Critical spin dynamics of Heisenberg ferromagnets revisited

Tarasevych, Dmytro; Kopietz, Peter

doi:10.1103/physrevb.105.024403

Cited by 6 publications

(6 citation statements)

References 57 publications

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“…In this work, we study dimerized quantum spin systems using the functional renormalization group (FRG) approach to quantum spin systems recently developed in Refs. [23][24][25][26][27][28]. Our spin FRG approach generalizes and extends earlier work by Machado and Dupuis [29] who developed a lattice FRG group approach for classical spin systems.…”

Section: Introductionsupporting

confidence: 60%

“…The present work has established the applicability and power of the our recently developed spin FRG formalism [23][24][25][26][27][28] for dimerized quantum spin systems. Using a deformation scheme where the spin-correlation functions of isolated dimers define the initial conditions for the FRG flow, we have shown that even relatively simple truncations of the flow equations yield quantitatively accurate results for the spectrum and thermodynamics in the entire quantum paramagnetic, ferromagnetic, and thermally disordered phases.…”

Section: Discussionmentioning

confidence: 86%

“…A and H > H c2 we then have M 0 ≈ 1 ≈ m 0 and p s ≈ 0 ≈ p 0 . Then the two high-energy triplet modes disappear completely from the propagators (28), so that at the end of the flow we obtain a spin-wave like dispersion for the remaining low-energy mode,…”

Section: B Tadpole Resummationmentioning

confidence: 99%

“…[23] and further developed in Refs. [24][25][26][27][28] is based on a formally exact renormalization group flow equation for the generating functional of connected spin correlation functions. As such, it does not require projecting the physical spin operators onto auxiliary bosons or fermions with restricted Hilbert spaces.…”

Section: Frg Flow Equations For Dimerized Quantum Spin Systemsmentioning

confidence: 99%

“…In Refs. [23][24][25][26][27][28] we have developed several strategies to avoid these technical difficulties. In contrast to methods based on auxiliary bosons [3,4,8,10,11,13,15,16,20], our spin FRG directly manipulates the physical spin correlation functions, thus circumventing all issues associated with the expression of quantum spins in terms of bosonic or fermionic auxiliary degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

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Spin functional renormalization group for dimerized quantum spin systems

Rückriegel,

Arnold,

Goll

et al. 2022

Preprint

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We investigate dimerized quantum spin systems using the spin functional renormalization group approach proposed by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)] which directly focuses on the physical spin correlation functions and avoids the representation of the spins in terms of fermionic or bosonic auxiliary operators. Starting from decoupled dimers as initial condition for the renormalization group flow equations, we obtain the spectrum of the triplet excitations as well as the magnetization in the quantum paramagnetic, ferromagnetic, and thermally disordered phases at all temperatures. Moreover, we compute the full phase diagram of a weakly coupled dimerized spin system in three dimensions, including the correct mean field critical exponents at the two quantum critical points.

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Section: Introductionsupporting

confidence: 60%

Section: Discussionmentioning

confidence: 86%

Section: B Tadpole Resummationmentioning

confidence: 99%

Section: Frg Flow Equations For Dimerized Quantum Spin Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spin functional renormalization group for dimerized quantum spin systems

Rückriegel,

Arnold,

Goll

et al. 2022

Preprint

Self Cite

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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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