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Register a new userTopology and the one-dimensional Kondo-Heisenberg model
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The Kondo-Heinsberg chain is an interesting model of a strongly correlated system which has a broad superconducting state with pair-density wave (PDW) order. Some of us have recently proposed that this PDW state is a symmetry-protected topological (SPT) state, and the gapped spin sector of the model supports Majorana zero modes. In this work, we reexamine this problem using a combination of numeric and analytic methods. In extensive density matrix renormalization group calculations, we find no evidence of a topological ground state degeneracy or the previously proposed Majorana zero modes in the PDW phase of this model. This result motivated us to reexamine the original arguments for the existence of the Majorana zero modes. A careful analysis of the effective continuum field theory of the model shows that the Hilbert space of the spin sector of the theory does not contain any single Majorana fermion excitations. This analysis shows that the PDW state of the doped 1D Kondo-Heisenberg model is not an SPT with Majorana zero modes.
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We use the density matrix renormalization group method to study the properties of the one-dimensional Kondo-Heisenberg model doped with Kondo holes. We find that the perturbation of the Kondo holes to the local hybridization exhibits spatial oscillation pattern and its amplitude decays exponentially with distance away from the Kondo hole sites. The hybridization oscillation is correlated with both the charge density oscillation of the conduction electrons and the oscillation in the correlation function of the Heisenberg spins. In particular, we find that the oscillation wavelength for intermediate Kondo couplings is given by the Fermi wavevector of the large Fermi surface even before it is formed. This suggests that heavy electrons responsible for the oscillation are already present in this regime and start to accumulate around the to-be-formed large Fermi surface in the Brillouin zone.
We address some open questions regarding the phase diagram of the one-dimensional Hubbard model with asymmetric hopping coefficients and balanced species. In the attractive regime we present a numerical study of the passage from on-site pairing dominant correlations at small asymmetries to charge-density waves in the region with markedly different hopping coefficients. In the repulsive regime we exploit two analytical treatments in the strong- and weak-coupling regimes in order to locate the onset of phase separation at small and large asymmetries respectively.
For the one-dimensional Holstein model, we show that the relations among the scaling exponents of various correlation functions of the Tomonaga Luttinger liquid (LL), while valid in the thermodynamic limit, are significantly modified by finite size corrections. We obtain analytical expressions for these corrections and find that they decrease very slowly with increasing system size. The interpretation of numerical data on finite size lattices in terms of LL theory must therefore take these corrections into account. As an important example, we re-examine the proposed metallic phase of the zero-temperature, half-filled one-dimensional Holstein model without employing the LL relations. In particular, using quantum Monte Carlo calculations, we study the competition between the singlet pairing and charge ordering. Our results do not support the existence of a dominant singlet pairing state.
A perturbation spin-wave theory for the quantum Heisenberg antiferromagnets on a square lattice is proposed to calculate the uniform static magnetic susceptibility at finite temperatures, where a divergence in the previous theories due to an artificial phase transition has been removed. To the zeroth order, the main features of the uniform static susceptibility are produced: a linear temperature dependence at low temperatures and a smooth crossover in the intermediate range and the Curie law at high temperatures. When the leading corrections from the spin-wave interactions are included, the resulting spin susceptibility in the full temperature range is in agreement with the numerical quantum Monte Carlo simulations and high-temperature series expansions.
The previous theoretical study has shown that pulse irradiation to the Mott insulating state in the Hubbard model can induce the enhancement of superconducting correlation due to the generation of $eta$ pairs. Here, we show that the same mechanism can be applied to the Kondo lattice model, an effective model for heavy electron systems, by demonstrating that the pulse irradiation indeed enhances the $eta$-pairing correlation. As in the case of the Hubbard model, the non-linear optical process is essential to increase the number of photoinduced $eta$ pairs and thus the enhancement of the superconducting correlation. We also find the diffusive behavior of the spin dynamics after the pulse irradiation, suggesting that the increase of the number of $eta$ pairs leads to the decoupling between the conduction band and the localized spins in the Kondo lattice model, which is inseparably related to the photodoping effect.
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