Mobile impurities and orthogonality catastrophe in two-dimensional vortex lattices

Abstract

We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice in a Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight and effective impurity mass. The divergence of the effective mass in the low energy limit gives rise to a power law singularity in the impurity spectral function and provides an example of an emergent orthogonality catastrophe in a bosonic system.

Polaron in dilute 2D Bose gas at low temperatures

“…Below the transition temperature T BKT , i.e., in an ordered phase the density fluctuations of Bose gas are strongly developed (the appropriate situation is also observed in 1D at T = 0) and consequently the effective interaction potential between Bose polaron and bath particles is longranged (even if the bare one is short-ranged) which causes such a power-law decay of the impurity one-body density matrix at large distances. A similar logarithmicallydivergent behavior of the quasiparticle residue and effective mass is intrinsic and for the D-dimensional systems [28] at the Bose-Einstein condensation point and for the two-dimensional Bose polaron interacting with the Tkachenko modes [39].…”

Tunable breakdown of the polaron picture for mobile impurities in a topological semimetal

“…By contrast, the interaction is marginally relevant for m + < m − . The picture for the low-energy fixed point in this regime is the "self-trapping" of the impurity [46]. As M (Λ) grows without bound, we can analyze the RG equations for M m ± using F Z (r + , r − ) ≈ 1 and…”

“…. In the frequency domain, the line shape of the spectral function becomes asymmetric, approaching a power-law singularity as p → 0 [46]. At finite p, the singularity is broadened at the energy scale ∼ g 2 p 2 /M [E(p)] due to the recoil of the heavy impurity [55][56][57].…”

“…(3) is scale invariant with dynamical exponent z = 2 [31,41]. A bosonic analogue of this model appears in the problem of a mobile impurity immersed in a Bose-Einstein condensate in a vortex-lattice state [12,46]. An attempt to apply perturbation theory in γ reveals logarithmic singularities reminiscent of the behavior in critical one-dimensional (1D) systems [47][48][49].…”

“…The picture for the low-energy fixed point in this regime is the "self-trapping" of the impurity [46]. As M (Λ) grows without bound, we can analyze the RG equations for M m ± using F Z (r + , r − ) ≈ 1 and * the renormalized coupling in the low-energy limit.…”