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arXiv:cond-mat/0501175 · Physical Review B

Consequences of the local spin self-energy approximation on the heavy-fermion quantum phase transition

Ping Sun, Gabriel Kotliar

Published Jun 6, 2005• 18 citations
arXivHTMLPDF

Abstract

We show, using the periodic Anderson model, that the local spin self-energy approximation, as implemented in the extended dynamical mean field theory (EDMFT), results in a first-order phase transition that persists to $T=0$. Around the transition, there is a finite coexistence region of the paramagnetic and antiferromagnetic (AFM) phases. The region is bounded by two critical transition lines that differ by an electron-hole bubble at the AFM ordering wave vector.

DOI
10.1103/physrevb.71.245104

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We show, using the periodic Anderson model, that the local spin self-energy approximation, as implemented in the extended dynamical mean field theory (EDMFT), results in a first-order phase transition that persists to T=0T=0T=0. Around the transition, there is a finite coexistence region of the paramagnetic and antiferromagnetic (AFM) phases. The region is bounded by two critical transition lines that differ by an electron-hole bubble at the AFM ordering wave vector.
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.
We investigate quantum phase transitions in the extended periodic Anderson model, which includes electron correlations within and between itinerant and localized bands. We calculate zero and finite temperature properties of the system using the combination of dynamical mean-field theory and the numerical renormalization group. At half filling, a first-order phase transition between a Mott insulating state and a Kondo insulating state occurs in the strong-coupling regime. We furthermore find that a metallic state is stabilized in the weak-coupling regime. This state should be adiabatically connected to the orbital selective Mott state with one orbital-localized and the other itinerant. The effect of hole doping is also addressed.
The nearest-neighbor quantum antiferromagnetic (AF) Heisenberg model for spin-1∕21∕21∕2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Qi=1{Q}_{i}=1Qi​=1 on each lattice site iii, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, $\ensuremath{\xi}(T)\ensuremath{\propto}\mathrm{exp}(aJ∕T)$, come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low TTT. This drawback, which is caused by overdamping, is overcome in a ``minimal self-consistent approximation'' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths $\ensuremath{\lambda}>\ensuremath{\xi}$ and in the short-range-order regime at $\ensuremath{\lambda}<\ensuremath{\xi}$. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.
We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant c electrons hybridizing with a lattice of localized f electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of f spins by c electrons breaks down, so that f excitations change their character from somewhat itinerant to mainly localized, while c excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, T FL < T NFL . In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale T FL decreases toward and vanishes at the KB QCP; at temperatures below T FL , FL behavior emerges. At T = 0 , we find the following properties. The KB transition is continuous. The f quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the f band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise c f electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the f self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for f -electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024
We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition between a zero-temperature antiferromagnetic insulator and a Kondo insulator. In the quantum critical region, we determine a critical exponent γ=2 for the antiferromagnetic susceptibility. At higher temperatures, we have free spins with γ=1 instead, whereas at lower temperatures, there is an even stronger increase and suppression of the susceptibility below and above the quantum critical point, respectively.