Spatial correlations in dynamical mean-field theory

Smith, J. L.; Si, Qimiao

doi:10.1103/physrevb.61.5184

Cited by 175 publications

(236 citation statements)

References 27 publications

Supporting

Mentioning

232

Contrasting

Order By: Relevance

“…Such a feedback is absent in previous studies of the magnetic quantum critical point, and it has been argued that this is an important limitation for them [7,11]. A different route to incorporating these feedback effects has been taken in some recent studies [12]; however, they discuss only the paramagnetic state of their model, and the extent to which magnetically ordered states preempt their results remains to be clarified. This paper is organized as follows : In Section I, we present our spin glass model and give an outline of our results, including the phase diagram.…”

mentioning

confidence: 78%

Quantum fluctuations of a nearly critical Heisenberg spin glass

2001

View full text Add to dashboard Cite

We describe the interplay of quantum and thermal fluctuations in the infinite-range Heisenberg spin glass. This model is generalized to SU (N ) symmetry, and we describe the phase diagram as a function of the spin S and the temperature T . The model is solved in the large N limit and certain universal critical properties are shown to hold to all orders in 1/N . For large S, the ground state is a spin glass, but quantum effects are crucial in determining the low T thermodynamics: we find a specific heat linear in T and a local spectral density of spin excitations, χ ′′ loc (ω) ∼ ω for a spin glass state which is marginally stable to fluctuations in the replicon modes. For small S, the spin-glass order is fragile, and a spin-liquid state with χ ′′ loc ∼ tanh(ω/2T ) dominates the properties over a significant range of T and ω. We argue that the latter state may be relevant in understanding the properties of strongly-disordered transition metal and rare earth compounds.The study of intermetallic compounds of the transition metals and rare earths has been a subject at the forefront of condensed matter physics for some time now [1,2]. A rich and complex variety of behaviors is observed in low temperature electrical and magnetic measurements, much of which lacks a comprehensive theoretical description. The complexity arises from the dominant role played by the local magnetic moments on the d and f orbitals and their interactions with each other and the itinerant charge carriers.It is convenient to begin our discussion in a phase with well-established magnetic order, in which each magnetic moment is effectively static. This static moment could be polarized in a regular manner (as in a commensurate antiferromagnet or an incommensurate spin density wave), or point in random directions (as in a spin glass state). In most realistic systems, the magnetic moment is either quite small, or has averaged to zero by dynamic quantum fluctuations: so it is useful to consider mechanisms which reduce the magnetic moment, and eventually cause it to vanish at a quantum phase transition to some paramagnetic state. Two distinct routes to such a quantum phase transition can be envisaged, and, we believe, the interplay between them is at the heart of the complexity of the problem. In the first route, originally discussed by Doniach [3], the moment is quenched by Kondo screening by the itinerant electrons: theories of such quantum critical points have been proposed [4,5,6,7] in which the predominant role of the itinerancy is to overdamp the collective magnetic excitations. In the second route, the exchange interactions between the moments play a more fundamental role: a pair of spins interacting with an antiferromagnetic exchange prefers to form a singlet valence bond, and the proliferation of such singlets can destroy the magnetic order. Analytic theories for such transitions has been made mainly for systems without quenched disorder [8]. Simple models of crossovers between these two routes have also been presented [9,10,11].This paper will...

show abstract

mentioning

confidence: 78%

Quantum fluctuations of a nearly critical Heisenberg spin glass

2001

View full text Add to dashboard Cite

show abstract

“…If the bath is integrated out, one obtains an impurity action with retarded hoppings. Extended dynamical mean field theory [2][3][4][5][6][7][8][9][10] (EDMFT) extends the DMFT idea to systems with long-range interactions. It does so by mapping a lattice problem with long-range interactions onto an effective impurity model with self-consistently determined fermionic and bosonic baths, or, in the action formulation, an impurity model with retarded hoppings and retarded interactions.…”

