Role of disorder on the quantum critical point of a model for heavy fermions (original) (raw)
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Quantum phase transitions in the Kondo-necklace model
2011
Abstract: Kondo-necklace model can describe the magnetic low-energy limit of strongly correlated heavy fermion materials. There exists multiple energy scales in this model, each of which indicates a phase. Here, we study quantum phase transitions between these different phases, and show the effect of anisotropies in terms of quantum information properties and the vanishing of energy gap.
Thermodynamic quantum critical behavior of the Kondo necklace model
Physical Review B, 2007
We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions d using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in d ≥ 3 there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T = 0. The line of Neel transitions for d > 2 varies with the distance to the quantum critical point QCP |g| as, TN ∝ |g| ψ where the shift exponent ψ = 1/(d − 1). In the paramagnetic side of the phase diagram, the spin gap behaves as ∆ ≈ p |g| for d ≥ 3 consistent with the value z = 1 found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for kBT ≫ ∆ and along the non-Fermi liquid trajectory. For kBT ≪ ∆, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.
Field induced magnetic quantum critical behavior in the Kondo necklace model
Journal of Magnetism and Magnetic Materials, 2008
The Kondo necklace model augmented by a Zeeman term, serves as a useful model for heavy fermion compounds in an applied magnetic field. The phase diagram and thermodynamic behavior for arbitrary dimensions d has been investigated previously in the zero field case [D. Reyes, M. Continentino, Phys. Rev. B 76 (2007) 075114. ]. Here we extend the treatment to finite fields using a generalized bond operator representation for the localized and conduction electrons spins. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. Two critical magnetic fields are found namely, a critical magnetic field called henceforth h c1 and a saturation field nominated h c2 . Then three important regions can be investigated: (i) Kondo spin liquid state (KSL) at low fields hoh c1 ; (ii) destruction of KSL state at hXh c1 and appearance of a antiferromagnetic state; and (iii) saturated paramagnetic region above the upper critical field h c2 .
The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the ‘perturbative continuous unitary transformations’ approach to calculate the energy gap and spin–spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green’s function analyses. In addition, we employ concurrence, a bipartite entanglement measure, to study the criticality of the model. Absence of singularities in the derivative of concurrence in two and three dimensions in the Kondo-necklace model shows that this model features multipartite entanglement. We also discuss crossover from the one-dimensional to the two-dimensional model via the ladder structure.
Disorder Induced Cross-Over Effects at Quantum Critical Points
Physical Review Letters, 2001
Critical properties of quantum spin chains with varying degrees of disorder are studied at zero temperature by analytical and extensive density matrix renormalization methods. Generally the phase diagram is found to contain three phases. The weak disorder regime, where the critical behavior is controlled by the fixed points of the pure system, and the strong disorder regime, which is attracted by an infinite randomness fixed point, are separated by an intermediate disorder regime, where dynamical scaling is anisotropic and the static and dynamical exponents are disorder dependent.
Thermodynamic quantum critical behavior of the anisotropic Kondo necklace model
Journal of Magnetism and Magnetic Materials, 2009
The Ising-like anisotropy parameter δ in the Kondo necklace model is analyzed using the bond-operator method at zero and finite temperatures for arbitrary d dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. At zero temperature and in the paramagnetic side of the phase diagram, we determine the spin gap exponent νz ≈ 0.5 in three dimensions and anisotropy between 0 ≤ δ ≤ 1, a result consistent with the dynamic exponent z = 1 for the Gaussian character of the bond-operator treatment. At low but finite temperatures, in the antiferromagnetic phase, the line of Neel transitions is calculated for δ ≪ 1 and δ ≈ 1. For d > 2 it is only re-normalized by the anisotropy parameter and varies with the distance to the quantum critical point QCP |g| as, T N ∝ |g| ψ where the shift exponent ψ = 1/(d − 1). Nevertheless, in two dimensions, long range magnetic order occurs only at T = 0 for any δ. In the paramagnetic phase, we find a power law temperature dependence on the specific heat at the quantum liquid trajectory J/t = (J/t) c , T → 0. It behaves as C V ∝ T d for δ ≤ 1 and δ ≈ 1, in concordance with the scaling theory for z = 1.
Quantum criticality out of equilibrium in the pseudogap Kondo model
Physical Review B, 2012
We theoretically investigate the non-equilibrium quantum phase transition in a generic setup: the pseudogap Kondo model where a quantum dot couples to two-left (L) and right (R)-voltage-biased fermionic leads with power-law density of states (DOS) with respect to their Fermi levels µ L/R , ρ c,L(R) (ω) ∝ |ω − µ L(R) | r , and 0 < r < 1. In equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo correlations, in the presence of particle-hole symmetry this model exhibits a quantum phase transition from a unscreened local moment (LM) phase to the Kondo phase. Via a controlled frequency-dependent renormalization group (RG) approach, we compute analytically and numerically the non-equilibrium conductance, conduction electron T-matrix and local spin susceptibility at finite bias voltages near criticality. The current-induced decoherence shows distinct nonequilibrium scaling, leading to new universal non-equilibrium quantum critical behaviors in the above observables. Relevance of our results for the experiments is discussed.
Phase diagram of the Kondo necklace: a mean-field renormalization group approach
Journal of Physics A: Mathematical and General, 2001
In this paper we investigate the magnetic properties of heavy fermions in the antiferromagnetic and dense Kondo phases in the framework of the Kondo necklace model. We use a mean field renormalization group approach to obtain a temperature versus Kondo coupling (T − J) phase diagram for this model in qualitative agreement with Doniach's diagram, proposed on physical grounds. We further analyze the magnetically disordered phase using a two-sites approach. We calculate the correlation functions and the magnetic susceptibility that allow to identify the crossover between the spin-liquid and the local moment regimes, which occurs at a coherence temperature.
Green’s function approach to quantum criticality in the anisotropic Kondo necklace model
Physical Review B, 2008
We have studied the quantum phase transition between the antiferromagnetic and spin liquid phase for the two dimensional anisotropic Kondo necklace model. The bond operator formalism has been implemented to transform the spin Hamiltonian to a bosonic one. We have used the Green's function approach including a hard core repulsion to find the low energy excitation spectrum of the model. The bosonic excitations become gapless at the quantum critical point where the phase transition from the Kondo singlet state to long range antiferromagnetic order takes place. We have studied the effect of both inter-site (δ) and local (∆) anisotropies on the critical point and on the critical exponent of the excitation gap in the paramagnetic phase. We have also compared our results with previous bond operator mean field calculations.
Field-induced quantum phase transition in the anisotropic Kondo necklace model
Physical Review B, 2007
Kondo-necklace-KN-type models are useful to discuss the quantum phase transitions between Kondo singlet and antiferromagnetically ordered states such as found in heavy fermion compounds. 1–5 They were originally proposed by Doniach 6 for the one-dimensional case as a simplified version of the itinerant Kondo lattice KL models. 7 Thereby, the kinetic energy of conduction electrons is replaced by an intersite exchange term. For a pure xy-type intersite exchange, this may be obtained by a Jordan-Wigner transformation. ...