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arXiv:2411.16357 · Physical review. B./Physical review. B

Bosonic Peierls state emerging from the one-dimensional Ising-Kondo interaction

Jingtao Fan, Xiaofan Zhou, Suotang Jia

Published Feb 19, 2025• 0 citations
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Abstract

As an important effect induced by the particle-lattice interaction, the Peierls transition, a hot topic in condensed matter physics, is usually believed to occur in one-dimensional fermionic systems. We here study a bosonic version of the one-dimensional Ising-Kondo lattice model, which describes two-species itinerant bosons, essentially acting as pseudospins, interacting with the localized magnetic moments via only longitudinal Kondo exchange. We show that, by means of perturbation analysis and numerical density-matrix renormalization group method, a bosonic analog of the Peierls state can occur in proper parameter regimes. The Peierls state here is characterized by the formation of a long-range spin-density-wave order, the periodicity of which is set by the density of the itinerant bosons. The ground-state phase diagram is mapped out by extrapolating the finite-size results to the thermodynamic limit. Apart from the bosonic Peierls state, we also reveal the presence of some other magnetic orders, including a paramagnetic phase and a ferromagnetic phase. We finally propose a possible experimental scheme with ultracold atoms in optical lattices. Our results broaden the frontiers of current understanding of the one-dimensional particle-lattice interaction system.

DOI
10.1103/physrevb.111.064110

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As an important effect induced by the particle-lattice interaction, the Peierls transition, a hot topic in condensed matter physics, is usually believed to occur in one-dimensional fermionic systems. We here study a bosonic version of the one-dimensional Ising-Kondo lattice model, which describes two-species itinerant bosons, essentially acting as pseudospins, interacting with the localized magnetic moments via only longitudinal Kondo exchange. We show that, by means of perturbation analysis and numerical density-matrix renormalization group method, a bosonic analog of the Peierls state can occur in proper parameter regimes. The Peierls state here is characterized by the formation of a long-range spin-density-wave order, the periodicity of which is set by the density of the itinerant bosons. The ground-state phase diagram is mapped out by extrapolating the finite-size results to the thermodynamic limit. Apart from the bosonic Peierls state, we also reveal the presence of some other magnetic orders, including a paramagnetic phase and a ferromagnetic phase. We finally propose a possible experimental scheme with ultracold atoms in optical lattices. Our results broaden the frontiers of current understanding of the one-dimensional particle-lattice interaction system.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.
We study numerically the one-dimensional Kondo and Hund lattices consisting of localized spins interacting antiferromagnetically or ferromagnetically with the itinerant electrons, respectively. Using the density-matrix renormalization group we find, for both models and in the small coupling regime, the existence of new magnetic phases where the local spins order forming ferromagnetic islands coupled antiferromagnetically. Furthermore, by increasing the interaction parameter |J| we find that this order evolves toward the ferromagnetic regime through a spiral-like phase with longer characteristic wavelengths. These results shed new light on the zero temperature magnetic phase diagram for these models.
We investigate the ground-state properties of a recently proposed model for a topological Kondo insulator in one dimension (i.e., the ppp-wave Kondo-Heisenberg lattice model) by means of the density-matrix renormalization-group method. The nonstandard Kondo interaction in this model is different from the usual (i.e., local) Kondo interaction in that the localized spins couple to the ``ppp-wave'' spin density of conduction electrons, inducing a topologically nontrivial insulating ground state. Based on the analysis of the charge- and spin-excitation gaps, the string order parameter, and the spin profile in the ground state, we show that, at half filling and low energies, the system is in the Haldane phase and hosts topologically protected spin-1/2 end states. Beyond its intrinsic interest as a useful ``toy model'' to understand the effects of strong correlations on topological insulators, we show that the ppp-wave Kondo-Heisenberg model could be experimentally implemented in $p\text{\ensuremath{-}}\mathrm{band}$ optical lattices loaded with ultracold Fermi gases.
We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZXXZXXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.
We investigate the magnetic order of a one-dimensional spin-1/2 fermion dynamical lattice, where itinerant fermions are coupled to bond-centered localized spins via an Ising-like spin dependent hopping. The model provides an anisotropic dynamical extension of conventional spin-1/2 fermion systems, in which the motion of itinerant fermions is directly modulated by the configuration of localized spins. Using density matrix renormalization group simulations, we map out the ground state phase diagram in various parameter spaces. Depending on the interplay among the hopping dependent on localized spins, the longitudinal field, and the external Zeeman field, two distinct phases are obtained: a paramagnetic phase and a spin-density-wave phase. Most notably, in the partially spin-polarized fermion phase, the spin-density wave ordering wave vector exhibits two distinct phenomena, corresponding respectively to the nesting vectors 2kF↑2k_{F\uparrow}2kF↑​ and 2kF↓2k_{F\downarrow}2kF↓​ of the spin-resolved Fermi surfaces. We further demonstrate that the two spin-density wave phases are robust against the repulsive Hubbard interaction between itinerant fermions. Our results reveal a novel route for tuning magnetic modulations in one-dimensional correlated systems and enrich the microscopic understanding of dynamical lattice magnetism.
We analyze the possible types of ordering in a boson-fermion model. The Hamiltonian is inherently related to the Bose-Hubbard model for vector two-species bosons in optical lattices. We show that such a model can be reduced to the Kugel-Khomskii type spin-pseudospin model, but in contrast to the usual version of the latter model, we are dealing here with the case of spin S=1S=1S=1 and pseudospin 1/21/21/2. We show that the interplay of spin and pseudospin degrees of freedom leads to a rather nontrivial magnetic phase diagram including the spin-nematic configurations. Tuning the spin-channel interaction parameter Us{U}_{s}Us​ gives rise to quantum phase transitions. We find that the ground state of the system always has the pseudospin domain structure. On the other hand, the sign change of Us{U}_{s}Us​ switches the spin arrangement of the ground state within domains from a ferro- to antiferromagnetic one. Finally, we revisit the spin (pseudospin)-1/2 Kugel-Khomskii model and see the inverse picture of phase transitions.