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arXiv · 1506.06765

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

Lea F. Santos·Francisco Pérez-Bernal
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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.

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Lea F. Santos, Francisco Pérez-Bernal. 2015-11-25. Structure of eigenstates and quench dynamics at an excited state quantum phase transition. https://doi.org/10.1103/physreva.92.050101

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