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

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 $s^{\ast }<s<1$, 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 $s<s^{\ast }$, 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.

13 pages, 15 figures