2017/12/31 by Johannes Lang, B. Frank, Bernhard Frank +1
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Critical point (mathematics) #Dynamical systems theory #Field (mathematics) #Ising model #Mathematical analysis #Mathematics #Opinion Dynamics and Social Influence #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum #Quantum critical point #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Statistical physics #Transverse field #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.97.174401
published as Phys. Rev. B 97, 174401 (2018) · journal article, 15 pages, 12 figures. Final version
arxiv created 2018/04/17 · openalex publication_date 2018/05/03 · arxiv updated 2018/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of ℤ2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.