Frustrated quantum magnetism in the Kondo lattice on the zigzag ladder

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 densitycorrelation 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 dim c ≈ 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 • quantum spin spiral with quasi-long-range order at J mag c ≈ 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 = π/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. arXiv:1709.05642v2 [cond-mat.str-el] 12 Mar 2018 As the spin gap, the charge gap ∆ C is of the order of J in the strong-J regime. It decreases with decreasing J but stays finite at and below J mag c . This is consistent with our expectation that the systems is an insulator for arbitrary J > 0 at half-filling.

Phase diagram of the Kondo model on the zigzag ladder

“…Short-range spin correlations SiSj (color code) as obtained from DMRG for a chain with L = 52 sites at J = 0.7t1 and for various values of the next-nearest neighbor hopping t2 as indicated.relations S i S i+1 while next-nearest neighbor correlations S i S i+2 are ferromagnetic. Contrary, as has been shown in Ref 9,. the Kondo model on the zigzag lattice with t 2 = t 1 has weakly antiferromagnetic spin correlations on the rungs as well as for nearest neighbors along the legs of the ladder for strong J and undergoes a spin-dimerization transition at J = J…”

“…Indeed, on the t 1 = t 2 line, for example, we find 6.4t ≈ J (dim) c,class J (dim) c ≈ 0.62t instead, see Ref. 9. Below we will argue that spin dimerization cannot occur in the strong-J limit and it is rather the alleviation of frustration which drives spin dimerization.…”

“…This can be seen as a simple effective theory of the spin dimerization found in the full quantum-spin Kondo lattice. 9 Clearly, due to the mean-field character inherent to the classical-spin theory, one cannot expect correct order of magnitude for the critical parameters but still the comparison with the exact DMRG results is instructive. One would expect that the necessary critical interaction strength J (dim) c,class would be much stronger than J (dim) c , the DMRG value, since mean-field-like and classical approaches tend to overestimate ordering, i.e., dimerization due to absence of quantum fluctuations that act against ordering.…”

“…7), as in known from our previous work. 9 In view of the strong geometrical frustrations, this is quite surprising. The magnetic state shows up on top of the spin dimerization, and the magnetic order is given by a 90 • spin spiral rather than a collinear antiferromagnetic state.…”

Charge density wave in a doped Kondo chain

“…Fig.4(a) shows that the correlation has k = π 2 oscillations with a superposition of incommensurate oscillations with k = π L which is size dependent. Generally in a valence bond solid, the dimer order described by the short-ranged spin correlation should be L independent away from the boundary, as the example of the KL on the zigzag ladder at half filling [39]. Quantum fluctuations will destroy any incommensurate order in 1D, so the leading order at the weak coupling of n = 3 4 is just the charge order.…”