Spin-functional renormalization group for the 
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 quantum Heisenberg model

Tarasevych, Dmytro; Rückriegel, Andreas; Keupert, Savio; Mitsiioannou, Vasilios; Kopietz, Peter

doi:10.1103/physrevb.106.174412

Cited by 4 publications

(4 citation statements)

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“…Up to now, performant numerical approaches treating the system of resulting flow equations in its full complexity have not yet been implemented. Instead, several approximations were employed which however lead to promising results [181,[213][214][215][216][217][218] which will be reviewed in the following.…”

Section: Working Without Partons: Spin-frgmentioning

confidence: 99%

“…Moreover, one can hope that the low-temperature problem can be alleviated to a certain extent by the flow of such higher-order spin vertices. In part, this optimism is fueled by the percent-range accuracy for critical temperatures of classical [211] and quantum [181] spin models achieved by the Kopietz group with vertex parametrization approximated even at the 2-point level. Also, the inclusion of magnetic fields seems possible at a moderate numerical effort within spin-FRG.…”

Section: Working Without Partons: Spin-frgmentioning

confidence: 99%

“…. .S αn i (τ n ) c,0 are non-trivial at every order n but can still be computed [181,220]. The spin-FRG takes advantage of this non-trivial information by starting the flow at the free-spin limit Λ = 0.…”

Section: Working Without Partons: Spin-frgmentioning

confidence: 99%

“…In the context of spin-fRG of section 8.4, the flow around the Wilson-Fisher fixed point can be constructed from a suitable cutoff scheme, see[181].…”

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confidence: 99%

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Pseudo-fermion functional renormalization group for spin models

Müller,

Kiese,

Niggemann

et al. 2024

Rep. Prog. Phys.

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For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of $m$-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.

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Section: Working Without Partons: Spin-frgmentioning

confidence: 99%

Section: Working Without Partons: Spin-frgmentioning

confidence: 99%

Section: Working Without Partons: Spin-frgmentioning

confidence: 99%

“…In the context of spin-fRG of section 8.4, the flow around the Wilson-Fisher fixed point can be constructed from a suitable cutoff scheme, see[181].…”

mentioning

confidence: 99%

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