Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model

Physical Review X, Journal Year: 2021, Volume and Issue: 11(1)

Published: March 23, 2021

The Hubbard model represents the fundamental for interacting quantum systems and electronic correlations. Using two-dimensional half-filled at weak coupling as a testing ground, we perform comparative study of comprehensive set state-of-the-art many-body methods. Upon cooling into its insulating antiferromagnetic ground state, hosts rich sequence distinct physical regimes with crossovers between high-temperature incoherent regime, an intermediate-temperature metallic low-temperature regime pseudogap created by fluctuations. We assess ability each method to properly address these through computation several observables probing both quasiparticle properties magnetic correlations, two numerically exact methods (diagrammatic determinantal Monte Carlo methods) serving benchmark. By combining computational results analytical insights, elucidate nature role spin fluctuations in regimes. Based on this analysis, explain how quasiparticles can coexist increasingly long-range correlations why dynamical mean-field theory is found provide remarkably accurate approximation local quantities regime. also critically discuss whether imaginary-time are able capture non-Fermi-liquid singularities fully nested system.32 MoreReceived 18 June 2020Revised 2 November 2020Accepted 21 December 2020DOI:https://doi.org/10.1103/PhysRevX.11.011058Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Fermi liquid theoryTechniquesTheoretical & Computational TechniquesMany-body techniquesFermi theoryResearch AreasAntiferromagnetismMetal-insulator transitionSpin fluctuationsPhysical SystemsMagnetic insulatorsStrongly correlated systemsTechniquesFermi theoryHubbard modelNon-Fermi-liquid theoryNumerical techniquesCondensed Matter, Materials Applied Physics

Language: Английский

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Pseudo-fermion functional renormalization group for spin models

Reports on Progress in Physics, Journal Year: 2024, Volume and Issue: 87(3), P. 036501 - 036501

Published: Jan. 19, 2024

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

Language: Английский

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Compactness of quantics tensor train representations of local imaginary-time propagators

SciPost Physics, Journal Year: 2025, Volume and Issue: 18(1)

Published: Jan. 8, 2025

Space-time dependence of imaginary-time propagators, vital for ab initio and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X 13, 021015 (2023)]. However, the impact system parameters, like temperature, data size remains underexplored. This paper provides a comprehensive numerical analysis compactness local propagators in QTT one-time/-frequency objects two-time/-frequency objects, considering truncation terms Frobenius maximum norms. To study worst-case scenarios, we employ random pole models, where number poles grows logarithmically with inverse temperature coefficients are random. The Green’s functions generated by these models expected more difficult compress than those from physical systems. reveals that highly QTT, outperforming state-of-the-art approaches such as intermediate representation discrete Lehmann reprensentation. For bond dimensions saturate at low temperatures, especially norm. We provide counting-number arguments saturation while origin this clarified. paper’s findings highlight critical need further research selection methods, tolerance levels, choice between imaginary-frequency representations practical applications.

Language: Английский

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Discrete Lehmann representation of three-point functions

Physical review. B./Physical review. B, Journal Year: 2025, Volume and Issue: 111(3)

Published: Jan. 16, 2025

Language: Английский

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Multiscale Space-Time Ansatz for Correlation Functions of Quantum Systems Based on Quantics Tensor Trains

Physical Review X, Journal Year: 2023, Volume and Issue: 13(2)

Published: April 27, 2023

The correlation functions of quantum systems—central objects in field theories—are defined high-dimensional space-time domains. Their numerical treatment thus suffers from the curse dimensionality, which hinders application sophisticated many-body theories to interesting problems. Here, we propose a multiscale ansatz for systems based on quantics tensor trains (QTTs), "qubits" describing exponentially different length scales. then assumes separation scales by decomposing resulting tensors into (also known as matrix product states). We numerically verify various equilibrium and nonequilibrium demonstrate compression ratios several orders magnitude challenging cases. Essential building blocks diagrammatic equations, such convolutions or Fourier transforms, are formulated compressed form. stability efficiency proposed methods Dyson Bethe-Salpeter equations. QTT representation provides unified framework implementing efficient computations theories.20 MoreReceived 8 November 2022Revised 16 February 2023Accepted 2 March 2023DOI:https://doi.org/10.1103/PhysRevX.13.021015Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasFinite temperature theoryPhysical SystemsStrongly correlated systemsCondensed Matter, Materials & Applied Physics

Language: Английский

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Non-perturbative intertwining between spin and charge correlations: A ``smoking gun'' single-boson-exchange result

