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arXiv:2107.10272 · Physical review. B./Physical review. B

Zooming in on heavy fermions in Kondo lattice models

Bimla Danu, Zihong Liu, Fakher F. Assaad, Marcin Raczkowski

Published Oct 19, 2021• 25 citations
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Abstract

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.

DOI
10.1103/physrevb.104.155128

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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/Jk{e}^{\ensuremath{-}W/{J}_{k}}e\ensuremath−W/Jk​ with WWW the bandwidth and Jk{J}_{k}Jk​ the Kondo coupling, the residue of the composite fermion tracks Jk{J}_{k}Jk​. This result holds down to Jk/W=0.05{J}_{k}/W=0.05Jk​/W=0.05 and confirms the point of view that magnetic ordering, present below Jk/W=0.18{J}_{k}/W=0.18Jk​/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 SU(N)\mathrm{SU}(N)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-NNN, large-SSS, and large Jk{J}_{k}Jk​. 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.
We map out the ground-state phase diagram of a one-dimensional SU(N)\mathrm{SU}(N)SU(N) Kondo-Heisenberg lattice model at half-filling and in the fully antisymmetric self-adjoint representation as a function of 1N\frac{1}{N}N1​ and Kondo coupling Jk/t{J}_{k}/tJk​/t. On the basis of auxiliary field quantum Monte Carlo (QMC) simulations with even NNN up to 8, we show that the enlarged $\mathrm{SU}(N\ensuremath{\ge}4$) symmetry realizes a quantum phase transition separating a valence bond solid (VBS) phase occupying a weak-coupling part of the phase diagram and the Kondo insulator (KI) state dominating in the strong Jk/t{J}_{k}/tJk​/t limit. Along the phase boundary, we always observe critical exponents that belong to a two-dimensional classical Ising universality class. We next trace the evolution of the composite fermion and spin spectral functions across the phase boundary and conclude that VBS order triggers a bond order wave state of conduction electrons, both coexisting with Kondo screening. Upon further reducing Jk/t{J}_{k}/tJk​/t, we observe that composite quasiparticles lose their spectral weight indicating that VBS order gradually liberates localized fff spins from forming Kondo singlets with conduction electron spins. We contrast the QMC results with a static large-NNN approximation, and we show that in the limit of infinite degeneracy $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the order-disorder transition becomes of first order and is accompanied by a full decoupling of conduction electrons and localized fff spins. We complete our analysis by considering the limit of a vanishing Heisenberg coupling Jh=0{J}_{h}=0Jh​=0, and we provide evidence that the enlarged SU(N)\mathrm{SU}(N)SU(N) symmetry and low dimensionality of the Ruderman-Kittel-Kasuya-Yosida exchange interaction are not sufficient to induce VBS order in the conventional SU(N)\mathrm{SU}(N)SU(N) Kondo chain, which hosts solely a KI phase. Finally, we quantify the role of increasing NNN in reducing the separation of charge and spin timescales specific to the KI state, and we show that the latter is adiabatically connected to a trivial band insulator captured by the large-NNN approximation.
In the local-moment regime, heavy fermions are most economically described by a compact U(1) gauge theory. Motivated by this perspective, we study a minimal compact U(1) lattice gauge model describing a spin chain coupled to two-dimensional Dirac conduction electrons. The spin chain is described by fermionic partons carrying spin and U(1) gauge charge. The heavy-fermion quasiparticle is a bound state of a U(1) matter field carrying unit electric charge and U(1) gauge charge, and the fermionic parton. Using sign-problem-free determinant quantum Monte Carlo simulations, we identify two symmetry-equivalent regimes: a heavy-fermion metal with a sharp composite-fermion resonance and robust low-frequency transport, and a Kondo-breakdown metal with an incoherent resonance and vanishing low-frequency transport. For any finite lattice extent in the direction perpendicular to the chain, the Luttinger volume of the heavy-fermion phase counts both composite and conduction electrons, while in the Kondo-breakdown phase it counts only the conduction electrons. The evolution of the composite-fermion spectrum, dynamical spin structure factor, and optical conductivity provides a nonperturbative demonstration of gauge-mediated Kondo breakdown and establishes transport fingerprints of an orbital-selective Mott transition in the context of U(1) gauge theories of heavy fermions.
