Double symmetry breaking and two-dimensional quantum phase diagram in spin-boson systems

Abstract

The quantum ground-state and excitation properties of two independent chains of pseudospins (two-level systems) interacting with the same bosonic field are theoretically investigated. Each chain is coupled to a different quadrature of the field, leading to two independent symmetry breakings for increasing values of the two collective spin-boson interaction constants ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. A phase diagram is provided in the plane (${\ensuremath{\Omega}}_{C}$,${\ensuremath{\Omega}}_{I}$), with four phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via geometric Berry effects. In particular, when ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$ are both larger than two critical values, the fundamental subspace has a fourfold degeneracy. Finite-size properties are shown for both critical and ultrastrong values of ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. Possible implementations in superconducting quantum circuits are detailed.