TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.034
TI  - Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model
PY  - 2024/08/05
UR  - https://scipost.org/SciPostPhys.17.2.034
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 034
A1  - Nikolaenko, Alexander
AU  - Zhang, Ya-Hui
AB  - 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 $J_K$ at fixed doping x. At large positive $J_K$, we confirm the expected conventional Luttinger liquid phase with $2k_F=\frac{1+x}{2}$ (in units of $2\pi$), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the $J_K ≤ 0$ side, our simulation finds the existence of a fractional Luttinger liquid (LL$\star$) phase with $2k_F=\frac{x}{2}$, 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 $J_K$. 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 $J_K$, 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 $0.035 J$) 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.
ER  -

@Article{10.21468/SciPostPhys.17.2.034,
	title={{Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model}},
	author={Alexander Nikolaenko and Ya-Hui Zhang},
	journal={SciPost Phys.},
	volume={17},
	pages={034},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.034},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.034},
}