SciPost Physics, Journal Year: 2024, Volume and Issue: 16(2)

Published: Feb. 23, 2024

We study the microscopic mechanism controlling interplay between local charge and spin fluctuations in correlated electron systems via a thorough investigation of generalized on-site susceptibility several fundamental many-electron models, such as Hubbard atom, Anderson impurity model, model. By decomposing numerically determined terms physically transparent single-boson exchange processes, we unveil mechanisms responsible for breakdown self-consistent perturbation expansion. In particular, unambiguously identify origin significant suppression its diagonal entries (Matsubara) frequency space slight increase off-diagonal ones which cause breakdown. The effect on elements originates directly from electronic scattering magnetic moments, reflecting their increasingly longer lifetime well enhanced effective coupling with electrons. Instead, diffuse enhancement can be mostly ascribed to multiboson processes. strong intertwining sectors is partly weakened at Kondo temperature due progressive reduction spin-fermion low regime. Our analysis, thus, clarifies precise through physical information transferred different channels interacting problems highlights pivotal role played by an physics electrons beyond perturbative

Language: Английский

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Single-boson exchange representation of the functional renormalization group for strongly interacting many-electron systems

Physical Review Research, Journal Year: 2022, Volume and Issue: 4(1)

Published: Jan. 14, 2022

We present a reformulation of the functional renormalization group (fRG) for many-electron systems, which relies on recently introduced single boson exchange (SBE) representation parquet equations [Phys. Rev. B 100, 155149 (2019)]. The latter exploits diagrammatic decomposition, classifies contributions to full scattering amplitude in terms their reducibility with respect cutting one interaction line, naturally distinguishing processes mediated by different channels. apply this idea fRG splitting one-loop flow vertex function into SBE and residual four-point fermionic vertex. Similarly as case solvers, recasting algorithm offers both computational interpretative advantages: decomposition not only significantly reduces numerical effort treating high-frequency asymptotics flowing vertices, but it also allows clear physical identification collective degrees freedom at play. illustrate advantages an formulation fRG-based schemes, computing through merger dynamical mean-field theory susceptibilities Yukawa couplings two-dimensional Hubbard model from weak strong coupling, we intuitive explanation results. paves promising route future multiboson multiloop extensions algorithms.

Language: Английский

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Self-consistency in GWΓ formalism leading to quasiparticle-quasiparticle couplings

Physical review. B./Physical review. B, Journal Year: 2022, Volume and Issue: 106(16)

Published: Oct. 26, 2022

Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy $\mathrm{\ensuremath{\Sigma}}$ of any dynamically correlated interacting system, provided one can evaluate interaction vertex $\mathrm{\ensuremath{\Gamma}}$ exactly. This is, however, impossible, in general, for it involves functional derivative with respect Green's function. Here, we analyze structure this derivative, splitting into four contributions and outlining type quasiparticle interactions that each them generate. Moreover, show how, implementation self-consistency, action these be classified two: A quantitative renormalization previously included terms inclusion qualitatively distinct through successive derivatives itself. Implementing latter self-consistency extend validity perturbative approximations based on equations toward high limit, as example Hubbard dimer. Our analysis also provides unifying perspective theory landscape, showing how T-matrix approach is completely contained formalism.

Language: Английский

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Symmetric improved estimators for multipoint vertex functions

Physical review. B./Physical review. B, Journal Year: 2024, Volume and Issue: 109(12)

Published: March 21, 2024

The authors develop here a new representation of two-particle vertices, the effective interaction between quantum particles in many-body environment. This yields numerical results with much higher accuracy and robustness than previously possible. By avoiding error-prone inversion, their ``symmetric improved estimators'' successfully pass stringent precision tests both real- imaginary-frequency frameworks field theory. scheme allows field-theoretic methods for strongly correlated electrons to expand into real-frequency direction.

Language: Английский

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How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

Journal of Physics Condensed Matter, Journal Year: 2021, Volume and Issue: 33(21), P. 214001 - 214001

Published: March 2, 2021

While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview different approaches which have been recently developed applied identify dominant two-particle scattering processes controlling shape one-particle functions and, in some cases, physical response system. In particular, will discuss general idea, common threads specific peculiarities all proposed approaches. them rely on selective analysis Schwinger-Dyson (or Bethe-Salpeter) equation, methodological differences originate from vertex be computed decomposed. Finally, illustrate potential strength these methodologies by means their applications two-dimensional Hubbard model, provide an outlook over future perspective developments this for understanding electrons.

Language: Английский

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