Quantum criticality in sub-Ohmic systems with three competing terms: beyond conventional spin-boson physics

TL;DR

This paper explores quantum phase transitions in the spin-boson model with sub-Ohmic baths, revealing complex phase diagrams, novel phases, and multi-stage transitions beyond traditional understanding.

Contribution

It provides a systematic variational analysis of the spin-boson model with multiple interaction terms, uncovering new phases and transition behaviors at low spectral exponents.

Findings

Discovery of a rich phase diagram at low spectral exponent s<1/2

Identification of a novel U(1)-symmetric phase

Observation of multi-stage quantum phase transitions for certain tunneling strengths

Abstract

Quantum phase transitions (QPTs) in the spin-boson model with/without the rotating-wave approximation (RWA) are systematically investigated through variational calculations using a sub-Ohmic bath with high spectral density. Four cases involving different system-environment interactions are examined, where transition points and critical exponents are accurately determined across varying tunneling strengths. Contrary to prior work, a rich phase diagram is revealed in the tunneling-coupling plane even at the low spectral exponent $s<1/2$, with a novel U(1)-symmetric phase being identified. As coupling increases, a multi-stage QPT sequence arises for the tunneling $0<\Delta < \Delta^*=0.074(1)$, whereas a single transition occurs beyond this range. Furthermore, an odd-parity phase is found to emerge even under the positive tunneling, exhibiting distinct characteristics relative to the prototype model.