Onsager reaction terms for quantum many-body systems: Application to antiferromagnetic and superconducting order in the Hubbard model

1991 ◽  
Vol 43 (4) ◽  
pp. 3475-3482 ◽  
Author(s):  
Antoine Georges ◽  
Jonathan S. Yedidia
Keyword(s):  
Hubbard Model ◽  
Many Body ◽  
Many Body Systems

scholarly journals Self-consistent effective Hamiltonian theory for fermionic many-body systems

2020 ◽  
pp. 2150019
Author(s):  
Xindong Wang ◽  
Hai-Ping Cheng
Keyword(s):  
Hubbard Model ◽  
Order Parameter ◽  
Cooper Pair ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Body System ◽  
Many Body ◽  
Hamiltonian Theory ◽  
Self Consistent ◽  
Many Body Systems

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

scholarly journals From dynamical localization to bunching in interacting Floquet systems

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Yuval Baum ◽  
Everard van Nieuwenburg ◽  
Gil Refael
Keyword(s):  
Hubbard Model ◽  
Dynamical Localization ◽  
Body System ◽  
Many Body ◽  
Many Body Systems

We show that a quantum many-body system may be controlled by means of Floquet engineering, i.e., their properties may be controlled and manipulated by employing periodic driving. We present a concrete driving scheme that allows control over the nature of mobile units and the amount of diffusion in generic many-body systems. We demonstrate these ideas for the Fermi-Hubbard model, where the drive renders doubly occupied sites (doublons) the mobile excitations in the system. In particular, we show that the amount of diffusion in the system and the level of fermion-pairing may be controlled and understood solely in terms of the doublon dynamics. We find that under certain circumstances the diffusion in 11D systems may be eliminated completely for extremely long times. We conclude our work by generalizing these ideas to generic many-body systems.

scholarly journals QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Phillip Weinberg ◽  
Marin Bukov
Keyword(s):  
Hubbard Model ◽  
Time Evolution ◽  
Quantum Dynamics ◽  
Free Particle ◽  
Transverse Field ◽  
Theoretical Research ◽  
Many Body ◽  
Imaginary Time ◽  
Many Body Systems ◽  
Python Package

We present a major update to QuSpin, SciPostPhys.2.1.003 – an open-source Python package for exact diagonalization and quantum dynamics of arbitrary boson, fermion and spin many-body systems, supporting the use of various (user-defined) symmetries in one and higher dimension and (imaginary) time evolution following a user-specified driving protocol. We explain how to use the new features of QuSpin using seven detailed examples of various complexity: (i) the transverse-field Ising chain and the Jordan-Wigner transformation, (ii) free particle systems: the Su-Schrieffer-Heeger (SSH) model, (iii) the many-body localized 1D Fermi-Hubbard model, (iv) the Bose-Hubbard model in a ladder geometry, (v) nonlinear (imaginary) time evolution and the Gross-Pitaevskii equation on a 1D lattice, (vi) integrability breaking and thermalizing dynamics in the translationally-invariant 2D transverse-field Ising model, and (vii) out-of-equilibrium Bose-Fermi mixtures. This easily accessible and user-friendly package can serve various purposes, including educational and cutting-edge experimental and theoretical research. The complete package documentation is available under http://weinbe58.github.io/QuSpin/index.html.

scholarly journals Spin-imbalance in a 2D Fermi-Hubbard system

Science ◽  
2017 ◽  
Vol 357 (6358) ◽  
pp. 1385-1388 ◽  
Author(s):  
Peter T. Brown ◽  
Debayan Mitra ◽  
Elmer Guardado-Sanchez ◽  
Peter Schauß ◽  
Stanimir S. Kondov ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Metallic Phase ◽  
Strong Interactions ◽  
Temperature Phase ◽  
Strongly Correlated ◽  
Many Body ◽  
Open Questions ◽  
Antiferromagnetic Correlations ◽  
Strongly Correlated Fermions ◽  
Many Body Systems

The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model—a paradigm for strongly correlated fermions on a lattice—in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping the low-temperature phase diagram of the Fermi-Hubbard model as a function of both doping and spin polarization, for which many open questions remain.

scholarly journals String patterns in the doped Hubbard model

Science ◽  
2019 ◽  
Vol 365 (6450) ◽  
pp. 251-256 ◽  
Author(s):  
Christie S. Chiu ◽  
Geoffrey Ji ◽  
Annabelle Bohrdt ◽  
Muqing Xu ◽  
Michael Knap ◽  
...  
Keyword(s):  
Hubbard Model ◽  
Strongly Correlated Electrons ◽  
Cold Atom ◽  
Strongly Correlated ◽  
Many Body ◽  
Spin Order ◽  
Open Questions ◽  
Modern Physics ◽  
Many Body Systems ◽  
The Individual

Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.

scholarly journals Chaos in the Bose-Hubbard model and Random Two-Body Hamiltonians

2021 ◽  
Author(s):  
Lukas Pausch ◽  
Edoardo G Carnio ◽  
Andreas Buchleitner ◽  
Alberto Rodríguez González
Keyword(s):  
Hubbard Model ◽  
Fock Space ◽  
Fractal Dimensions ◽  
Chaotic Regime ◽  
Particle Interactions ◽  
Many Body ◽  
Expectation Value ◽  
Matrix Ensemble ◽  
Gaussian Orthogonal Ensemble ◽  
Many Body Systems

Abstract We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

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