Many-body thermodynamics on quantum computers via partition function zeros

Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.

Automated summary

Partition functions play a crucial role in physics for determining thermodynamic properties and phase transitions of many-body systems. This study demonstrates a scalable approach for finding partition function zeros on quantum computers, showing a transition from XY-like behavior to Ising-like behavior with varying anisotropy. While quantum computers are not yet capable of reaching the thermodynamic limit, this work paves the way for future calculations of critical phenomena beyond classical computing limits.