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Description
A systematic study of bosons in a one-dimensional quasiperiodic optical lattice is performed using the Quantum Monte Carlo time-dependent Variational Monte Carlo (tVMC) method [1], following the procedures established by some of the authors in an earlier study [2]. In quasiperiodic lattices, formed by the superposition of two optical lattices with incommensurate wave numbers, even a weak secondary lattice is known to induce localization in non-interacting systems [3, 4]. The present work investigates the delocalization effect of two-body contact interactions. Ground state observables, such as the density profile and pair distribution function $g_2(r)$, are obtained via imaginary-time evolution for different quasiperiodic lattice configurations, where the relative strength of the secondary lattice is varied and both shallow and deep primary lattices are considered. A weak perturbation pulse is then applied within the linear response regime to study the system’s dynamical behaviour via real-time evolution, characterized by the dynamic structure factor $S(k, \omega)$. Comparison with selected results from periodic optical lattices [2], as well as a broader analysis spanning from the weakly interacting regime to the strongly interacting limit, is performed. The tVMC method enables the exploration of regimes beyond mean-field-like and Hubbard model approximations. The results reveal the emergence of rich structural and dynamical phenomena in quasiperiodic lattices compared to their periodic counterparts.
References:
[1] G. Carleo et al., Phys. Rev. A 89, 031602 (2014).
[2] M. Gartner et al., SciPost Phys. 13, 025 (2022).
[3] P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[4] E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).