mentioning

confidence: 99%

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

et al. 2017

View full text Add to dashboard Cite

In electronic systems with long-range Coulomb interaction, the nonlocal Fock-exchange term has a bandwidening effect. While this effect is included in combined many-body perturbation theory and dynamical mean field theory (DMFT) schemes, it is not taken into account in standard extended DMFT (EDMFT) calculations. Here, we include this instantaneous term in both approaches and investigate its effect on the phase diagram and dynamically screened interaction. We show that the largest deviations between previously presented EDMFT and GW +EDMFT results originate from the nonlocal Fock term, and that the quantitative differences are especially large in the strong-coupling limit. Furthermore, we show that the charge-ordering phase diagram obtained in GW +EDMFT methods for moderate interaction values is very similar to the one predicted by dual-boson methods that include the fermion-boson or four-point vertex. DOI: 10.1103/PhysRevB.95.245130 Dynamical mean field theory (DMFT) [1] self-consistently maps a correlated Hubbard lattice problem with local interactions onto an effective impurity problem consisting of a correlated orbital hybridized with a noninteracting fermionic bath. If the bath is integrated out, one obtains an impurity action with retarded hoppings. Extended dynamical mean field theory [2-10] (EDMFT) extends the DMFT idea to systems with long-range interactions. It does so by mapping a lattice problem with long-range interactions onto an effective impurity model with self-consistently determined fermionic and bosonic baths, or, in the action formulation, an impurity model with retarded hoppings and retarded interactions.While EDMFT captures dynamical screening effects and charge-order instabilities, it has been found to suffer from qualitative shortcomings in finite dimensions. For example, the charge susceptibility computed in EDMFT does not coincide with the derivative of the average charge with respect to a small applied field [11], nor does it obey local charge conservation rules [12] essential for an adequate description of collective modes such as plasmons.The EDMFT formalism has an even more basic deficiency: since it is based on a local approximation to the self-energy, it does not include even the first-order nonlocal interaction term, the Fock term. The combined GW +EDMFT [13][14][15] scheme corrects this by supplementing the local self-energy from EDMFT with the nonlocal part of the GW diagram, where G is the interacting Green's function and W the fully screened interaction. Indeed, the nonlocal Fock term [Gv] nonloc is included in the nonlocal [GW ] nonloc diagram. As described in more detail in Ref. [15] (see also the appendix of Ref.[16]), the GW +EDMFT method is formally obtained by constructing an energy functional of G and W , the Almbladh [17] functional , and by approximating as a sum of two terms, one containing all local diagrams (corresponding to EDMFT) and the other containing the simplest nonlocal correction (corresponding to the GW approximation [18]). This functional construct...

show abstract

“…This issue has been discussed thouroughly in the context of EDMFT. 19,35,38 Here, a similar strategy can be taken to handle the ordered phase in EVCA. EVCA equations developed in Secs.…”

Section: A Evca For Ordered Phasementioning

confidence: 99%

“…This problem of EDMFT was observed previously. 19,38 In the EVCA formula, it appears in the second expression of Eq. (69) where the absolute value is used in the argument of logarithm.…”

Section: B Evca For Density-density Interactionmentioning

confidence: 99%

See 1 more Smart Citation

Extended variational cluster approximation for correlated systems

Tong

2005

Phys. Rev. B

View full text Add to dashboard Cite

The variational cluster approximation (VCA) proposed by M. Potthoff et al. [Phys. Rev. Lett. 91, 206402 (2003)] is extended to electron or spin systems with nonlocal interactions. By introducing more than one source field in the action and employing the Legendre transformation, we derive a generalized self-energy functional with stationary properties. Applying this functional to a proper reference system, we construct the extended VCA (EVCA). In the limit of continuous degrees of freedom for the reference system, EVCA can recover the cluster extension of the extended dynamical mean-field theory (EDMFT). For a system with correlated hopping, the EVCA recovers the cluster extension of the dynamical mean-field theory for correlated hopping. Using a discrete reference system composed of decoupled three-site single impurities, we test the theory for the extended Hubbard model. Quantitatively good results as compared with EDMFT are obtained. We also propose VCA (EVCA) based on clusters with periodic boundary conditions. It has the (extended) dynamical cluster approximation as the continuous limit. A number of related issues are discussed.

show abstract

Spatial correlations in dynamical mean-field theory

Cited by 175 publications

References 27 publications

Quantum fluctuations of a nearly critical Heisenberg spin glass

Quantum fluctuations of a nearly critical Heisenberg spin glass

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

Extended variational cluster approximation for correlated systems

Contact Info

Product

Resources

About