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arXiv:2010.00616 · Physical review. B./Physical review. B

Competition of spinon Fermi surface and heavy Fermi liquid states from the periodic Anderson to the Hubbard model

Chuan Chen, Inti Sodemann, Patrick A. Lee

Published Feb 19, 2021• 19 citations
arXivHTMLPDF

Abstract

We study a model of correlated electrons coupled by tunneling to a layer of itinerant metallic electrons, which allows us to interpolate from a frustrated limit favorable to spin liquid states to a Kondo-lattice limit favorable to interlayer coherent heavy metallic states. We study the competition of the spinon Fermi-surface state and the interlayer coherent heavy Kondo metal that appears with increasing tunneling. Employing a slave rotor mean-field approach, we obtain a phase diagram and describe two regimes where the spin liquid state is destroyed by weak interlayer tunneling: (i) the Kondo limit in which the correlated electrons can be viewed as localized spin moments and (ii) near the Mott metal-insulator transition where the spinon Fermi surface transitions continuously into a Fermi liquid. We study the shape of local density of states (LDOS) spectra of the putative spin liquid layer in the heavy Fermi-liquid phase and describe the temperature dependence of its width arising from quasiparticle interactions and disorder effects throughout this phase diagram, in an effort to understand recent scanning tunneling microscopy experiments of the candidate spin liquid $1\mathrm{T}\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$ residing on metallic $1\mathrm{H}\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$. Comparison of the shape and temperature dependence of the theoretical and experimental LDOS suggests that this system is either close to the localized Kondo limit or in an intermediate coupling regime where the Kondo coupling and the Heisenberg exchange interaction are comparable.

