Frustrated quantum magnetism in the Kondo lattice on the zigzag ladder

TL;DR

This study investigates the complex magnetic phases of the Kondo lattice on a zigzag ladder, revealing two critical points where frustration leads to a dimerized state and a quantum spin spiral, using DMRG calculations.

Contribution

It provides the first detailed analysis of frustration-induced quantum phase transitions in the one-dimensional Kondo lattice on a zigzag ladder.

Findings

Identification of a dimerized state at J_c ≈ 0.89t due to frustration alleviation.

Discovery of a magnetic transition to a 90° quantum spin spiral at J_c ≈ 0.84t.

Contrasts with the bipartite chain, showing no finite spin gap for all J>0.

Abstract

The interplay between Kondo effect, indirect magnetic interaction and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group (DMRG), the ground state and various short- and long-range spin- and density-correlation functions are calculated for the model at half-filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$ where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at $J^{\rm dim}_{\rm c} \approx 0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a $90^{\circ}$ quantum spin spiral with quasi-long-range order at $J^{\rm mag}_{\rm c} \approx 0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing $J$) and a divergence of the spin-correlation length and of the spin-structure factor $S(q)$ at wave vector $q=\pi/2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all $J>0$ at half-filling.