Speaker
Description
Quantum phase transitions are characterized by non-analytic changes in ground-state properties as a control parameter is varied. At non-zero temperature, however, thermal fluctuations smooth out these singularities in static observables, making direct signatures of quantum criticality difficult to access experimentally. In this talk, I will show that dynamical properties can retain clear fingerprints of the underlying critical point even at finite temperature. Focusing on the Transverse-field Ising model as a paradigmatic example, we study the finite-temperature dynamics of the order parameter and demonstrate that its correlation time exhibits non-analytic behavior as the transverse field is tuned across the quantum critical point. In contrast to equilibrium expectation values, this dynamical quantity remains sharply sensitive to the underlying quantum phase transition and provides a direct probe of criticality in experimentally relevant finite-temperature regimes. I will discuss the scaling properties of this effect and its physical interpretation in terms of competing quantum and thermal fluctuations. As an outlook, these findings suggest that such non-analytic dynamical signatures may extend beyond the transverse-field Ising model, pointing toward a broader framework for detecting quantum criticality through finite-temperature correlation dynamics.