Anatomy of quantum critical wave functions in dissipative impurity problems

TL;DR

This paper investigates the structure of quantum critical wave functions in dissipative impurity models, revealing emergent symmetries and universal behaviors near quantum phase transitions through a combination of variational and field theory methods.

Contribution

It introduces the coherent state expansion as a new approach to analyze critical wave functions and uncovers universal features of low-energy modes at quantum criticality.

Findings

Emergent symmetry in low-energy displacement distribution

Algebraic decay of average displacement at criticality

Universal constant average squeezing amplitude

Abstract

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.