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arXiv:1710.03345 · Physical Review Letters

Model for a Ferromagnetic Quantum Critical Point in a 1D Kondo Lattice

Yashar Komijani, Piers Coleman

Published Apr 13, 2018• 48 citations
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Abstract

Motivated by recent experiments, we study a quasi-one-dimensional model of a Kondo lattice with ferromagnetic coupling between the spins. Using bosonization and dynamical large-N techniques, we establish the presence of a Fermi liquid and a magnetic phase separated by a local quantum critical point, governed by the Kondo breakdown picture. Thermodynamic properties are studied and a gapless charged mode at the quantum critical point is highlighted.

DOI
10.1103/physrevlett.120.157206

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Motivated by recent experiments, we study a quasi-one-dimensional model of a Kondo lattice with ferromagnetic coupling between the spins. Using bosonization and dynamical large-N techniques, we establish the presence of a Fermi liquid and a magnetic phase separated by a local quantum critical point, governed by the Kondo breakdown picture. Thermodynamic properties are studied and a gapless charged mode at the quantum critical point is highlighted.
We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.
The continuous quantum phase transition and the nature of the quantum critical point (QCP) in a modified Kondo lattice model with Ising anisotropic exchange interactions are studied within the density-matrix renormalization group algorithm. We investigate the effect of quantum fluctuations on critical Kondo destruction QCP by probing static and dynamic properties of the magnetic order and the Kondo effect. In particular, we identify that local Kondo physics itself becomes critical at the magnetic phase transition point, providing unbiased evidences for local quantum criticality between two insulators without involving the Fermi surface.
Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling J_K J K at fixed doping x. At large positive J_K J K , we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2} 2 k F = 1 + x 2 (in units of 2\pi 2 π ), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0 J K ≤ 0 side, our simulation finds the existence of a fractional Luttinger liquid (LL \star ⋆ ) phase with 2k_F=\frac{x}{2} 2 k F = x 2 , accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL \star ⋆ ) phase in higher dimensions. The LL \star ⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_K J K . Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of J_K J K , the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035 J 0.035 J ) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z=+ z = + . The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.
We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the decoupled fixed point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum Monte Carlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.
We generalize the dynamical large-NNN multichannel Schwinger-boson approach to study the quantum phase transition of a two-dimensional Kondo-Heisenberg model, relevant for heavy electron systems, close to an antiferromagnetic Kondo destruction quantum critical point. By breaking up a Kondo singlet into a charge fermion (holon) and a bosonic spinon, we identify and characterize the quantum phase transition from an antiferromagnetically ordered state to a Kondo-dominated paramagnetic state, and attribute a jump in the holon phase shift to Kondo breakdown. We calculate transport and thermodynamic quantities. The global finite-temperature phase diagram and the critical behavior of various physical observables therein show a close resemblance to experimental observations.
We study a lattice realization of a Luttinger liquid interacting with quantum spins in terms of an antiferromagnetic S=1∕2S=1∕2S=1∕2 Heisenberg chain, where each spin is also coupled to a $\ensuremath{\sigma}=1∕2$ Kondo spin degree of freedom. This model describes the low-energy spin dynamics in quasi-one-dimensional materials, where the electronic spins of the magnetic ions interact with those of impurities, nuclei, and possibly other spin species present in their environment. For large ferromagnetic and antiferromagnetic Kondo interaction ${J}^{\ensuremath{'}}$, there are two phases corresponding to an effective spin-1 Heisenberg chain and a dimerized spin-1∕21∕21∕2 ladder, respectively. For weak Kondo interaction, we establish that the Kondo interaction drives the system to a strong coupling regime. This suggests that ${J}^{\ensuremath{'}}=0$ is the only critical point in the system.