First-order excited-state quantum phase transition in the transverse Ising model with a longitudinal field
Yun-Tong Yang, Hong‐Gang Luo
Abstract Investigations into first-order quantum phase transition (QPT) remain unclear in comparison to those of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and, at the same time, the concepts of universality class and critical scaling can be characterized by critical exponents. Here, we present a comparison study of these two kinds of QPT in the transverse Ising model; the emphasis is on the first-order QPT. In the absence of a longitudinal field, the ground state of the model exhibits a second-order QPT from the paramagnetic phase to the ferromagnetic phase, which is smeared out once the longitudinal field is applied. Surprisingly, the first excited state involves a first-order QPT as the longitudinal field increases, which has not been reported in the literature. Within the framework of the pattern picture, we clearly identify the difference between these two kinds of QPT: for the continuous QPT, only the pattern flavoring the ferromagnetic phase is always dominant over the others. By contrast, there are at least two competitive patterns in the first-order QPT, which is further indicated by the patterns’ occupancies, calculated by pattern projections on the ground- and first excited-state wavefunctions. Our results not only have a fundamental significance in the understanding of the nature of QPTs, but also a practical interest in quantum simulations used to test the present findings.
arXiv:2301.02066•Communications in Theoretical Physics•Aug 6, 2025•1 citation