Introduction

Lode, Axel U. J.

doi:10.1007/978-3-319-07085-8_1

Cited by 1 publication

(2 citation statements)

References 48 publications

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“…It can be demonstrated that MCTDHB delivers solutions of the Schrödinger equation at a significantly increased accuracy in comparison to exact diagonalization approaches when the same number of single-particle basis states is employed, see Refs. 53,65 . for a demonstration with the harmonic interaction model and Appendix A for a demonstration with dipole-dipole interactions, i.e., the Hamiltonian in Eqs.…”

Section: Methodsmentioning

confidence: 99%

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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: Methodsmentioning

confidence: 99%

“…If only a single eigenvalue ρ i ( NO ) is macroscopic, then the state |Ψ〉 describes a Bose-Einstein condensate 60 . The case when multiple eigenvalues ρ i ( NO ) are comparable to the number of particles N is referred to as fragmentation 43,44,53,54,61–63 .…”

Section: Hamiltonian One- and Two-body Densitymentioning

confidence: 99%