Theory of dynamical phase transitions in collective quantum systems
- URL: http://arxiv.org/abs/2205.03443v1
- Date: Fri, 6 May 2022 18:38:24 GMT
- Title: Theory of dynamical phase transitions in collective quantum systems
- Authors: \'Angel L. Corps, Armando Rela\~no
- Abstract summary: We present a theory for the two kinds of dynamical quantum phase transitions, sometimes termed DPT-I and DPT-II, in collective many-body systems.
For quenches below the critical energy, the existence of an additional conserved charge, identifying the corresponding phase, allows for a non-zero value of the dynamical order parameter characterizing DPTs-I.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a theory for the two kinds of dynamical quantum phase transitions,
sometimes termed DPT-I and DPT-II, in collective many-body systems. Both are
triggered by excited-state quantum phase transitions. For quenches below the
critical energy, the existence of an additional conserved charge, identifying
the corresponding phase, allows for a non-zero value of the dynamical order
parameter characterizing DPTs-I, and precludes the mechanism giving rise to
non-analyticities in the return probability, trademark of DPTs-II. We propose a
statistical ensemble describing the long-time averages of order parameters in
DPTs-I, and provide a theoretical proof for the absence of true DPT-II critical
times in the thermodynamic limit in the phase with this additional conserved
charge. Our results are numerically illustrated in the fully-connected
transverse-field Ising model, which exhibits both kinds of dynamical phase
transitions.
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