Structure of eigenstates and quench dynamics at an excited state quantum phase transition

TL;DR

This paper investigates the structure and dynamics of eigenstates near an excited state quantum phase transition in two-level pairing models, revealing localization phenomena and slow dynamics that can be experimentally observed.

Contribution

It provides a detailed analysis of eigenstate localization and dynamical slowdown at ESQPTs in algebraic models, linking theoretical predictions to potential experimental tests.

Findings

Eigenstates near E_{ESQPT} are highly localized in the U(n)-basis.

System dynamics slow down significantly near the ESQPT energy.

Signatures of ESQPT are observable in eigenstate structure and quench dynamics.

Abstract

We study the structure of the eigenstates and the dynamics of a system that undergoes an excited state quantum phase transition (ESQPT). The analysis is performed for two-level pairing models characterized by a U(n+1) algebraic structure. They exhibit a second order phase transition between two limiting dynamical symmetries represented by the U(n) and SO(n+1) subalgebras. They are, or can be mapped onto, models of interacting bosons. We show that the eigenstates with energies very close to the ESQPT critical point, E_{ESQPT}, are highly localized in the U(n)-basis. Consequently, the dynamics of a system initially prepared in a U(n)-basis vector with energy close to E_{ESQPT} may be extremely slow. Signatures of an ESQPT can therefore be found in the structures of the eigenstates and in the speed of the system evolution after a sudden quench. Our findings can be tested experimentally with trapped ions.