Thermal Suppression of Dynamical Quantum Phase Transitions in Finite-Dimensional Systems: A Quasi-Hermitian Framework

This study investigates the influence of finite temperature on dynamical quantum phase transitions (DQPTs) in finite-dimensional quantum systems. While DQPTs are typically studied in pure states at zero temperature, the authors seek to understand how thermal equilibrium states and the dimensionality of the Hilbert space affect the emergence and suppression of these transitions when a system is subjected to a sudden quench.

The authors develop a self-contained framework for mixed-state quench dynamics using quasi-Hermitian quantum mechanics. By employing a metric-stationary pseudo-Hermitian approach, they construct a generalized Loschmidt amplitude from first principles. This framework allows for a rigorous treatment of the density matrix evolution and purification in systems where the Hamiltonian is self-adjoint under a positive-definite metric. They apply this to an N-level model consisting of a two-level sector coupled to N-2 spectator states to observe how thermal occupation of these spectator states influences the dynamical criticality.

The study reveals that temperature acts as a control parameter for DQPTs. In the proposed N-level model, thermal excitations redistribute weights among eigenstates, which can dilute the interference signals necessary for the existence of Loschmidt amplitude zeros. The authors identify a dimensionality-dependent threshold temperature, T_th(N). For systems with a Hilbert-space dimension of five or greater, this threshold becomes finite. When the system temperature exceeds this value, the Loschmidt amplitude loses all real zeros, effectively suppressing the DQPTs. This suggests a universal mechanism where thermal occupation can be used to tune or eliminate dynamical criticality in finite-dimensional systems.