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We consider a two-dimensional quantum spin system described by a Heisenberg model that is embedded in a three-dimensional metal. The two systems couple via an antiferromagnetic Kondo interaction. In such a setup, the ground state generically remains metallic down to the lowest temperatures and allows us to study magnetic quantum phase transitions in metallic environments. From the symmetry point of view, translation symmetry is present in two out of three lattice directions such that crystal momentum is only partially conserved. Importantly, the construction provides a route to study, with negative-sign-free auxiliary-field quantum Monte Carlo methods, the physics of local moments in metallic environments. Our large-scale numerical simulations show that as a function of the Kondo coupling, the system has two metallic phases. In the limit of strong Kondo coupling, a paramagnetic heavy-fermion phase emerges. Here, the spin degree of freedom is screened by means of the formation of a composite quasiparticle that participates in the Luttinger count. At weak Kondo coupling, magnetic order is present. This phase is characterized by Landau-damped Goldstone modes. Furthermore, the aforementioned composite quasiparticle remains intact across the quantum phase transition.
Quantum criticality that goes beyond the Landau framework of order-parameter fluctuations is playing a central role in elucidating the behavior of strange metals. A prominent case appears in Kondo lattice systems, which have been extensively analysed in terms of an effective Bose-Fermi Kondo model. Here, a spin is simultaneously coupled to conduction electron bands and gapless vector bosons that represent magnetic fluctuations. The Bose-Fermi Kondo model features interacting fixed points of Kondo destruction with such properties as dynamical Planckian (ℏω/kBT\hbar ω/ k_{\rm B} Tℏω/kB​T) scaling and loss of quasiparticles. Here we carry out a renormalization-group analysis of the model with spin isotropy and identify pair-wise annihilations of the fixed points as the spectrum of the bosonic bath evolves. Our analysis not only provides an essentially complete understanding of the previous numerical results of an SU(2)-symmetric model, but also reveals a surprising feature of sequential fixed-point annihilation. Our results lay the foundation for the understanding of quantum criticality in spin-isotropic heavy-fermion metals as well as in doped Mott-Hubbard systems.
This thesis discusses mainly two Fermionic lattice systems, first a Kondo lattice with additional Hubbard interaction and second a Hubbard Hamiltonian augmented with additional spin and charge interactions. We first introduce the Quantum Monte Carlo technique, which is then employed to study the two respective systems. We present an innovation that allows to calculate time displaced Greens functions more efficiently. Compared with previously used numerically stable algorithms the new method gains an order of magnitude in speed, but is just as precise, and very simple to implement. In the second chapter we consider the Kondo lattice model in two dimensions at half filling. In addition to the Fermionic hopping integral t and the superexchange coupling J the role of a Coulomb repulsion U in the conduction band is investigated. We find the model to display a magnetic order-disorder transition in the U-J plane with a critical value of Jc which is decreasing as a function of U. The single-particle spectral function A(k,ω) is computed across this transition. We conclude that (i) the local screening of impurity spins determines the low-energy behavior of the spectral function and (ii) one cannot deform continuously the spectral function of the half-filled Hubbard model at J=0 to that of the Kondo insulator at J>Jc. In the third chapter we investigate the phase diagram of a new model that exhibits a first order transition between s-wave superconducting and antiferromagnetic phases. The model, a generalized Hubbard model augmented with competing spin-spin and pair-pair interactions, was investigated using the projector quantum Monte Carlo method. Upon varying the Hubbard U from attractive to repulsive, we find a first order phase transition between superconducting and antiferromagnetic states.