Quantized Berry phases proposed as local order parameters for gapped quantum liquids at zero temperature are studied to detect the Kondo singlet phase which is known as a theoretical prototype of the Kondo insulators. We deal with the Kondo lattice model and the periodic Anderson model as two basic models for heavy fermions. We show that the Berry phase is actually quantized as trivial or non-trivial value, i.e., 0 or π, and analytically obtained both in the strong coupling limit of the Kondo lattice model and in the weak coupling limit of the periodic Anderson model. In addition, the Heisenberg Kondo lattice model is studied numerically by the quantized Berry phase.Quantized Berry phases proposed as local order parameters for gapped quantum liquids at zero temperature are studied to detect the Kondo singlet phase which is known as a theoretical prototype of the Kondo insulators. We deal with the Kondo lattice model and the periodic Anderson model as two basic models for heavy fermions. We show that the Berry phase is actually quantized as trivial or non-trivial value, i.e., 0 or π, and analytically obtained both in the strong coupling limit of the Kondo lattice model and in the weak coupling limit of the periodic Anderson model. In addition, the Heisenberg Kondo lattice model is studied numerically by the quantized Berry phase.

Journal of Physics Conference SeriesMar 1, 20096 citations

Quantum phase transition in the Kondo lattice model

Ki‐Seok Kim, Mun Dae Kim

Aug 10, 20060 citations

Zooming in on heavy fermions in Kondo lattice models

Bimla Danu, Zihong Liu, Fakher F. Assaad +1 more

Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that, for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as ${e}^{\ensuremath{-}W/{J}_{k}}$ with $W$ the bandwidth and ${J}_{k}$ the Kondo coupling, the residue of the composite fermion tracks ${J}_{k}$ . This result holds down to ${J}_{k}/W=0.05$ and confirms the point of view that magnetic ordering, present below ${J}_{k}/W=0.18$ , does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for $\mathrm{SU}(N)$ generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large- $N$ , large- $S$ , and large ${J}_{k}$ . Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.Resolving the heavy fermion band in the conduction electron momentum resolved spectral function of the Kondo lattice model is challenging since, in the weak coupling limit, its spectral weight is exponentially small. In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator. Using approximation free auxiliary field quantum Monte Carlo simulations we show that, for the SU(2) spin-symmetric model on the square lattice at half filling, the composite fermion acts as a magnifying glass for the heavy fermion band. In comparison to the conduction electron residue that scales as ${e}^{\ensuremath{-}W/{J}_{k}}$ with $W$ the bandwidth and ${J}_{k}$ the Kondo coupling, the residue of the composite fermion tracks ${J}_{k}$. This result holds down to ${J}_{k}/W=0.05$ and confirms the point of view that magnetic ordering, present below ${J}_{k}/W=0.18$, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for $\mathrm{SU}(N)$ generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-$N$, large-$S$, and large ${J}_{k}$. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.

arXiv:2107.10272Physical review. B./Physical review. BOct 19, 202125 citations

Phase diagram of the 1D Kondo lattice model

Ian P. McCulloch, M. Gulácsi, S. Caprara +2 more

arXiv:cond-mat/9908414Journal of Low Temperature PhysicsNov 1, 199921 citations

TWO KONDO IMPURITY PROBLEM: RELEVANCE TO HEAVY FERMIONS

Barbara Jones, C. M. Varma

Elsevier eBooksJan 1, 19871 citation

NUMERICAL ANALYSIS OF COUPLED SPIN-FERMION MODEL — PAIRING MECHANISM THROUGH EXTENDED KONDO SINGLET

Masatoshi Imada, Yasuhiro Hatsugai, Naoto Nagaosa

A coupled spin-fermion model is investigated by the exact diagonalization of finite lattices to discuss magnetic mechanism of superconductivity. An extended cloud of singlet liquid (extended Kondo singlet) is found around the fermion in a strong coupling region characterized by strong Kondo coupling and large transfer. The existence of the bound state of two fermions is found. The relevance of its Cooper pairing to high-Tc superconductivity is discussed. The relation to the weak coupling region and also to the small transfer region in this model is discussed.A coupled spin-fermion model is investigated by the exact diagonalization of finite lattices to discuss magnetic mechanism of superconductivity. An extended cloud of singlet liquid (extended Kondo singlet) is found around the fermion in a strong coupling region characterized by strong Kondo coupling and large transfer. The existence of the bound state of two fermions is found. The relevance of its Cooper pairing to high-Tc superconductivity is discussed. The relation to the weak coupling region and also to the small transfer region in this model is discussed.

International Journal of Modern Physics BOct 1, 198813 citations

W

the bandwidth and

{J}_{k}

the Kondo coupling, the residue of the composite fermion tracks

{J}_{k}

. This result holds down to

{J}_{k}/W=0.05

and confirms the point of view that magnetic ordering, present below

{J}_{k}/W=0.18

, does not destroy the heavy quasiparticle. We furthermore investigate the spectral function of the composite fermion in the ground state and at finite temperatures, for

\mathrm{SU}(N)

generalizations of the Kondo lattice model, as well as for ferromagnetic Kondo couplings, and compare our results to analytical calculations in the limit of high temperatures, large-

N

, large-

S

, and large

{J}_{k}

. Based on these calculations, we conjecture that the composite fermion operator provides a unique tool to study the destruction of the heavy fermion quasiparticle in Kondo breakdown transitions. The relation of our results to scanning tunneling spectroscopy and photoemission experiments is discussed.