Rényi entropy helps distinguish weak first-order quantum phase transitions

Researchers at Westlake University in Hangzhou have developed a method using Rényi thermal entropy and its derivative to reliably identify weak first-order quantum phase transitions, a type of transition that appears continuous in standard computer simulations due to its extremely large correlation length. The team established a complete finite-size scaling theory for detecting and characterizing these transitions, addressing a fundamental challenge in quantum many-body computation where weak first-order transitions are often missed. Their work demonstrates accurate data collapse and extraction of critical exponents, and provides a “smoking-gun signature” for weak first-order transitions through a distinct double-peak structure observed in models like the J-Q models. This approach offers a general, unbiased and numerically efficient tool for probing the universal properties of quantum phase transitions, resolving long-standing…