Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

Xu, Zhihao; Li, Linhu; Xianlong, Gao; Chen, Shu

doi:10.1088/0953-8984/25/5/055601

Cited by 8 publications

(12 citation statements)

References 49 publications

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“…Our work complements the findings in Ref. 39 by providing a comparison of single-component (“spin-0”) bosons with contact and long-ranged dipolar interactions in continuous space without a lattice and without resorting to a Hubbard-tight-binding-description.…”

Section: Introductionsupporting

confidence: 63%

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Bera¹,

Chakrabarti²,

Gammal³

et al. 2019

Sci Rep

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Fermionization is what happens to the state of strongly interacting repulsive bosons interacting with contact interactions in one spatial dimension. Crystallization is what happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization and fermionization resemble each other: in both cases – due to their repulsion – the bosons try to minimize their spatial overlap. We trace these two hallmark phases of strongly correlated one-dimensional bosonic systems by exploring their ground state properties using the one- and two-body density matrix. We solve the N-body Schrödinger equation accurately and from first principles using the multiconfigurational time-dependent Hartree for bosons (MCTDHB) and for fermions (MCTDHF) methods. Using the one- and two-body density, fermionization can be distinguished from crystallization in position space. For N interacting bosons, a splitting into an N-fold pattern in the one-body and two-body density is a unique feature of both, fermionization and crystallization. We demonstrate that this splitting is incomplete for fermionized bosons and restricted by the confinement potential. This incomplete splitting is a consequence of the convergence of the energy in the limit of infinite repulsion and is in agreement with complementary results that we obtain for fermions using MCTDHF. For crystalline bosons, in contrast, the splitting is complete: the interaction energy is capable of overcoming the confinement potential. Our results suggest that the spreading of the density as a function of the dipolar interaction strength diverges as a power law. We describe how to distinguish fermionization from crystallization experimentally from measurements of the one- and two-body density.

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Section: Introductionsupporting

confidence: 63%

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Bera¹,

Chakrabarti²,

Gammal³

et al. 2019

Sci Rep

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show abstract

“…The two particles can be either two electrons with opposite spins in a crystalline potential or two atoms trapped in an optical lattice. In the former case, the particles are distinguishable and the hopping dynamics is described by the extended Fermi-Hubbard model (EHM) with Hamiltonian [46][47][48][49] ∑ ∑…”

Section: The Modelmentioning

confidence: 99%

“…We assumed =  1. The EHM is a prototype model in condensed matter theory that exhibits a rich phase diagram [46][47][48][49]. In solid-state systems, nonlocal interaction arises from Coulomb repulsion of electrons in adjacent sites, due to nonperfect screening of electron charges.…”

Section: The Modelmentioning

confidence: 99%

Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles

Longhi

2014

New J. Phys.

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We predict that two correlated particles hopping on a one-dimensional Hubbard lattice can show transient self-acceleration and self-induced Bloch oscillations as a result of anti-Newtonian dynamics. Self-propulsion occurs for two particles with opposite effective mass on the lattice and requires long-range particle interaction. A photonic simulator of the two-particle Hubbard model with controllable long-range interaction, where self-propulsion can be observed, is discussed.

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“…While this is expected to happen in low-density systems with longrange interactions, contact interactions typically do not favor formation of a crystal [23]. Therefore we expect a strongly-correlated state which is translationally invariant to have even lower energy than WC state.…”

Section: Wigner Crystal Statementioning

confidence: 88%

“…The WC state obviously has lower energy than a meanfield BEC at low densities, however it is a crystalline state which breaks translational symmetry. While this is expected to happen in low-density systems with longrange interactions, contact interactions typically do not favor formation of a crystal [23]. Therefore we expect a strongly-correlated state which is translationally invariant to have even lower energy than WC state.…”

Section: Wigner Crystal Statementioning

confidence: 88%

Strong correlation effects in a two-dimensional Bose gas with quartic dispersion

Radić¹,

Natu²,

Galitski³

2015

Phys. Rev. A

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Motivated by the fundamental question of the fate of interacting bosons in flat bands, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This type of band structure can be realized using the NIST scheme of spinorbit coupling [Y.-J. Lin, K. Jiménez-Garcia, and I. B. Spielman, Nature 471, 83 (2011) (2013)]. We numerically compare the ground state energies of the mean-field Bose-Einstein condensate (BEC) and various trial wave-functions, where bosons avoid each other at short distances. We discover that, at low densities, several types of strongly correlated states have an energy per particle ( ), which scales with density (n) as ∼ n 4/3 , in contrast to ∼ n for the weakly interacting Bose gas. These competing states include a Wigner crystal, quasi-condensates described in terms of properly symmetrized fermionic states, and variational wave-functions of Jastrow type. We find that one of the latter has the lowest energy among the states we consider. This Jastrow-type state has a strongly reduced, but finite condensate fraction, and true off-diagonal long range order, which suggests that the ground state of interacting bosons with quartic dispersion is a strongly-correlated condensate reminiscent of superfluid Helium-4. Our results show that even for weakly-interacting bosons in higher dimensions, one can explore the crossover from a weakly-coupled BEC to a stronglycorrelated condensate by simply tuning the single particle dispersion or density.

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Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

Cited by 8 publications

References 49 publications

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Sorting Fermionization from Crystallization in Many-Boson Wavefunctions

Anti-Newtonian dynamics and self-induced Bloch oscillations of correlated particles

Strong correlation effects in a two-dimensional Bose gas with quartic dispersion

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