Dissipative spin dynamics in hot quantum paramagnets

Tarasevych, Dmytro; Kopietz, Peter

doi:10.1103/physrevb.104.024423

Cited by 11 publications

(8 citation statements)

References 60 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%

“…[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: Frg Flow Equations For Dimerized Quantum Spin Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spin functional renormalization group for dimerized quantum spin systems

Rückriegel,

Arnold,

Goll

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…for temperatures T T C in D = 3 respectively at zero magnetic field in D ≤ 2, no distinct excitations exist leading to an isotropic structure factor dominated by a diffusive central peak, whose origin is usually explained in terms of a hydrodynamic picture [85] (for a recent microscopic spin FRG calculation, see Ref. [133]). In the presence of a finite magnetization transverse and longitudinal parts evidently require a separate analysis.…”

Section: Outlinementioning

confidence: 99%

Spin functional renormalization group analysis of quantum Heisenberg ferromagnets

Goll¹

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In this thesis we investigate the thermodynamic and dynamic properties of the D-dimensional quantum Heisenberg ferromagnet within the spin functional renormalization group (FRG); a formalism describing the evolution of the system’s observables as the magnetic exchange inter-action is artificially deformed. Following an introduction providing a self contained summary of the conceptual and mathematical background, we present the spin FRG as developed by Krieg and Kopietz in references [1] and [2] in chapter two. Thereto, the generating functional of the imaginary time-spin correlation functions and its exact flow equation describing the deformation process of the exchange interaction are introduced. In addition, it is highlighted that - in contrast to conventional field-theoretic FRG approaches - the related Legendre trans-formed functional cannot be defined if the exchange interaction is initially switched off. Next, we show that this limitation can be circumvented within an alternativ hybrid approach, which treats transverse and longitudinal spin fluctuations differently. The relevant functionals are introduced and the relations of the corresponding functional Taylor coefficients with the spin correlation functions are discussed. Lastly, the associated flow equations are derived and the possibility of explicit or spontaneous symmetry breaking is taken into account. In chapter three, we benchmark the hybrid formalism against a calculation of the thermo-dynamic properties of the one and two-dimensional Heisenberg model at low temperatures T and finite magnetic field H. For this purpose, we devise an anisotropic deformation scheme of the exchange interaction which allows for a controlled truncation of the infinite hierarchy of FRG flow equations. Thereby, contact with mean-field and spin-wave theory is made and the violation of the Mermin-Wagner theorem is discussed. To fulfill the latter, the truncation scheme is then complemented by a Ward identity relating the transverse self-energy and the magnetization. The resulting magnetization M (H, T ) and isothermal susceptibility χ(H, T ) are in quantitative agreement with the literature and the established behavior of the transverse correlation length and the zero-field susceptibility close to the critical point is qualitatively reproduced in the limit H → 0. Finally, we investigate the longitudinal dynamics at low temperatures. To this end, the hierarchy of flow equations is solved within the same anisotropic deformation scheme complemented by an expansion in the inverse interaction range, and the resulting longitudinal dynamic structure factor is calculated within a low-momentum expansion. In D = 3, the large phase space accessible for the decay into transverse magnons yields only a broad hump centered at zero frequency whose width scales linearly in momentum. In contrast, at low temperatures and in a certain range of magnetic fields, a well-defined quasiparticle peak with linear dispersion emerges in D ≤ 2, which we identify as zero-magnon sound. Sound velocity and damping are discussed as a function of temperature and magnetic field, and the relevant momentum-frequency window is estimated and compared to the hydrodynamic second-magnon regime.

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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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Dissipative spin dynamics in hot quantum paramagnets

Cited by 11 publications

References 60 publications

Spin functional renormalization group for dimerized quantum spin systems

Spin functional renormalization group for dimerized quantum spin systems

Spin functional renormalization group analysis of quantum Heisenberg ferromagnets

Pseudo-fermion functional renormalization group for spin models

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