2015/05/13 by Markus Schmitt, Stefan Kehrein · 149 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Classification of discontinuities #Condensed matter physics #Curse of dimensionality #Degenerate energy levels #Honeycomb #Lattice (music) #Massless particle #Materials science #Mathematical analysis #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Thermodynamic limit #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.92.075114
published in Physical Review B 92(7) (American Physical Society)
arxiv created 2015/05/13 · openalex publication_date 2015/08/10 · arxiv updated 2015/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The notion of a dynamical quantum phase transition (DQPT) was recently introduced [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)] as the nonanalytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model is studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the nondegenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model.