Spin-Incoherent Behavior in the Ground State of Strongly Correlated Systems

It is commonly believed that strongly interacting one-dimensional Fermi systems with gapless excitations are effectively described by Luttinger liquid theory. However, when the temperature of the system is high compared to the spin energy, but small compared to the charge energy, the system becomes “spin incoherent.” We present numerical evidence showing that the one-dimensional “$t\mathrm{\text{−}}J$-Kondo” lattice, consisting of a $t\mathrm{\text{−}}J$ chain interacting with localized spins, displays all the characteristic signatures of spin-incoherent physics, but in the ground state. We argue that similar physics may be present in a wide range of strongly interacting systems.

Figure 1

(a) Proposed phase diagram of the $t\mathrm{\text{−}}J$-Kondo model with $J=0.05$, as a function of the density and Kondo coupling $J_K$, obtained with exact diagonalization on small systems (solid symbols) and DMRG (open symbols). The gray shading corresponds to the FM phase, while the empty region is PM. The dashed line is a guide to the eye. (b) Derivative of $⟨H_{t\mathrm{\text{−}}J}⟩$ with respect to the Kondo coupling $J_K$, as explained in the text, for a chain with $L=32$, $N=24$ fermions, and $S_{\mathrm{tot}}^z=4$. (c) spin structure factor and (d) momentum distribution of a $t\mathrm{\text{−}}J$-Kondo chain with $L=64$ sites and $N=48$ fermions, for different values of the Kondo coupling $J_K$.

Figure 2

Momentum resolved spectrum of a $t\mathrm{\text{−}}J$-Kondo chain of $L=32$ sites, with $J/t=0.05$ and density $n=0.75$, calculated with time-dependent density matrix renormalization group method, showing a transfer of the spectral weight as $J_K$ increases, toward a spectrum that resembles a spin-incoherent Luttinger liquid at a crossover value of $J_K\sim 0.05$.