Self-energy flows in the two-dimensional repulsive Hubbard model

Giering, Kay-Uwe; Salmhofer, Manfred

doi:10.1103/physrevb.86.245122

Cited by 58 publications

(107 citation statements)

References 50 publications

(106 reference statements)

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“…(152) In order to evaluate Ω in a stationary point and to compare the free energies of different gap solutions, we apply (152) and obtain the following expression for the free energy in a stationary solution…”

Section: Resultsmentioning

confidence: 99%

“…[152] for a detailed listing). In the situation of an evolving FS due to selfenergy flow, one faces the problem that k-space cutoffs around the free FS with an appropriate self-energy feedback, cannot provide an adequate regularization.…”

Section: Discussionmentioning

confidence: 99%

“…This poses fundamental challenges in the technical setup of FRG. Recently, a very promising scheme has been proposed and successfully applied by the Salmhofer group to the 2D-Hubbard model [152]. The main idea, which facilitated the substantial progress, was the use of the "channel-decomposition" of the interaction vertex [152].…”

Section: Discussionmentioning

confidence: 99%

“…Recently, a very promising scheme has been proposed and successfully applied by the Salmhofer group to the 2D-Hubbard model [152]. The main idea, which facilitated the substantial progress, was the use of the "channel-decomposition" of the interaction vertex [152]. It allows to calculate the ω and k-dependence of the fermionic selfenergy and the interaction vertex in the whole ω-range without simplifying assumptions on its functional form.…”

Section: Discussionmentioning

confidence: 99%

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Functional renormalization group for multi-orbital Fermi surface instabilities

Platt

Hanke

Thomale

2013

Advances in Physics

192

253

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Technological progress in material synthesis, as well as artificial realization of condensed matter scenarios via ultra-cold atomic gases in optical lattices or epitaxial growth of thin films, is opening the gate to investigate a plethora of unprecedented strongly correlated electron systems. In a large subclass thereof, a metallic state of layered electrons undergoes an ordering transition below some temperature into unconventional states of matter driven by electronic correlations, such as magnetism, superconductivity, or other Fermi surface instabilities. While this type of phenomena has been a well-established direction of research in condensed matter for decades, the variety of today's accessible scenarios pose fundamental new challenges to describe them. A core complication is the multi-orbital nature of the low-energy electronic structure of these systems, such as the multi-d orbital nature of electrons in iron pnictides and transition-metal oxides in general, but also electronic states of matter on lattices with multiple sites per unit cell such as the honeycomb or kagome lattice. In this review, we propagate the functional renormalization group (FRG) as a suited approach to investigate multi-orbital Fermi surface instabilities. The primary goal of the review is to describe the FRG in explicit detail and render it accessible to everyone both at a technical and intuitive level. Summarizing recent progress in the field of multi-orbital Fermi surface instabilities, we illustrate how the unbiased fashion by which the FRG treats all kinds of ordering tendencies guarantees an adequate description of electronic phase diagrams and often allows to obtain parameter trends of sufficient accuracy to make qualitative predictions for experiments. This review includes detailed and illustrative illustrations of magnetism and, in particular, superconductivity for the iron pnictides from the viewpoint of FRG. Furthermore, it discusses candidate scenarios for topological bulk singlet superconductivity and exotic particle-hole condensates on hexagonal lattices such as sodium-doped cobaltates, graphene doped to van Hove filling, and the kagome Hubbard model. In total, the FRG promises to be one of the most versatile and revealing numerical approaches to address unconventional Fermi surface instabilities in future fields of condensed matter research.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Functional renormalization group for multi-orbital Fermi surface instabilities

Platt

Hanke

Thomale

2013

Advances in Physics

192

253

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“…It has proven useful in a wide range of complex physical contexts. Examples include models with competing orders [26][27][28][29] or situations out of equilibrium [30][31][32]. The formalism by itself sheds light on fundamental aspects of critical phenomena (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of the two-dimensionalXYmodel from functional renormalization

Jakubczyk

Eberlein

2016

Phys. Rev. E

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We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on φ 4 -type truncations. Our computation indicates that such an approximation is insufficient in the high-T phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.

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Hierarchical parallelisation of functional renormalisation group calculations — hp-fRG

Rohe¹

2016

Computer Physics Communications

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The functional renormalisation group (fRG) has evolved into a versatile tool in condensed matter theory for studying important aspects of correlated electron systems. Practical applications of the method often involve a high numerical effort, motivating the question in how far High Performance Computing (HPC) can leverage the approach.In this work we report on a multi-level parallelisation of the underlying computational machinery and show that this can speed up the code by several orders of magnitude. This in turn can extend the applicability of the method to otherwise inaccessible cases.We exploit three levels of parallelisation: Distributed computing by means of Message Passing (MPI), shared-memory computing using OpenMP, and vectorisation by means of SIMD units (single-instruction-multiple-data). Results are provided for two distinct High Performance Computing (HPC) platforms, namely the IBM-based BlueGene/Q system JUQUEEN and an Intel SandyBridge-based development cluster. We discuss how certain issues and obstacles were overcome in the course of adapting the code. Most importantly, we conclude that this vast improvement can actually be accomplished by introducing only moderate changes to the code, such that this strategy may serve as a guideline for other researcher to likewise improve the efficiency of their codes.

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Self-energy flows in the two-dimensional repulsive Hubbard model

Cited by 58 publications

References 50 publications

Functional renormalization group for multi-orbital Fermi surface instabilities

Functional renormalization group for multi-orbital Fermi surface instabilities

Thermodynamics of the two-dimensionalXYmodel from functional renormalization

Hierarchical parallelisation of functional renormalisation group calculations — hp-fRG

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