Effects of excited state quantum phase transitions on system dynamics

TL;DR

This paper investigates how excited state quantum phase transitions (ESQPTs) influence the dynamics of many-body quantum systems, revealing that near the ESQPT critical point, the system's evolution can be unexpectedly slow, even in models with long-range interactions.

Contribution

It extends previous studies by analyzing the impact of ESQPTs on system dynamics, especially the slow evolution near critical points in various algebraic models.

Findings

System evolution near ESQPTs can be extremely slow.

Slow dynamics occur in models with pairing interactions and specific algebraic structures.

The results are compared across models with different algebraic symmetries (v=1, 2, 3).

Abstract

This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann.Phys. 323, 1106 (2008). In many-body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel with a singularity in the energy spectrum that propagates to higher energies as the control parameter increases beyond the QPT critical point. The analysis of the spectrum has been a main tool for the detection of these ESQPTs. 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 studied in experiments with ion traps. Its Hamiltonian has a U(2) algebraic structure. More generally, the slow dynamics described here occurs in two-level bosonic or fermionic models with pairing interactions and a U(v+1) Hamiltonian exhibiting 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.