Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhase diagram of the Kondo model on the zigzag ladder
88
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The effect of next-nearest-neighbor hopping $t_{2}$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite $t_{2}$, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that $t_{2}$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker $J$, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order which is found at weaker couplings. The phase diagram at weak $J$, with gapless quasi-long-range order on top of the two-fold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.
rate research
Read More
The magnetic ground state phase diagram of the ferromagnetic Kondo-lattice model is constructed by calculating internal energies of all possible bipartite magnetic configurations of the simple cubic lattice explicitly. This is done in one dimension (1D), 2D and 3D for a local moment of S = 3/2. By assuming saturation in the local moment system we are able to treat all appearing higher local correlation functions within an equation of motion approach exactly. A simple explanation for the obtained phase diagram in terms of bandwidth reduction is given. Regions of phase separation are determined from the internal energy curves by an explicit Maxwell construction.
The interplay between the Kondo effect and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange interaction, $J_perp$, between the localized and the conduction electrons, this model also contains the local repulsion, $U$, between the conduction electrons. We use variational cluster approximation to investigate the competition between the antiferromagnetic phase, the Kondo singlet phase, and a ferrimagnetic phase on square lattice. At half-filling, the Neel antiferromagnetic phase dominates from small to moderate $J_perp$ and $UJ_perp$, and the Kondo singlet elsewhere. Sufficiently away from half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic phase (in which the localized spins order ferromagnetically, and the conduction electrons do likewise, but the two mutually align antiferromagnetically), and then to the Kondo singlet phase.
In heavy-fermion systems, the competition between the local Kondo physics and intersite magnetic fluctuations results in unconventional quantum critical phenomena which are frequently addressed within the Kondo lattice model (KLM). Here we study this interplay in the SU($N$) symmetric generalization of the two-dimensional half-filled KLM by quantum Monte Carlo simulations with $N$ up to 8. While the long-range antiferromagnetic (AF) order in SU($N$) quantum spin systems typically gives way to spin-singlet ground states with spontaneously broken lattice symmetry, we find that the SU($N$) KLM is unique in that for each finite $N$ its ground-state phase diagram hosts only two phases -- AF order and the Kondo-screened phase. The absence of any intermediate phase between the $N=2$ and large-$N$ cases establishes adiabatic correspondence between both limits and confirms that the large-$N$ theory is a correct saddle point of the KLM fermionic path integral and a good starting point to include quantum fluctuations. In addition, we determine the evolution of the single-particle gap, quasiparticle residue of the doped hole at momentum $(pi,pi)$, and spin gap across the magnetic order-disorder transition. Our results indicate that increasing $N$ modifies the behavior of the coherence temperature: while it evolves smoothly across the magnetic transition at $N=2$ it develops an abrupt jump -- of up to an order of magnitude -- at larger but finite $N$. We discuss the magnetic order-disorder transition from a quantum-field-theoretic perspective and comment on implications of our findings for the interpretation of experiments on quantum critical heavy-fermion compounds.
Studies of free particles in low-dimensional quantum systems such as two-leg ladders provide insight into the influence of statistics on collective behaviour. The behaviours of bosons and fermions are well understood, but two-dimensional systems also admit excitations with alternative statistics known as anyons. Numerical analysis of hard-core $mathbb{Z}_3$ anyons on the ladder reveals qualitatively distinct behaviour, including a novel phase transition associated with crystallisation of hole degrees of freedom into a periodic foam. Qualitative predictions are extrapolated for all Abelian $mathbb{Z}_q$ anyon models.
Topological Kondo insulators are a rare example of an interaction-enabled topological phase of matter in three-dimensional crystals - making them an intriguing but also hard case for theoretical studies. Here, we aim to advance their theoretical understanding by solving the paradigmatic two-band model for topological Kondo-insulators using a fully spin-rotation invariant slave-boson treatment. Within a mean-field approximation, we map out the magnetic phase diagram and characterize both antiferromagnetic and paramagnetic phases by their topological properties. Among others, we identify an antiferromagnetic insulator that shows, for suitable crystal terminations, topologically protected hinge modes. Furthermore, Gaussian fluctuations of the slave boson fields around their mean-field value are included in order to establish the stability of the mean-field solution through computation of the full dynamical susceptibility.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
