Strong-coupling limit of depleted Kondo- and Anderson-lattice models

Abstract

Fourth-order strong-coupling degenerate perturbation theory is used to derive an effective lowenergy Hamiltonian for the Kondo-lattice model with a depleted system of localized spins. In the strong-J limit, completely local Kondo singlets are formed at the spinful sites which bind a fraction of conduction electrons. The low-energy theory describes the scattering of the excess conduction electrons at the Kondo singlets as well as their effective interactions generated by virtual excitations of the singlets. Besides the Hubbard term, already discussed by Nozières, we find a ferromagnetic Heisenberg interaction, an antiferromagnetic isospin interaction, a correlated hopping and, in more than one dimensions, three-and four-site interactions. The interaction term can be cast into highly symmetric and formally simple spin-only form using the spin of the bonding orbital symmetrically centered around the Kondo singlet. This spin is non-local. We show that, depending on the geometry of the depleted lattice, spatial overlap of the non-local spins around different Kondo singlets may cause ferromagnetic order. This is sustained by a rigorous argument, applicable to the half-filled model, by a variational analysis of the stability of the fully polarized Fermi sea of excess conduction electrons as well as by exact diagonalization of the effective model. A similar fourth-order perturbative analysis is performed for the depleted Anderson lattice in the limit of strong hybridization. Even in a parameter regime where the Schrieffer-Wolff transformation does not apply, this yields the same effective theory albeit with a different coupling constant.

Steered quantum coherence as a signature of quantum phase transitions in spin chains

“…6 the dependence of C na l 1 (ρ i,i+r ) and C na re (ρ i,i+r ) on λ with different α and r. Besides those behaviors observed in Fig. 5, one can observe that when r = 1 and α < 1/8, there are two cusplike minima which are pronounced for C na l 1 (ρ i,i+r ) and are not obvious for C na re (ρ i,i+r ), but they are not critical points of QPTs [53]. In this sense, the SQCs of long-distance spin pairs are more reliable than that of the neighboring spin pair in detecting QPTs of the three-spin interaction XX model.…”

“…Besides the three critical lines, there is a critical line indicated by the minimum of the SQC, but as was shown in Ref. [53], it is not a boundary of QPT.…”

“…(3). The ground-state phase diagram consists of four sectors [53]: the spin-saturated phase in the regions of λ > λ c 1 and λ < λ c i (i = 2 when α < 1/8 and i = 3 otherwise), the spin liquid I phase in the region of λ ∈ (λ c 2 , λ c 1 ), and the spin liquid II phase in the region of λ ∈ (λ c 3 , λ c 2 ) and α > 1/8. Here, λ c 1 ,c 2 = 2α ± 1 and λ c 3 = −(1 + 32α 2 )/16α.…”

Compressible ferrimagnetism in the depleted periodic Anderson model

“…As a consequence, simulations for this parameter regime become very challenging for DQMC. The dependence of J eff on V has been studied in perturbation theory 66 .…”

Dynamical quantum phase transitions in extended transverse Ising models

“…In this paper, we study DQPTs following a sudden quench of the Hamiltonian for an extended transverse Ising (ETI) chain [70,71] which incorporates an additional three-spin interaction term in such a way that the spin-chain is still integrable in terms of Jordan-Wigner fermions. The generalized versions of the quantum XY/Ising Hamiltonians have been studied extensively both in the equilibrium [72][73][74][75][76] and non equilibrium [46,77] situations. Remarkably, Zhang et al, [70] showed that the ground states of the Hamiltonian in this model can be represented through loops in a twodimensional auxiliary space spanned by the parameters of the Hamiltonian.…”