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 J_KJK at fixed doping x. At large positive J_KJK, we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2}2kF=1+x2 (in units of 2\pi2π), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0JK≤0 side, our simulation finds the existence of a fractional Luttinger liquid (LL\star⋆) phase with 2k_F=\frac{x}{2}2kF=x2, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL\star⋆) phase in higher dimensions. The LL\star⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_KJK. 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 J_KJK, 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 0.035 J0.035J) 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=+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.