费米子的李-杨定理
Lee-Yang theorem for fermions
Chaithanya Rayudu, Takahiro Misawa, Andrew Zhao, Jun Takahashi
AI 速读 基于摘要
作者证明了一类广泛相互作用的费米子模型配分函数的李-杨零点不存在定理，并据此给出估计基态能量的可证明高效量子算法。
quant-ph · cond-mat.stat-mech · cond-mat.str-el · cs.CC · math-ph
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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.