Entanglement entropy has become an important tool for identifying phases of matter and phase transitions in quantum systems using quantum Monte Carlo methods. While such approaches have achieved great success in systems composed of interacting spins/bosons, their application to interacting fermionic systems remains limited due to substantially higher computational cost. Here we show a more efficient Monte Carlo algorithm for fermionic systems that enables systematic exploration of entanglement entropy across a wide range of physical parameters. Based on the incremental technique along physical parameters, the method significantly reduces computational effort while maintaining accuracy. Using this approach, we study a two-dimensional square lattice Hubbard model, revealing the phase diagram that includes the Fermi surface and Goldstone modes. We further apply the method to the Gross-Neveu criticality and find that the scaling of the entanglement entropy follows a universal form quantified by the critical exponent ν. Further investigation reveals that the leading coefficient of the entanglement entropy decreases monotonically, rather than developing a local maximum as O(N) transition point. Entanglement entropy is a powerful tool for identifying quantum phases and phase transitions but calculating it in interacting fermionic systems remains challenging. Here, the authors introduce an efficient Monte Carlo method that reduces computational cost and reveals universal scaling across Gross-Neveu fermionic phase transitions.

Nature is a scientific journal publishing research articles, reviews, and commentary across a wide range of scientific disciplines. Readers can find articles on topics such as biology, chemistry, physics, and environmental science. Additionally, they can learn about  research, scientific discoveries, and advances in understanding the natural world.

Nature

A new high-efficiency fermionic quantum Monte Carlo algorithm is introduced to study entanglement entropy in interacting fermionic systems. Using an incremental technique along physical parameters, the method significantly reduces computational cost while maintaining accuracy. Applied to a 2D square lattice Hubbard model and Gross-Neveu criticality, the approach reveals that entanglement entropy scaling follows a universal form quantified by the critical exponent ν, and that the leading coefficient decreases monotonically near the O(N) transition point rather than developing a local maximum.

Uncovering entanglement entropy near Gross-Neveu criticality by a high-efficiency fermionic quantum Monte Carlo scanning