Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei

Excited state quantum phase transitions in many-body systems

“…Recently, analogous singular behavior has been noted for states throughout the excitation spectrum of certain many-body models [4][5][6][7][8][9][10], namely the Lipkin model [11] and the interacting boson model (IBM) for nuclei [12]. These singularities have been loosely described as "excited state quantum phase transitions" (ESQPTs) [9]. In this article, we more closely and systematically examine the characteristics of such excited state singularities as phase transitions, to provide a foundation for future investigations.…”

“…This last real- ization falls into the two-level boson model categorization, as the L = 0 case. So far, excited state QPTs have been considered in the Lipkin model [5,6] and the IBM [7][8][9], both of which are examples of s-b two-level models.…”

“…The semiclassical dynamics for these potentials has been studied in depth [33][34][35][36][37], and the connection with ESQPT phenomena in the Lipkin model and higher-dimensional s-b boson models has been made in Refs. [4,6,8,9]. In particular, at the energy of the top of the barrier, the classical action undergoes a logarithmic singularity, which leads semiclassically to the prediction of an infinite level density.…”

“…We find that ESQPTs are universal to these models, suggesting that the ESQPT phenomena may be broadly relevant, at least to systems dominated by pairing interactions. The semiclassical analysis of a "sombrero" potential provides a basis for understanding many of the properties of the quantum many-body ESQPT [6,9]. The semiclassical analysis of Refs.…”

“…The semiclassical analysis of Refs. [6,9] is extended in Sec. 3 to address several properties relevant to the definition of phase transitions.…”