Unveiling quantum entanglement and correlation of sub-Ohmic and Ohmic baths for quantum phase transitions in dissipative systems

TL;DR

This study investigates quantum entanglement and correlations in dissipative systems using the spin-boson model, revealing phase transition singularities and scaling behaviors in sub-Ohmic and Ohmic baths through quantum information measures.

Contribution

It introduces a detailed numerical analysis of quantum phase transitions in dissipative systems, highlighting differences in quantum discord scaling between sub-Ohmic and Ohmic regimes.

Findings

Identified three types of singularities for phase transitions.

Accurately determined transition points and critical exponents.

Discovered distinct behaviors of quantum discord related to entanglement and correlations.

Abstract

By employing the spin-boson model in a dense limit of environmental modes, quantum entanglement and correlation of sub-Ohmic and Ohmic baths for dissipative quantum phase transitions are numerically investigated based on the variational principle. With several measures borrowed from quantum information theory, three different types of singularities are found for the first-order, second-order, and Kosterlitz-Thouless phase transitions, respectively, and the values of transition points and critical exponents are accurately determined. Besides, the scaling form of the quantum discord in the Ohmic case is identified, quite different from that in the sub-Ohmic regime. In a two-spin model, two distinct behaviors of the quantum discord are uncovered: one is related to the quantum entanglement between two spins and the other is decided by the correlation function in the position space rather than the entanglement.