Even-odd effect of a spin-S impurity coupled to a quantum critical system
Abstract
We discuss an even-odd effect for an impurity with N -fold-degenerate internal states immersed in a two-dimensional superfluid-Mott-insulator quantum critical bath which is described by a spin-S XY Bose-Kondo impurity model with N =2 S +1 . Using a dimensional- and momentum-cutoff regularized renormalization group and unbiased large-scale Monte Carlo numerical simulations, we establish the phase diagram for the S =1 impurity with all relevant terms included. We show that a threefold-degenerate S =1 impurity coupled to a critical bath has a nondegenerate ground state with a quantized charge, in qualitative contrast to the spin-1/2 case where the impurity is partially screened. We then argue that all impurities with odd-2 S degeneracy share the same universal physics as the spin-1/2 case and all impurities with even-2 S degeneracy are the same as the spin-1 case. We validate our conjecture with unbiased Monte Carlo simulations up to S =2 . A physical consequence of this even-odd effect is that two spin-1 /2 impurities in the critical bath form a long-range entangled state at a low temperature, which can be realized in ultracold atoms in an optical lattice.
- Publication:
-
Physical Review B
- Pub Date:
- September 2019
- DOI:
- 10.1103/PhysRevB.100.094514
- arXiv:
- arXiv:1810.12812
- Bibcode:
- 2019PhRvB.100i4514C
- Keywords:
-
- Condensed Matter - Quantum Gases
- E-Print:
- Phys. Rev. B 100, 094514 (2019)