The Hubbard Model: A Computational Perspective

Annual Review of Condensed Matter Physics, Journal Year: 2021, Volume and Issue: 13(1), P. 275 - 302

Published: Nov. 29, 2021

The Hubbard model is the simplest of interacting fermions on a lattice and similar importance to correlated electron physics as Ising statistical mechanics or fruit fly biomedical science. Despite its simplicity, exhibits an incredible wealth phases, phase transitions, exotic correlation phenomena. While analytical methods have provided qualitative description in certain limits, numerical tools shown impressive progress achieving quantitative accurate results over last years. This article gives introduction model, motivates common questions, illustrates that has been achieved years revealing various aspects model.

Language: Английский

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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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Quantitative theory of magnetic interactions in solids

Reviews of Modern Physics, Journal Year: 2023, Volume and Issue: 95(3)

Published: Sept. 11, 2023

Magnetic moments in solids become useful and interesting due to the interatomic exchange that causes them align. Developments calculations of electronic structure have led ability predictively compute these interactions many materials. This review describes development their application describing behavior materials including technologically important hard soft magnetic materials, novel two-dimensional magnets, elemental solids, alloys, antiferromagnets, noncollinear molecules containing hundreds atoms.

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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Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study

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

Published: Jan. 10, 2025

Language: Английский

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SOLAX: A Python solver for fermionic quantum systems with neural network support

SciPost Physics Codebases, Journal Year: 2025, Volume and Issue: unknown

Published: Feb. 20, 2025

Numerical modeling of fermionic many-body quantum systems presents similar challenges across various research domains, necessitating universal tools, including state-of-the-art machine learning techniques. Here, we introduce SOLAX, a Python library designed to compute and analyze using the formalism second quantization. SOLAX provides modular framework for constructing manipulating basis sets, states, operators, facilitating simulation electronic structures determining states in finite-size Hilbert spaces. The integrates capabilities mitigate exponential growth space dimensions large clusters. core low-level functionalities are implemented recently developed JAX. Demonstrated through its application Single Impurity Anderson Model, offers flexible powerful tool researchers addressing broad spectrum fields, atomic physics, chemistry, condensed matter physics.

Language: Английский

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Mott Insulating States with Competing Orders in the Triangular Lattice Hubbard Model

Physical Review X, Journal Year: 2021, Volume and Issue: 11(4)

Published: Oct. 19, 2021

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from metal-insulator transition, intriguing thermodynamic behavior, and putative spin liquid phase at intermediate coupling, ultimately becoming magnetic insulator strong coupling. In this multimethod study, we combine finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo cellular dynamical mean-field theory, to establish several aspects model. We elucidate evolution metallic insulating regime complementary perspectives brought by these different methods. compute full thermodynamics on width-four cylinder using METTS in coupling regime. find that state hosts large entropy temperatures, which increases strength Correspondingly, consistently Maxwell relation, double occupancy has minimum as function temperature is manifestation Pomeranchuk effect increased localization upon heating. found exhibit both pronounced chiral well stripy antiferromagnetic correlations. propose scenario time-reversal symmetry-broken compete stripy-spin lowest temperatures.

Language: Английский

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Phase Diagram of Nickelate Superconductors Calculated by Dynamical Vertex Approximation

Frontiers in Physics, Journal Year: 2022, Volume and Issue: 9

Published: Jan. 21, 2022

We review the electronic structure of nickelate superconductors with and without effects correlations. As a minimal model, we identify one-band Hubbard model for Ni 3 dx2−y2 orbital plus pocket around A -momentum. The latter, however, merely acts as decoupled electron reservoir. This reservoir makes careful translation from nominal Sr-doping to doping mandatory. Our dynamical mean-field theory calculations, in part already supported by experiment, indicate that Γ pocket, Nd 4 f orbitals, oxygen 2 p , other d orbitals are not relevant superconducting regime. physics is completely different if topotactic hydrogen present or reduction incomplete. Then, two-band hosted id="m2">dx2−y2 id="m3">d3z2−r2 emerges. Based on our modeling, calculated T c vs. x phase diagram prior experiment using vertex approximation. For such notoriously difficult determine quantity agreement astonishingly good. prediction enhanced pressure compressive strain has been confirmed experimentally well. supports an appropriate model.

Language: Английский

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Magnetic correlations in infinite-layer nickelates: An experimental and theoretical multimethod study

Physical Review Research, Journal Year: 2022, Volume and Issue: 4(2)

Published: May 2, 2022

We report a comprehensive study of magnetic correlations in ${\mathrm{LaNiO}}_{2}$, parent compound the recently discovered family infinite-layer (IL) nickelate superconductors, using multiple experimental and theoretical methods. Our specific heat, muon-spin rotation ($\ensuremath{\mu}\mathrm{SR}$), susceptibility measurements on polycrystalline ${\mathrm{LaNiO}}_{2}$ show that long-range order remains absent down to 2 K. Nevertheless, we detect residual entropy low-temperature which is compatible with model fit includes paramagnon excitations. The $\ensuremath{\mu}\mathrm{SR}$ low-field static dynamic indicate presence short-range glassy spin dynamics, attribute local oxygen nonstoichiometry average crystal structure. This behavior can be suppressed strong external fields, allowing us extract intrinsic paramagnetic susceptibility. Remarkably, find shows non-Curie-Weiss at high temperatures, analogy doped cuprates possess robust nonlocal fluctuations. distinct temperature dependence theoretically understood by multimethod single-band Hubbard apply complementary cutting-edge quantum many-body techniques (dynamical mean-field theory, cellular dynamical vertex approximation) investigate influence both short- long-ranged correlations. results suggest profound between (undoped) IL nickelates cuprates.

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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