Effects of excited state quantum phase transitions on system dynamics

Francisco Pérez-Bernal, Lea F. Santos

Published 2016-04-23Version 1

In systems that exhibit an excited state quantum phase (ESQPT), the ground state quantum phase transition (QPT) occurs in parallel with a singularity in the energy spectrum. This corresponds to a local divergence in the density of states that propagates to higher energies as the control parameter increases beyond the ground state critical point. The analysis of the spectrum has been a main tool for the detection of an ESQPT. Studies of the effects of this transition on the system dynamics are more limited. Here, we extend our previous works and show that the evolution of an initial state with energy close to the ESQPT critical point may be extremely slow. This result is surprising, because it may take place in systems with long-range interactions, where the dynamics is usually expected to be very fast. A timely example is the one-dimensional spin-1/2 model with infinite-range Ising interaction in a transverse field, accessible to experiments with ion traps. Its Hamiltonian has a U(2) algebraic structure. More generally, ESPQTs can occur in any U(v+1) Hamiltonian that exhibits a QPT between its limiting U(v) and SO(v+1) dynamical symmetries. In this work, we compare the results for v=1, 2, and 3. They represent, respectively, the one-, two-, and three-dimensional limits of the molecular vibron model.