# Bose-Fermi Anderson Model with SU(2) Symmetry: Continuous-Time Quantum Monte Carlo Study

## TL;DR

This study develops a specialized continuous-time Quantum Monte Carlo method to analyze the phase diagram and critical points of the Bose-Fermi Anderson model with SU(2) symmetry, revealing two types of Kondo destruction quantum critical points depending on the bosonic bath spectrum.

## Contribution

The paper introduces a low-temperature, SU(2)-symmetric CT-QMC method for the Bose-Fermi Anderson model, clarifying its phase diagram and critical points with new insights into Kondo destruction.

## Key findings

- Identified two types of Kondo destruction quantum critical points depending on the bosonic bath exponent.
- Confirmed the relation η=ε at the quantum critical points, consistent with analytical predictions.
- Validated the CT-QMC results against renormalization-group calculations for certain parameter regimes.

## Abstract

In quantum critical heavy fermion systems, local moments are coupled to both collective spin fluctuations and conduction electrons. As such, the Bose-Fermi Kondo model, describing the coupling of a local moment to both a bosonic and a fermionic bath, has been of extensive interest. For the model in the presence of SU(2) spin rotational symmetry, questions have been raised about its phase diagram. Here we develop a version of continuous-time Quantum Monte Carlo (CT-QMC) method suitable for addressing this issue; this procedure can reach sufficiently low temperatures while preserving the SU(2) symmetry. Using this method for the Bose-Fermi Anderson model, we clarify the renormalization-group fixed points and the phase diagram for the case with a constant fermionic-bath density of states and a power-law bosonic-bath spectral function $\rho_{b}(\omega) \propto \omega^{s}$ ($0<s<1$). We find two types of Kondo destruction QCP, depending on the power-law exponent $s$ in the bosonic bath spectrum. For $s^{*}<s<1$, both types of QCPs exist and, in the parameter regime accessible by an analytical $\epsilon$-expansion renormalization-group calculation (here $\epsilon=1-s$), the CT-QMC result is fully consistent with prior predictions by the latter method. For $s<s^{*}$, there is only one type of QCP. At both type of Kondo destruction QCPs, we find that the exponent of the local spin susceptibility $\eta$ obeys the relation $\eta=\epsilon$, which has important implications for Kondo destruction QCP in the Kondo lattice problem.