DOI
10.1103/physrevb.103.085128

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We study a model of correlated electrons coupled by tunneling to a layer of itinerant metallic electrons, which allows us to interpolate from a frustrated limit favorable to spin liquid states to a Kondo-lattice limit favorable to interlayer coherent heavy metallic states. We study the competition of the spinon Fermi-surface state and the interlayer coherent heavy Kondo metal that appears with increasing tunneling. Employing a slave rotor mean-field approach, we obtain a phase diagram and describe two regimes where the spin liquid state is destroyed by weak interlayer tunneling: (i) the Kondo limit in which the correlated electrons can be viewed as localized spin moments and (ii) near the Mott metal-insulator transition where the spinon Fermi surface transitions continuously into a Fermi liquid. We study the shape of local density of states (LDOS) spectra of the putative spin liquid layer in the heavy Fermi-liquid phase and describe the temperature dependence of its width arising from quasiparticle interactions and disorder effects throughout this phase diagram, in an effort to understand recent scanning tunneling microscopy experiments of the candidate spin liquid 1T\ensuremath-TaSe21\mathrm{T}\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}1T\ensuremath-TaSe2​ residing on metallic 1H\ensuremath-TaSe21\mathrm{H}\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}1H\ensuremath-TaSe2​. Comparison of the shape and temperature dependence of the theoretical and experimental LDOS suggests that this system is either close to the localized Kondo limit or in an intermediate coupling regime where the Kondo coupling and the Heisenberg exchange interaction are comparable.
Motivated by recent experimental observations of Kondo resonances in cobalt atoms on single layer 1T-TaSe2_{2}2​, we theoretically investigate the effect of coupling a U(1) quantum spin liquid with a spinon Fermi surface to a lattice of Anderson impurities. Within the slave-rotor formalism, we find that above a critical coupling strength between the spin liquid and impurity lattice, the spinons hybridize to form heavy quasiparticles near the Fermi level, realizing a {\it spinon Kondo lattice phase} analogous to heavy fermion materials. Using the Bethe-Salpeter equation and accounting for emergent gauge fluctuations, we compute the spectral density and density of states, revealing the formation of spinon-chargon bound states in the spinon Kondo lattice phase. We characterize the thermodynamic and spectroscopic signatures of this phase, demonstrating specific heat and neutron scattering responses distinct from a pure quantum spin liquid. Our findings establish the spinon Kondo lattice as a framework to study the rich physics of spin liquids.
Motivated by recent experimental observations of Kondo resonances in cobalt atoms on single layer $1T\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$, we theoretically investigate the effect of coupling a U(1) quantum spin liquid with a spinon Fermi surface to a lattice of Anderson impurities. Within the slave-rotor formalism, we find that above a critical coupling strength between the spin liquid and impurity lattice, the spinons hybridize to form heavy quasiparticles near the Fermi level, realizing a spinon Kondo lattice phase analogous to heavy fermion materials. Using the Bethe-Salpeter equation and accounting for emergent gauge fluctuations, we compute the spectral density and density of states, revealing the formation of spinon-chargon bound states in the spinon Kondo lattice phase. We characterize the thermodynamic and spectroscopic signatures of this phase, demonstrating specific heat and neutron scattering responses distinct from a pure quantum spin liquid. Our findings establish the spinon Kondo lattice as a framework to study the rich physics of spin liquids.
The Hubbard model in the strong-coupling regime is mainly studied by Kondo-lattice theory or 1/d expansion theory, with d the spatial dimensionality. In two dimensions and higher, the ground state within the Hilbert subspace with no order parameter is a normal Fermi liquid except for n=1 and U/W=+infinity, with n the electron density per unit cell, U the on-site repulsion, and W the bandwidth; the cooperation between the Kondo effect, which favors a local singlet on each unit cell, and a resonating-valence-bond effect, which favors a local singlet on each pair of nearest-neighbor unit cells, stabilizes the Fermi liquid, whose ground state is a singlet as a whole, in the strong-coupling regime. In the whole Hilbert space with no restriction, the normal Fermi liquid is unstable at least against a magnetic or superconducting state. This analysis confirms an early Fermi-liquid theory of high-temperature superconductivity, F. J. Ohkawa, Jpn. J. Appl. Phys. 26, L652 (1987). The ground state for n=1 and U/W=+infinity is a Mott insulator. Actual metal-insulator transitions cannot be explained within the Hubbard model. In order to explain them, the electron-phonon interaction, multi-band or multi-orbital effects, and effects of disorder should be considered beyond the Hubbard model. The crossover between local-moment magnetism and itinerant-electron magnetism corresponds to that between a localized spin and a normal Fermi liquid in the Kondo effect and it is simply a Mott metal-insulator crossover.
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.
The Hubbard model is studied for the Mott-transition region in the limit of high dimension d →+∞. Leading-order effects with respect to 1/ d are local spin fluctuations, all of which are fully included in the single-site approximation (SSA). Because the SSA is reduced to solving the Anderson model, it is argued that a normal heavy-electron liquid forms through the Kondo effect. The Fermi-liquid relations are proven within the SSA. The other leading-order effects are mean fields of magnetism caused by exchange interaction. Therefore it depends on the competition between the Kondo effect and the exchange interaction which the ground state is, magnetic or paramagnetic. However, any other effect is a higher-order effect. The 1/ d expansion from the heavy-electron liquid in the SSA is one of the most useful methods in examining lower-temperature phases in the real dimension.
We explore the physics of a spin-1/2 Heisenberg chain with Kondo interaction, Jk{J}_{k}Jk​, to a two-dimensional electron gas. At weak Jk{J}_{k}Jk​ the problem maps onto a Heisenberg chain locally coupled to a dissipative Ohmic bath. At the decoupled fixed point, the dissipation is a marginally relevant perturbation and drives long-range antiferromagnetic order along the chain. In the dynamical spin structure factor we observe a quadratic low-energy dispersion akin to Landau-damped Goldstone modes. At large Jk{J}_{k}Jk​ Kondo screening dominates, and the spin correlations of the chain inherit the power law of the host metal, akin to a paramagnetic heavy Fermi liquid. In both phases we observe heavy bands near the Fermi energy in the composite-fermion spectral function. Our results, obtained from auxiliary-field quantum Monte Carlo simulations, provide a negative-sign-free realization of a quantum transition between an antiferromagnetic metal and a heavy-fermion metal. We discuss the relevance of our results in the context of scanning tunneling spectroscopy experiments of magnetic adatom chains on metallic surfaces.