Quantum phase transitions, frustration, and the Fermi surface in the Kondo lattice model

Abstract

The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a onedimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.

Hybridization oscillation in the one-dimensional Kondo-Heisenberg model with Kondo holes

“…We note that there has been debate on the exact value of the critical Kondo coupling in the 1D Kondo-Heisenberg model. Different from the DMRG results 23 , 24 , 28 , some theories argue that the critical Kondo coupling should be at J K = 0 29 . In this case, there would be no preformed heavy electrons before the formation of the large Fermi surface, but this would seem to be in contradiction with our observed existence of the weak coupling regime.…”

Direct observation of the momentum distribution and renormalization factor in lithium

“…The renormalization factor may be considered as a quantity that defines how correlated electrons are in a given material. For example, in strongly correlated systems such as heavy fermion meterials, a substantially reduced Z k F (or similar features) is reported [6][7][8]. Nonetheless, there is very little opportunity to directly measure the momentum distribution since very few experimental techniques allow us to estimate the Z k F in a quantitative manner.…”

Ground-state and spectral properties of an asymmetric Hubbard ladder

“…The one-dimensional (1D) Kondo-Heisenberg model is the most studied asymmetric ladder system. It was used to investigate exotic superconducting correlations in stripe-ordered hightemperature superconductors [15][16][17][18] as well as quantum phase transitions in heavy-fermion materials [19]. Additionally, a two-band Hubbard model on a ladder lattice was the starting point of an investigation of pairing mechanisms in strongly repulsive fermion systems [20].…”

“…It can also be seen as a special case of the general two-band Hubbard model used to investigate pairing mechanisms [20]. The model is further related to the Kondo-Heisenberg model [15][16][17][18][19] because the Hubbard chain at half-filling has the same low-energy spin excitations as a Heisenberg chain. Thus, the asymmetric Hubbard ladder can be seen as a generalization of the Kondo-Heisenberg model (which corresponds to a Mott insulator with infinitely large charge gap on the interacting leg) to the case of a Mott insulator with a finite gap for charge excitations.…”