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Journal of the Physical Society of Japan

Fixed Point of the Spin-Fermion Model Doped with a Single Fermion

Nobuo Furukawa, Masatoshi Imada

Published Jun 1, 1992• 3 citations
Publisher

Abstract

Spin-fermion model on a square lattice is investigated in the perturbation expansion in terms of the spin-fermion Kondo coupling. The fermion self-energy is calculated in a self-consistent treatment by a dominant pole approximation. The quasi-particle excitation of a doped fermion turns out to be totally incoherent. It suggests that the low energy excitations should be described by the bound state of a fermion and spins as a collective mode and imply that the fixed point of the spin-fermion model with a single fermion is the t - J model. It also suggests the spin-charge separation of the low energy excitations in the light doping region of these two models.

DOI
10.1143/jpsj.61.2048

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Spin-fermion model on a square lattice is investigated in the perturbation expansion in terms of the spin-fermion Kondo coupling. The fermion self-energy is calculated in a self-consistent treatment by a dominant pole approximation. The quasi-particle excitation of a doped fermion turns out to be totally incoherent. It suggests that the low energy excitations should be described by the bound state of a fermion and spins as a collective mode and imply that the fixed point of the spin-fermion model with a single fermion is the t - J model. It also suggests the spin-charge separation of the low energy excitations in the light doping region of these two models.
Heavy-fermion or Kondo lattice materials are considered to be typical strongly correlated systems, for which mean-field approximations have shown that the Coulomb interaction increases the effective mass and narrows the band gap. In this paper, to clarify interaction effects on the electronic excitation, the spectral function of the Kondo lattice and periodic Anderson models is studied around Kondo insulators in the strong-coupling regime, by using the non-Abelian dynamical density-matrix renormalization group method and perturbation theory. Upon doping a Kondo insulator, an electronic mode emerges in the Kondo insulating gap, exhibiting the momentum-shifted magnetic dispersion relation. Although the ground-state properties are similar to those of a doped band insulator, the emergence of the electronic mode reflecting spin-charge separation of the Kondo insulator is a crucial interaction effect that allows us to regard the Kondo-insulator--metal transition as a type of Mott transition. In addition, electronic modes emerge even in the high-energy regime by doping in the periodic Anderson model. These strong-correlation effects have not been expected in conventional mean-field approximations and would bring a different perspective on heavy-fermion or Kondo lattice systems.
We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.
Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high-TcT_{\rm c}Tc​ cuprates.
We present a new method for studying the low energy excitations in finite cluster systems and apply it to clarify the nature of the low energy spin excitations in the moderately doped t-J model. We find that the character of the low energy spin excitations changes within the Brillouin zone, with the dominant excitation for momentum transfer (pi,pi) being a spin wave-like collective mode. Spin excitations with momentum transfer different from (pi,pi) have particle-hole character. We give an explicit construction of a low energy collective spin mode in a system with `almost broken symmetry' and demonstrate its validity by explicit numerical check.
We study the effects of hole doping on the two-dimensional Heisenberg-Kondo model around the quantum critical point, where the spin liquid phase (Kondo insulator) and the magnetically ordered phase are separated via a second-order phase transition. By means of the self-consistent Born approximation within the bond operator formalism as well as the standard spin wave theory, we discuss dynamical properties of a doped hole. It is clarified that a quasi-particle state stabilized in the spin liquid phase is gradually obscured as the system approaches the quantum critical point. This is also the case for the magnetically ordered phase. We argue the similarity and the difference between these two cases.
Magnetic correlations of doped Mott insulators hold the key to the unusual characteristics of many quantum materials. Recent experiments with ultracold atoms in optical lattices have provided new information about the magnetic properties of the Fermi-Hubbard model on a square lattice. We demonstrate that recent measurements indicate that a single doping-dependent energy scale determines both static correlations and dynamical response of these systems. To understand these experimental findings, we employ a self-consistent formalism to describe the coupling between antiferromagnetic magnons and doped holes, and we uncover the emergence of a universal magnetic energy scale at finite doping, which we denote by J∗J^*J∗. We present the single- and two-magnon spectral properties at finite doping and discuss the appearance of a bimagnon peak in lattice-modulation spectroscopy, at frequencies set by J∗J^*J∗. Furthermore, we argue that this same energy scale sets the onset of pseudogap phenomena, leading to the hypothesis kBT∗=cJ∗k_BT^* = c J^*kB​T∗=cJ∗, with ccc an order one number. We identify another low-energy scale emerging from our analysis of magnetic excitations, and argue that it controls the stability of Néel order at the lowest temperatures, ultimately driving a transition to an incommensurate spin-density-wave at finite doping. We discuss the relation between this low-energy scale and the nature of fermionic quasiparticles. Our analysis suggests that stability of the commensurate antiferromagentic phase at finite doping can be controlled experimentally by introducing additional quasiparticle broadening via disorder or low-frequency noise.