Lee-Yang theorem shows efficient quantum energy calculation for fermions
Lee-Yang theorem for fermions
Computational Complexity
Summary
Studying many interacting particles called fermions helps us understand materials and physics. The authors proved a mathematical property (Lee-Yang zero-freeness) for many fermion models that means their lowest energy states can be found efficiently using quantum computers. This also shows these models don't have sudden changes (phase transitions) when a small external influence is applied. Their results cover important models like the Hubbard and Hofstadter models used in condensed matter physics.
What this means in practice
- •For quantum algorithm developers: Use the zero-freeness property to design guaranteed efficient quantum algorithms for computing ground-state energies of interacting fermion systems.
- •For condensed matter simulation teams: Rely on the absence of phase transitions under external fields to simplify simulations of fermion models like the Hubbard model on bipartite graphs.
A theory result. No direct application yet.
Authors
Chaithanya Rayudu, Takahiro Misawa, Andrew Zhao, Jun Takahashi
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.