CMSP Seminar (Joint ICTP/SISSA Statistical Physics): Scaling symmetry of quantum correlations in quadratic Hamiltonians and its applications
Starts 27 Sep 2022 11:00
Ends 27 Sep 2022 12:00
Central European Time
room 138, SISSA (via Bonomea 265) + via Zoom
In quadratic Hamiltonians, various quantum correlation measures such as entanglement entropy, fidelity, and Loschmidt echo possess an inherent scaling symmetry that the Hamiltonian of the system does not have. We exploit this symmetry to address various problems in quantum field theory and semi-classical gravity. To begin with, it helps us attribute any occurrence of entropy divergence, even in the UV limit, to the generation of zero-modes in time-independent systems. For (1+1)-dimensional massive scalar fields, the scaling symmetry also provides a way to understand the crossover near the zero-mode limit. The scaling symmetry can be further generalized to time-dependent systems. Such systems may evolve to develop inverted or zero-mode instabilities that potentially apply to various physical phenomena. We show that, asymptotically, in the presence of instabilities, the leading order dynamics of various correlation measures --- entanglement entropy, fidelity, and Loschmidt echo --- are related via simple expressions. We quantify such instabilities in terms of scrambling time and Lyapunov exponents and show that the system mimics classicality under certain conditions in the chaotic regime. We also show that the entropy scaling oscillates between the area-law and volume-law for a scalar field that undergoes a global quench. We then discuss its implications for the quantum-classical transition of primordial density perturbations in the early Universe.