Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

Abstract

Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling JK at fixed doping x. At large positive JK, we confirm the expected conventional Luttinger liquid phase with 2kF = 1+2x (in units of 2π), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the JK ≤ 0 side, our simulation finds the existence of a fractional Luttinger liquid (LL*) phase with 2kF = x2 , accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL*) phase in higher dimensions. The LL* phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive JK. Then we mainly focus on the ‘critical regime’ between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of JK, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035J) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z = +∞. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.