Luttinger-Ward functional approach in the Eliashberg framework : A systematic derivation of scaling for thermodynamics near a quantum critical point

Abstract

Scaling expressions for the free energy are derived, using the Luttinger-Ward (LW) functional approach in the Eliashberg framework, for two different models of quantum critical point (QCP). First, we consider the spin-density-wave (SDW) model for which the effective theory is the Hertz-Moriya-Millis (HMM) theory, describing the interaction between itinerant electrons and collective spin fluctuations. The dynamic of the latter are described by a dynamical exponent $z$ depending on the nature of the transition. Second, we consider the Kondo breakdown model for QCP's, one possible scenario for heavy-fermion quantum transitions, for which the effective theory is given by a gauge theory in terms of conduction electrons, spinons for localized spins, holons for hybridization fluctuations, and gauge bosons for collective spin excitations. For both models, we construct the thermodynamic potential, in the whole phase diagram, including all kinds of self-energy corrections in a self-consistent way, at the one loop level. We show how Eliashberg framework emerges at this level and use the resulting Eliashberg equations to simplify the LW expression for free energy . it is found that collective boson excitations play a central role. The scaling expression for the singular part of the free energy near the Kondo breakdown QCP is characterized by two length scales : one is the correlation length for hybridization fluctuations, and the other is that for gauge fluctuations, analogous to the penetration depth in superconductors.

15 pages, 12 figures + 1 added in final version as published in J. Phys.: Condens. Matter

References in corpus (8)

• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Quantum critical behavior in itinerant electron systems -- Eliashberg theory and instability of a ferromagnetic quantum-critical point
• Kondo Breakdown as a Selective Mott Transition in the Anderson Lattice
• T=0 heavy fermion quantum critical point as an orbital selective Mott transition
• Sum Rules and Ward Identities in the Kondo Lattice
• Selective Mott transition and heavy fermions
• Multi-scale fluctuations near a Kondo Breakdown Quantum Critical Point
• Grüneisen ratio at the Kondo breakdown quantum critical point

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• Preformed heavy-electrons at the Quantum Critical Point in heavy fermion compounds
• Emergent gauge fields and their nonperturbative effects in correlated electrons
• Role of vertex corrections in the $T$-linear resistivity at the Kondo breakdown quantum critical point
• Stoner instability revisited: Emergence of local quantum criticality?
• A phenomenological description on an incoherent Fermi liquid near optimal doping in high T_{c} cuprates
• Emergence of localized magnetic moments near antiferromagnetic quantum criticality