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arXiv:cond-mat/0304129 · Physical Review B

Transitions from small to large Fermi momenta in a one-dimensional Kondo lattice model

Eugene Pivovarov, Qimiao Si A

Published Mar 9, 2004• 15 citations
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Abstract

We study a one-dimensional system that consists of an electron gas coupled to a spin-1/2 chain by Kondo interaction away from half filling. We show that zero-temperature transitions between phases with ``small'' and ``large'' Fermi momenta can be continuous. Such a continuous but Fermi-momentum-changing transition arises in the presence of spin anisotropy, from a Luttinger liquid with a small Fermi momentum to a Kondo-dimer phase with a large Fermi momentum. We have also added a frustrating next-nearest-neighbor interaction in the spin chain to show the possibility of a similar Fermi-momentum-changing transition, between the Kondo phase and a spin-Peierls phase, in the spin isotropic case. This transition, however, appears to involve a region in which the two phases coexist.

DOI
10.1103/physrevb.69.115104

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We study a one-dimensional system that consists of an electron gas coupled to a spin-1/2 chain by Kondo interaction away from half filling. We show that zero-temperature transitions between phases with small'' and large'' Fermi momenta can be continuous. Such a continuous but Fermi-momentum-changing transition arises in the presence of spin anisotropy, from a Luttinger liquid with a small Fermi momentum to a Kondo-dimer phase with a large Fermi momentum. We have also added a frustrating next-nearest-neighbor interaction in the spin chain to show the possibility of a similar Fermi-momentum-changing transition, between the Kondo phase and a spin-Peierls phase, in the spin isotropic case. This transition, however, appears to involve a region in which the two phases coexist.
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 one-dimensional 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.
We study one dimensional {\it extended} Kondo lattice model, described by the t−Jt-Jt−J Hamiltonian for conduction electrons away from half filling and the Heisenberg Hamiltonian for localized spins at half filling. Following Shankar,\cite{Shankar} we find an effective field theory for this model, where doped holes are represented by massless Dirac fermions (holons) and spin excitations are fractionalized into relativistic bosons (spinons). These holons and spinons interact via U(1) gauge fluctuations. Effects of Berry phase to the localized spins disappear due to the presence of Kondo couplings, causing the spinon excitations gapped. Furthermore, the gauge fluctuations are suppressed by hole doping. As a result, massive spinons are deconfined to arise in the localized spins unless the Kondo hybridization is strong enough. When the Kondo hybridization strength exceeds a certain value, we find that the localized spin chain becomes critical. This indicates that the present one dimensional Kondo lattice model exhibits a phase transition from a spin-gapped phase to a critical state in the localized spin chain, driven by the Kondo interaction.
Fermi surface reconstruction in cuprates can lead to an abrupt change in the Fermi momentum kF{k}_{F}kF​ between different phases. This phenomenon remains a subject of debate and is at the heart of an ongoing discussion about the nature of the metallic state in the pseudogap regime. Here we study a minimal model of a kF{k}_{F}kF​ changing crossover in the one-dimensional Fermi-Hubbard model, where a tuning of the on-site interaction leads to a crossover between a spin-1/21/21/2 Luttinger liquid with small Fermi momentum and a spinless chargon liquid with large Fermi momentum. We attribute this to an emergent U(1)U(1)U(1) symmetry in the strongly correlated limit, which can be used to derive a modified Luttinger sum rule recovering the large Fermi momentum. We analyze Friedel oscillations at the edge of a system to directly probe the change of Fermi momentum at zero and nonzero temperature. This paves the way for a direct experimental observation of changes of the Fermi momentum using ultracold fermions in a quantum gas microscope, with possible extensions to higher dimensional systems.
Fermi surface reconstruction in cuprates can lead to an abrupt change in the Fermi momentum kFk_FkF​ between different phases. This phenomenon remains subject of debate and is at the heart of an ongoing discussion about the nature of the metallic state in the pseudogap regime. Here we study a minimal model of a kFk_FkF​ changing crossover in the one-dimensional Fermi-Hubbard model, where a tuning of the onsite interaction leads to a crossover between a spin-1/21/21/2 Luttinger liquid with small Fermi momentum and a spinless chargon liquid with large Fermi momentum. We attribute this to an emergent U(1)U(1)U(1) symmetry in the strongly correlated limit, which can be used to derive a modified Luttinger sum rule recovering the large Fermi momentum. We analyse Friedel oscillations at the edge of a system to directly probe the change of Fermi momentum at zero and non-zero temperature. This paves the way for a direct experimental observation of changes of the Fermi momentum using ultracold fermions in a quantum gas microscope, with possible extensions to higher dimensional systems.
A multichannel Kondo system, where a single quantum spin couples to multiple channels of an electronic bath, provides one of the simplest examples of a zero-dimensional non-Fermi liquid. It is natural to ask: what happens when an extensive number of such systems are coupled together? A simple renormalization group argument implies that in a chain of SU(N) multichannel quantum systems, where each spin is coupled to its own bath of K channels, the individual spins dynamically decouple at low energy when N>K, resulting in a 'sliding' non-Fermi liquid. Using Quantum Monte Carlo (QMC) simulations, we find evidences of a continuous, 'dimensionality-changing' phase transition out of this non-Fermi liquid into a valence-bond solid phase as the intersite coupling is increased. Remarkably, at the critical point, correlations exhibit a power-law behavior even along the direction in which the spins are coupled, indicating the breakdown of dynamical decoupling at the transition. We also develop an RG scheme to understand the universal aspects of this transition.
We study a lattice realization of a Luttinger liquid interacting with quantum spins in terms of an antiferromagnetic S=1∕2S=1∕2S=1∕2 Heisenberg chain, where each spin is also coupled to a $\ensuremath{\sigma}=1∕2$ Kondo spin degree of freedom. This model describes the low-energy spin dynamics in quasi-one-dimensional materials, where the electronic spins of the magnetic ions interact with those of impurities, nuclei, and possibly other spin species present in their environment. For large ferromagnetic and antiferromagnetic Kondo interaction ${J}^{\ensuremath{'}}$, there are two phases corresponding to an effective spin-1 Heisenberg chain and a dimerized spin-1∕21∕21∕2 ladder, respectively. For weak Kondo interaction, we establish that the Kondo interaction drives the system to a strong coupling regime. This suggests that ${J}^{\ensuremath{'}}=0$ is the only critical point in the system.