yang零点自由定理，由此推出高效量子算法估计基态能量，并严格确立非零局域外场下无相变。
AI 中文摘要
Lee-Yang定理是研究多体系统的有力工具，其应用范围从分析相变到证明某些经典和量子算法的效率。在这项工作中，我们证明了一类广泛的相互作用费米子模型配分函数的Lee-Yang零点自由定理，这意味着存在一个可证明高效的量子算法来估计它们的基态能量。该类模型包括几个著名的模型，如吸引Hubbard模型、二部图上的排斥Hubbard模型以及相互作用的Hofstadter模型。我们的结果还严格确立了这些模型在存在非零局域外场时不存在相变。
英文摘要
Lee-Yang theorems are a powerful tool for studying many-body systems, with applications ranging from analyzing phase transitions to proving the efficiency of certain classical and quantum algorithms. In this work, we prove a Lee-Yang zero-freeness theorem for the partition function of a broad class of interacting fermion models, implying the existence of a provably efficient quantum algorithm for estimating their ground-state energies. This class includes several well-known models such as the attractive Hubbard model, repulsive Hubbard model on bipartite graphs, and the interacting Hofstadter model. Our results also rigorously establish the nonexistence of phase transitions in these models in the presence of a nonzero local external field.
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