Quantum Phase Transitions

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.

Simone Montangero

Pedro D Sacramento

Tian Ma, Li, Da-peng, Ruikuan Liu +1 more

Quantum Phase Transition (QPT) is a phase transition between different quantum states by adjusting some control parameters. Based on the Principle of Hamilton Dynamics (PHD) and the Principle of Lagrangian Dynamics (PLD), a general QPT model is established. Also, a definition of QPT is given. The important point is that the QPT model is applied to Bose-Einstein Condensate (BEC) and the corresponding bifurcation solutions (i.e., the quantum states) are obtained by using steady state bifurcation theory.

M. A. Contínentino

Lin CONG, Chang Xiu, Wenting Dong +1 more

Structural evolutions in the U(5)-O(6) quantum phase transition are investigated within the framework of the interacting boson model by comparing the two types of effective order parameters in the ground-state quantum phase transition and excited-state quantum phase transition. It is found that the monopole-pair transfer intensities can show critical behaviors not only in the ground-state quantum phase transition but also in the excited-state quantum phase transition. It is thus suggested that the main features of the ESQPT should persist in nuclear systems.