2016/04/30 by F. Pérez‐Bernal, Francisco Pérez-Bernal, Lea F. Santos · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Critical point (mathematics) #Excited state #Ground state #Hamiltonian (control theory) #Ising model #Mathematics #Phase transition #Physics #Quantum #Quantum Information and Cryptography #Quantum critical point #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Singularity #Statistical physics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1002/prop.201600035
published as Fortschr. Phys. 65, 1600035 (2017) · 6 pages, 4 figures, accepted at the FQMT15 special volume of the Fortschritte der Physik
openalex publication_date 2016/06/23 · openalex created_date 2016/06/24 · arxiv created 2016/08/20 · arxiv updated 2018/01/08 · openalex updated_date 2026/08/05
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 Hamiltonian exhibiting a QPT between its limiting and dynamical symmetries. In this work, we compare the results for , and 3.