  Quantum phase transitions reflect singular changes taking place in a
many-body ground state, however, computing and analyzing large-scale critical
wave functions constitutes a formidable challenge. New physical insights into
the sub-Ohmic spin-boson model are provided by the coherent state expansion
(CSE), which represents the wave function by a linear combination of
classically displaced configurations. We find that the distribution of
low-energy displacements displays an emergent symmetry in the absence of
spontaneous symmetry breaking, while experiencing strong fluctuations of the
order parameter near the quantum critical point. Quantum criticality provides
two strong fingerprints in critical low-energy modes: an algebraic decay of the
average displacement and a constant universal average squeezing amplitude.
These observations, confirmed by extensive variational matrix product states
(VMPS) simulations and field theory arguments, offer precious clues into the
microscopics of critical many-body states in quantum impurity models.
