Variational study of two-impurity spin-boson model with a common Ohmic bath: Ground-state phase transitions

TL;DR

This study uses advanced variational methods to analyze quantum phase transitions in a two-impurity spin-boson model with a common Ohmic bath, revealing detailed critical behavior and phase transition orders.

Contribution

It introduces a highly accurate variational approach with extensive parameters, clarifies the critical coupling controversy, and distinguishes the order of phase transitions under different spin-spin couplings.

Findings

Accurate determination of transition points and critical exponents.

Ground state energies lower than previous methods with logarithmic grid.

First-order phase transition under strong antiferromagnetic coupling.

Abstract

By means of a trial wave function, the multi-D$_1$ ansatz, extensive variational calculations with more than ten thousand parameters have been carried out to study quantum phase transitions in the ground states of a two-impurity system embedded in a common Ohmic bath of bosons. Quantum criticality in both the impurity system and the Ohmic bosonic bath is investigated with relevant transition points and critical exponents determined accurately. With the linear grid of the Ohmic spectral density, our numerical calculations produce a much better description of the ground states with lower energies than other calculations employing a logarithmic grid with a discretization factor far greater than unity. It offers a possible solution to the considerable controversy on the critical coupling in the literature. Moreover, the ground-state phase transition is inferred to be of first order in the presence of strong antiferromagnetic spin-spin couplin}, at variance with that in the ferromagnetic regime or in the absence of spin-spin coupling where the transition belongs to the Kosterlitz-Thouless universality class.