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This research establishes a rigorous Lee-Yang zero-freeness theorem for interacting fermion models, directly enabling provably efficient quantum algorithms for estimating ground-state energies in systems like the Hubbard and Hofstadter models. By proving the absence of phase transitions under specific external fields, the work bridges statistical mechanics with quantum computational complexity, offering new pathways for solving strongly correlated electron problems on quantum hardware.
Lee-Yang theorem for fermions
arXiv:2609.23942v1 Announce Type: new Abstract: 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.
Abstract: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.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Computational Complexity (cs.CC); Mathematical Physics (math-ph)
arXiv:2609.23942 [quant-ph]
(or arXiv:2609.23942v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.23942 arXiv-issued DOI via DataCite (pending registration)
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