Core Concepts

The dynamic RKKY interaction, derived from time-dependent fluctuations of the conduction electron spin susceptibility, retains sensitivity to time-reversal symmetry breaking that is lost in the static approximation. This enables the induction of spin chirality by external magnetic fields or through proximity to topologically nontrivial materials.

Abstract

The paper studies the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction in various Kondo lattice systems. It argues that the weak Kondo coupling expansion contains certain physics which is lost in the usual static approximation to the spin susceptibility. Notably, while the static approximation is blind to time-reversal symmetry breaking, the dynamic RKKY interaction is sensitive to it.

Using exact diagonalization on small systems and a large-N approximation on extended lattices, the paper explores the impact of dynamic RKKY interaction on spin liquids and spinons. On a honeycomb Kondo lattice with Haldane fluxes, it is shown that the dynamic RKKY can induce topological chiral spin states, generating non-trivial edge modes. This provides a mechanism to engineer Dzyaloshinskii-Moriya-like effects, even in centrosymmetric systems, opening avenues for the design of chiral spin liquids and topologically ordered states in Kondo lattices.

The paper also discusses the spinon lifetime and delocalization temperature in the weak Kondo coupling regime, finding that the dynamic RKKY interaction leads to a finite spinon lifetime and affects the onset of spinon delocalization compared to the static RKKY approximation. Additionally, the paper demonstrates that the dynamic RKKY interaction can induce spin chirality in a Kondo triangle setup by breaking time-reversal symmetry through an external magnetic field.

To Another Language

from source content

arxiv.org

Stats

The paper presents the following key data and figures:
Fig. 2(a) shows the bandwidth of spinons (difference between maximum and minimum value of the real part of the self-energy) as a function of temperature for various values of the Kondo coupling strength J^2_K, exhibiting a mean-field-like delocalization transition.
Fig. 2(b) compares the spinon delocalization transition temperatures for both dynamic and static RKKY interactions as a function of J^2_K.
Fig. 3(a) shows the spin chirality on a Kondo triangle as a function of the magnetic flux threading the electrons, computed using exact diagonalization.
Fig. 3(b) presents the large-N results for the spin chirality on the Kondo triangle, confirming that the induced spin chirality is due to the dynamic RKKY interaction.
Fig. 4 depicts the spinon dispersion in a Kondo lattice with honeycomb geometry, where the time-reversal symmetry breaking in the conduction layer (induced by Haldane fluxes) is transferred to the spinons via the dynamic RKKY effect, opening a gap at the Dirac cones.

Quotes

"The dynamic RKKY interaction, derived from time-dependent fluctuations of the conduction electron spin susceptibility, retains certain key physical phenomena—such as sensitivity to time-reversal symmetry (TRS) breaking—that are lost in the static approximation."
"This tunable interaction provides a mechanism to engineer Dzyaloshinskii-Moriya-like effects, even in centrosymmetric systems, opening avenues for the design of chiral spin liquids and topologically ordered states in Kondo lattices."

Key Insights Distilled From

by Siqi Shao, Y... at **arxiv.org** 10-01-2024

Deeper Inquiries

The dynamic Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction presents a promising avenue for engineering novel quantum phases in various frustrated magnetic systems beyond Kondo lattices. By exploiting the sensitivity of the dynamic RKKY interaction to time-reversal symmetry (TRS) breaking, researchers can manipulate spin interactions in systems such as triangular or kagome lattices, which are known for their geometric frustration.
In these systems, the dynamic RKKY interaction can be tuned through external magnetic fields or proximity to topological materials, allowing for the induction of spin chirality and the emergence of chiral spin liquids. This tunability can lead to the realization of exotic phases such as spin-nematic states or even quantum spin liquids characterized by fractionalization of spin excitations. Furthermore, the interplay between dynamic RKKY interactions and other interactions, such as spin-orbit coupling or external perturbations, can facilitate the exploration of topologically ordered states, potentially leading to the discovery of new quantum phases that exhibit non-trivial edge states or fractional statistics.

Yes, the dynamic RKKY-induced topology on spinons can indeed be harnessed to realize exotic many-body states, including fractional topological insulators and Majorana modes. The dynamic RKKY interaction, by coupling the spinons to the conduction electrons, can induce a topological structure in the spinon spectrum, leading to the emergence of chiral edge states that are characteristic of topological phases.
In the context of fractional topological insulators, the interplay between the dynamic RKKY interaction and the underlying lattice geometry can facilitate the formation of fractional excitations, which are essential for realizing fractional statistics. The presence of chiral edge states can also support the existence of Majorana modes, which are non-abelian anyons that can be used for topological quantum computation. By carefully tuning the parameters of the system, such as the strength of the Kondo coupling or the external magnetic field, it is possible to manipulate the topological properties of the spinons, thereby enabling the realization of these exotic many-body states.

The ability to read off the dynamic spin susceptibility of f-electrons from the optical conductivity of c-electrons in the weak Kondo coupling regime has several significant applications in condensed matter physics. This technique provides a powerful tool for probing the spin dynamics of strongly correlated electron systems, particularly in cases where direct measurements of the f-electron states are challenging.
One potential application is in the study of quantum phase transitions in heavy fermion systems, where the interplay between f-electron and conduction electron states can lead to rich phase diagrams. By analyzing the optical conductivity, researchers can gain insights into the nature of the spin fluctuations and their role in driving these transitions.
Additionally, this approach can be utilized to investigate the emergence of topological order and the associated edge states in Kondo lattices and other correlated systems. By correlating the optical response of the conduction electrons with the dynamic spin susceptibility, it becomes possible to identify signatures of topological phases and to explore the conditions under which these phases arise.
Moreover, this method can facilitate the exploration of non-equilibrium dynamics in quantum materials, allowing for the study of how external perturbations affect the spin susceptibility and the resulting many-body states. Overall, the ability to extract dynamic spin susceptibility from optical measurements opens up new avenues for understanding complex quantum phenomena in correlated electron systems.

0