Physics

Pure mathematics

Mathematics

Quantum phase transition

Dynamical systems theory

Statistical physics

Phase transition

Mathematical analysis

Quantum critical point

Critical point (mathematics)

Condensed matter physics

Phase (matter)

Ising model

Quantum mechanics

Field (mathematics)

Transverse field

Quantum

Phase diagram

Physical review. B./Physical review. B

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 ${\mathbb{Z}}_{2}$ 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.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model