Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model

Si, Qimiao; Smith, J. L.

doi:10.1103/physrevlett.77.3391

Cited by 207 publications

(253 citation statements)

References 25 publications

(35 reference statements)

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“…Indeed, such methods have been proposed many years ago, in particular the combination of (2) and DMFT [19] and the combination of GW and DMFT [20]. These methods have been designed in particular to treat models with long-ranged Coulomb interactions, based on an extended DMFT (EDMFT) formalism [16,19,42,43], and because of recent methodological advances related to impurity problems with dynamically screened interactions [44,45], there has been a revival of interest in these approaches [15,16,46]. The same techniques can also be applied to model (1) with only an on-site Hubbard repulsion.…”

Section: Combinations Of Dmft With Weak-coupling Approximationsmentioning

confidence: 99%

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Gukelberger

Werner

2015

Phys. Rev. B

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We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second-order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW + DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second-order diagram. FLEX + DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

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Section: Combinations Of Dmft With Weak-coupling Approximationsmentioning

confidence: 99%

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Gukelberger

Werner

2015

Phys. Rev. B

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“…In such a case the question of how to scale these parameters has no unique answer since this depends on the physical effects one wishes to explore. 33,34 In any case, the scaling should be performed such that the model remains non-trivial and its free energy stays finite in the Z → ∞ limit. By "non-trivial" we mean that not only H 0 and H int , but also the competition between these terms as expressed by [H 0 , H int ] , should remain finite; here ... denotes the quantum and statistical average of operators.…”

Section: B Construction Of a Comprehensive Mean-field Theorymentioning

confidence: 99%

Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases

2008

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We formulate a bosonic dynamical mean-field theory (B-DMFT) which provides a comprehensive, thermodynamically consistent framework for the theoretical investigation of correlated lattice bosons. The B-DMFT is applicable for arbitrary values of the coupling parameters and temperature and becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In contrast to its fermionic counterpart the construction of the B-DMFT requires different scalings of the hopping amplitudes with Z depending on whether the bosons are in their normal state or in the Bose-Einstein condensate. A detailed discussion of how this conceptual problem can be overcome by performing the scaling in the action rather than in the Hamiltonian itself is presented. The B-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. It reproduces all previously investigated limits in parameter space such as the Beliaev-Popov and Hartree-Fock-Bogoliubov approximations and generalizes the existing mean-field theories of interacting bosons. The self-consistency equations of the B-DMFT are those of a bosonic single-impurity coupled to two reservoirs corresponding to bosons in the condensate and in the normal state, respectively. We employ the B-DMFT to solve a model of itinerant and localized, interacting bosons analytically. The local correlations are found to enhance the condensate density and the Bose-Einstein condensate (BEC) transition temperature TBEC. This effect may be used experimentally to increase TBEC of bosonic atoms in optical lattices.

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“…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

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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...

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Kosterlitz-Thouless Transition and Short Range Spatial Correlations in an Extended Hubbard Model

Cited by 207 publications

References 25 publications

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases

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

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