Spin and thermal current scaling at a $Y$-junction of XX spin chains

TL;DR

The paper investigates a Y-junction of three XX spin chains, focusing on the boundary phase diagram and low-temperature spin and heat transport. By combining RG analysis with boundary conformal field theory and leveraging Jordan–Warker/fermionic and bosonization descriptions, it identifies four fixed points: a disconnected point, two Ising-like fixed points, and a topological Kondo point that emerges only on the symmetric line J_1=J_2. It shows that XY anisotropy destabilizes the TK fixed point, while the Ising-like fixed points are stable, and it reveals spin fractionalization and modified Wiedemann–Franz behavior at the TK fixed point. These results illuminate how multi-channel Kondo physics can manifest in spin-chain junctions and outline experimental considerations for realizing and detecting such boundary phenomena, including the potential observation of spin–heat separation and WF-law violations.

Abstract

We study the boundary phase diagram and the low-temperature heat and magnetization transport at a $Y$-junction of XX spin chains. Depending on the magnetization axis anisotropy between the magnetic exchange interactions at the junction, the system exhibits two different strong-coupling regimes at low energies/temperatures, similar to the overscreened (topological) four- and to the two-channel Kondo fixed points. Using renormalization group arguments combined with boundary conformal field theory methods, we show the instability of the former under any XY-type anisotropy at the junction. We analyze the low-temperature spin and the heat conductances. We find evidence of spin fractionalization of the elementary excitations at the four-channel Kondo fixed point by means of the magnetic Wiedemann-Franz law. We caution that the instability under XY anisotropy may hinder the detection of the phenomenology related to the four-channel Kondo effect, therefore requiring careful control in experimental realizations.

Figures (4)

• Figure 1: Sketch of a Y junction of semi-infinite spin chains. The magnetic spin exchange interaction $J$ along the three chains is the same along the $x$- and the $y$-directions and is represented by a black bond. In the central triangle the magnetic exchange interaction can be different in the different representation, which we represent by dashed red lines. Each chain is connected to a magnetization and temperature reservoir.
• Figure 2: Sketch of the RG trajectories and of the phase diagram of the junction in the $J_1$-$J_2$ plane. There are four FPs: the disconnected FP, drawn as a full black dot, at $J_1=J_2=0$, which is fully unstable against the Kondo boundary interaction, the TK FP, drawn as a full green dot, which is reached along the RG trajectories at $J_1=J_2$, but is unsable against any asymmetry between couplings $J_1$ and $J_2$, the two Ising-like FPs ${\cal I}_1$ and ${\cal I}_2$, respectively drawn as a full blue and red dot, which are stable and are reached along the RG flow from whatever point in parameter space with $J_1>J_2$, or $J_1<J_2$, respectively.
• Figure 3: Sketch of the the elementary reflection/transmission processes supporting (perturbatively in the boundary couplings) spin- and heat-currents across the $Y$-junction, as determined respectively by the contribution to the boundary interaction term in Eq.(\ref{['cmh.15']}) proportional to $\bar{J}_1+\bar{J}_2$ ( a)), and $\propto \bar{J}_1-\bar{J}_2$ ( b)). To ease reading the figure, we use full black (red) dots to denote particle (hole) like excitations within each lead. We also evidenced the spin polarization of the excitation entering/exiting the junction in each process.
• Figure 4: Sketch of the Keldysh path with the two labels $_+$ and $_-$ attached to the corresponding branches.