Classification of Quantum Enhanced Squeezing via Finite-Temperature Symmetry Breaking

In the field of metrology, achieving the highest possible sensitivity remains a central goal. For sensors built by quantum many-body systems, extensive research over recent decades has demonstrated that such a goal inevitably requires harnessing entanglement and coherent collective behaviors within the sensor. While various types of structured entanglement can enhance sensitivity, one practical and powerful approach involves using the so-called squeezed states, which feature reduced variance of certain global observables. Perhaps the most tried and promising protocol for generating such squeezed states, both conceptually and experimentally, is to perform quench dynamics: initializing the many-body sensor in a simple short-range correlated state and evolving it under a time-independent Hamiltonian, aiming to obtain a squeezed state by terminating the evolution at a carefully chosen moment. Despite successes in a few isolated examples such as the one-axis twisting model, a long-standing puzzle remains as: how can we systematically identify the Hamiltonians capable of generating squeezed entanglement? In this talk, we will present a theorem that classifies all thermalizing Hamiltonians based on their ability to generate squeezing through quench dynamics. This classification draws on a deep connection between spontaneous symmetry breaking and quantum metrology. Specifically, we will show that the symmetry breaking pattern uniquely determines which observables become squeezed: each type-A Goldstone mode maps to one squeezed observable. In addition to outlining our rigorous proof for generic models, we will also provide a few concrete examples that highlight both theoretical insights and practical relevance of our framework.