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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Optimizing Superconductivity: From Cuprates via Nickelates to Palladates

Physical Review Letters, Journal Year: 2023, Volume and Issue: 130(16)

Published: April 20, 2023

Motivated by cuprate and nickelate superconductors, we perform a comprehensive study of the superconducting instability in single-band Hubbard model. We calculate spectrum transition temperature T_{c} as function filling Coulomb interaction for range hopping parameters, using dynamical vertex approximation. find sweet spot high to be at intermediate coupling, moderate Fermi surface warping, low hole doping. Combining these results with first principles calculations, neither nickelates nor cuprates are close this optimum within description. Instead, identify some palladates, notably RbSr_{2}PdO_{3} A_{2}^{'}PdO_{2}Cl_{2} (A^{'}=Ba_{0.5}La_{0.5}), virtually optimal, while others, such NdPdO_{2}, too weakly correlated.

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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Correlations tune the electronic structure of pentalayer nickelates into the superconducting regime

Physical Review Materials, Journal Year: 2022, Volume and Issue: 6(9)

Published: Sept. 6, 2022

Motivated by the recent discovery of superconductivity in pentalayer nickelate ${\mathrm{Nd}}_{6}{\mathrm{Ni}}_{5}{\mathrm{O}}_{12}$ [G. A. Pan et al., Nat. Mater. 21, 160 (2022)], we calculate its electronic structure and superconducting critical temperature. We find that correlations are essential for pushing into doping range as they shift electron pockets above Fermi energy. As a consequence, can be described with single ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbital per Ni. predict to overdoped; further improvements ${T}_{c}$ expected few additional layers. Instead, bilayer ${\mathrm{Nd}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{6}$ drive system three-orbital regime also involving Ni ${d}_{xz,yz}$ states. suggest, however, single-orbital physics optimal restored substituting 60% trivalent Nd or La tetravalent Zr.

Language: Английский

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Spin fluctuations sufficient to mediate superconductivity in nickelates

Physical review. B./Physical review. B, Journal Year: 2024, Volume and Issue: 109(23)

Published: June 12, 2024

Many mechanisms for unconventional superconductivity have been proposed, but actually proving which one is in charge challenging. Quite astonishingly, dynamical vertex approximation predict the superconducting phase diagram of novel nickelate superconductors, with microscopic origin being antiferromagnetic spin fluctuations. The authors compare fluctuations behind these calculations to experiment. again good agreement gives an overall coherent and complete picture, thus a high level confidence that nickelates indeed mediated by

Language: Английский

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Nonperturbative Calculations for Spectroscopic Properties of Cuprate High-Temperature Superconductors

Journal of the Physical Society of Japan, Journal Year: 2023, Volume and Issue: 92(9)

Published: July 12, 2023

We review nonperturbative numerical calculations on dynamical properties of the two-dimensional Hubbard model and their relevance to various spectroscopic experiments high-temperature superconducting cuprates. The unbiased theories have revealed existence a self-energy singularity in slightly doped Mott insulators, which is responsible for both pseudogap formation superconductivity. pole traces back gap at zero doping, underscoring that physics lies heart This mechanism relies neither competing order nor preformed pair while high transition temperature does not necessitate bosonic glue mediate Cooper pairing. Instead, mechanisms are linked singular inherent insulator. presence accounts anomalies reported so far experiments, deforming spectral structure manner beyond simple mass renormalization. low-energy electron dynamics, as computed with pole, suggest hidden fermionic excitation coupling quasiparticles.

Language: Английский

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Coupled system of electrons and exciton-polaritons: Screening, dynamical effects, and superconductivity

Physical review. B./Physical review. B, Journal Year: 2023, Volume and Issue: 108(2)

Published: July 31, 2023

Bose-Fermi systems such as mixtures of electrons with excitons or exciton-polaritons are extensively discussed candidates to host a variety intriguing phenomena, including polaron formation, drag effects, supersolidity, and superconductivity. In this work, assuming the strong-coupling regime between semiconductor cavity photons, we develop many-body theory approach addressing interplay different types interaction among various species in mixture, wherein take into account dynamical density responses both Bose-condensed two-dimensional electron gas inside an optical microcavity. As was anticipated previously, at high enough polariton densities lower hybrid mode system's excitation spectrum acquires roton minimum, making system prone superconducting pairing vicinity instability. We analyze possibility polariton-BEC-mediated superconductivity taking full momentum frequency dependence gap, well Eliashberg where is neglected, Bardeen-Cooper-Schrieffer that discards effects. Considering screening Thomas-Fermi random-phase approximations, estimate critical temperatures be not larger than 0.1 K possible realizations coupled polariton-electron system, quantum wells transition metal dichalcogenides considered.

Language: Английский

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Doping asymmetry in the three-band Hamiltonian for cuprate ladders: Failure of the standard model of superconductivity in cuprates

Physical review. B./Physical review. B, Journal Year: 2023, Volume and Issue: 107(24)

Published: June 27, 2023

The relevance of the single-band two-dimensional Hubbard model to superconductivity in doped cuprates has recently been questioned, based on density matrix renormalization group (DMRG) computations that found over an unrealistically broad doping region upon electron-doping, yet a complete absence for hole-doping. We report very similar results from DMRG calculations ${\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ two-leg ladder within parent three-band correlated-electron Hamiltonian. strong asymmetry our are contradiction deep and profound symmetry experimental phase diagrams electron- hole-doped cuprate superconductors, as seen occurrence quantum critical points superconducting domes both cases characterized by Fermi surface reconstruction, large jumps carrier density, strange metal behavior.

Language: Английский

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Multipolar ordering from dynamical mean field theory with application to CeB6

Physical review. B./Physical review. B, Journal Year: 2024, Volume and Issue: 110(3)

Published: July 1, 2024

Magnetic and multipolar ordering in $f$ electron systems takes place at low temperatures of order 1--10 Kelvin. Combinations first-principles with many-body calculations for such low-energy properties correlated materials are challenging problems. We address based on the dynamical mean-field theory (DMFT) combined density functional theory. derive momentum-dependent susceptibilities interactions two ways: by solving Bethe-Salpeter (BS) equation two-particle Green's function using a recently developed approximate strong-coupling formula. apply formalism to prototypical example ${\mathrm{CeB}}_{6}$ Hubbard-I solver, demonstrate that experimental quadrupole transition is correctly reproduced. The results formula show good agreement those BS equation. This DMFT has applications which beyond reach traditional RKKY In particular, more itinerant including $5f$, $4d$, $5d$ electrons can be addressed.

Language: Английский

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Fermi and Luttinger Arcs: Two Concepts, Realized on One Surface

Physical Review Letters, Journal Year: 2024, Volume and Issue: 133(16)

Published: Oct. 16, 2024

We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces results numerically demanding many-body calculations, here obtained using dynamical vertex approximation. Our analytical theory provides transparent description precise mechanism, capable driving formation disconnected segments along (the highly debated "Fermi arcs"), well opening pseudogap hole electron This occurs through specific mechanism: electronic states on arcs remain intact, while part where gap opens transforms into Luttinger arc.

Language: Английский

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