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.

scholarly journals A CORRELATION ESTIMATE FOR QUANTUM MANY-BODY SYSTEMS AT POSITIVE TEMPERATURE

2006 ◽  
Vol 18 (03) ◽  
pp. 233-253 ◽  
Author(s):  
ROBERT SEIRINGER
Keyword(s):  
Free Energy ◽  
Fock Space ◽  
Einstein Condensation ◽  
Positive Temperature ◽  
Coulomb Interactions ◽  
Many Body ◽  
Expectation Value ◽  
Many Body Systems ◽  
The Difference ◽  
Correlation Estimate

We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose–Einstein condensation.

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 Onset of universality in the dynamical mixing of a pure state

2021 ◽  
Author(s):  
M. Carrera-Núñez ◽  
A. M. Martínez-Argüello ◽  
J. M. Torres ◽  
E. J. Torres-Herrera
Keyword(s):  
Pure State ◽  
Matrix Theory ◽  
Chaotic Regime ◽  
Many Body ◽  
Analytical Treatment ◽  
Gaussian Unitary Ensemble ◽  
Time Dynamics ◽  
Spectral Statistics ◽  
Gaussian Orthogonal Ensemble ◽  
Unitary Ensemble

Abstract We study the time dynamics of random density matrices generated by evolving the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians. We show that the spectral statistics of the resulting mixed state is well described by random matrix theory (RMT) and undergoes a crossover from the Gaussian orthogonal ensemble to the Gaussian unitary ensemble (GUE) for short and large times, respectively. Using a semi-analytical treatment relying on a power series of the density matrix as a function of time, we find that the crossover occurs in a characteristic time that scales as the inverse of the dimension. The RMT results are contrasted with a paradigmatic model of many-body localization in the chaotic regime, where the GUE statistics is reached at large times, while for short times the statistics strongly depends on the peculiarity of the considered subspace.

scholarly journals Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
J. J. Mendoza-Arenas ◽  
F. J. Gómez-Ruiz ◽  
F. J. Rodríguez ◽  
L. Quiroga
Keyword(s):  
Quantum Transport ◽  
Minimal Model ◽  
Analytical Study ◽  
Particle Interactions ◽  
Many Body ◽  
Strongly Interacting ◽  
Maximal Violation ◽  
Many Body Systems

AbstractWe identify different schemes to enhance the violation of Leggett-Garg inequalities in open many-body systems. Considering a nonequilibrium archetypical setup of quantum transport, we show that particle interactions control the direction and amplitude of maximal violation, and that in the strongly-interacting and strongly-driven regime bulk dephasing enhances the violation. Through an analytical study of a minimal model we unravel the basic ingredients to explain this decoherence-enhanced quantumness, illustrating that such an effect emerges in a wide variety of systems.

Symplectic Schrödinger equation for many-body systems

2020 ◽  
Vol 35 (06) ◽  
pp. 2050033
Author(s):  
R. G. G. Amorim ◽  
M. C. B. Fernandes ◽  
F. C. Khanna ◽  
A. E. Santana ◽  
J. D. M. Vianna
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Basic Element ◽  
Space Representation ◽  
Many Body ◽  
Many Body Systems ◽  
The Green Function ◽  
Phase Space Representation

Using elements of symmetry, as gauge invariance, many aspects of a Schrödinger equation in phase space are analyzed. The number (Fock space) representation is constructed in phase space and the Green function, directly associated with the Wigner function, is introduced as a basic element of perturbative procedure. This phase space representation is applied to the Landau problem and the Liouville potential.

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 Fock Space Localization of Many-Body States in the Tilted Bose-Hubbard Model

2019 ◽  
Vol 136 (5) ◽  
pp. 834-840
Author(s):  
M. Schneider ◽  
A. Rodríguez ◽  
A. Buchleitner
Keyword(s):  
Hubbard Model ◽  
Fock Space ◽  
Many Body ◽  
Space Localization
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