Critical behavior of an impurity at the boson superfluid-Mott insulator transition

Abstract

We present a universal theory for the critical behavior of an impurity at the two-dimensional superfluid-Mott insulator transition. Our analysis is motivated by a numerical study of the Bose-Hubbard model with an impurity site by Huang et al. (Phys. Rev. B 94, 220502 (2016)), who found an impurity phase transition as a function of the trapping potential. The bulk theory is described by the $O(2)$ symmetric Wilson-Fisher conformal field theory, and we model the impurity by a localized spin-1/2 degree of freedom. We also consider a generalized model by considering an $O(N)$ symmetric bulk theory coupled to a spin-$S$ degree of freedom. We study this field theory using the $\epsilon =3-d$ expansion, where the impurity-bulk interaction flows to an infrared stable fixed point at the critical trapping potential. We determine the scaling dimensions of the impurity degree of freedom and the associated critical exponents near the critical point. We also determine the universal contribution of the impurity to the finite temperature compressibility of the system at criticality. Our results are compared with recent numerical simulations.

arXiv comment25 pages, 4 figures

References in corpus (11)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• Quantum critical behavior of ultracold atoms in two-dimensional optical lattices
• Quantum phase transitions in the Bose-Fermi Kondo model
• Theory of finite temperature crossovers near quantum critical points close to, or above, their upper-critical dimension
• Phase Diagram of Commensurate Two-Dimensional Disordered Bose Hubbard Model
• Static hole in a critical antiferromagnet: field-theoretic renormalization group
• Trapping Centers at the Superfluid-Mott-insulator Criticality: Transition between Charge-quantized States

Cited by in corpus (6)

• Finite-size Scaling of O($n$) Systems at the Upper Critical Dimensionality
• Deconfined critical point in a doped random quantum Heisenberg magnet
• The halon: a quasiparticle featuring critical charge fractionalization
• Critical anomalous metals near superconductivity in models with random interactions
• Quantized Magnetic Flux and the Magneto-halon Effect in a Critical Superconductor
• Even-Odd effect of an Spin-S impurity coupled to a quantum critical system