Kondo effect in the isotropic Heisenberg spin chain
- URL: http://arxiv.org/abs/2311.10569v2
- Date: Sat, 25 Nov 2023 15:12:30 GMT
- Title: Kondo effect in the isotropic Heisenberg spin chain
- Authors: Pradip Kattel, Parameshwar R. Pasnoori, J. H. Pixley, Patrick Azaria,
and Natan Andrei
- Abstract summary: impurity coupling strength is much weaker than that in the bulk, the impurity is screened in the ground state via the Kondo effect.
When the impurity coupling is ferromagnetic, the impurity is unscreened in the ground state.
When the absolute value of the ratio of the impurity and bulk coupling strengths is greater than $frac45$, the impurity can be screened by adding a bound mode.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate the boundary effects that arise when spin-$\frac{1}{2}$
impurities interact with the edges of the antiferromagnetic spin-$\frac{1}{2}$
Heisenberg chain through spin exchange interactions. We consider both cases
when the couplings are ferromagnetic or anti-ferromagnetic. We find that in the
case of antiferromagnetic interaction, when the impurity coupling strength is
much weaker than that in the bulk, the impurity is screened in the ground state
via the Kondo effect. The Kondo phase is characterized by the Lorentzian
density of states and dynamically generated Kondo temperature $T_K$. As the
impurity coupling strength increases, $T_K$ increases until it reaches its
maximum value $T_0=2\pi J$ which is the maximum energy carried by a single
spinon. When the impurity coupling strength is increased further, we enter
another phase, the bound mode phase, where the impurity is screened in the
ground state by a single particle bound mode exponentially localized at the
edge to which the impurity is coupled. We find that the impurity can be
unscreened by removing the bound mode. There exists a boundary eigenstate phase
transition between the Kondo and the bound-mode phases, a transition which is
characterized by the change in the number of towers of the Hilbert space. The
transition also manifests itself in ground state quantities like local impurity
density of states and the local impurity magnetization. When the impurity
coupling is ferromagnetic, the impurity is unscreened in the ground state;
however, when the absolute value of the ratio of the impurity and bulk coupling
strengths is greater than $\frac{4}{5}$, the impurity can be screened by adding
a bound mode that costs energy greater than $T_0$. When two impurities are
considered, the phases exhibited by each impurity remain unchanged in the
thermodynamic limit, but nevertheless the system exhibits a rich phase diagram.
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