We analyze topological properties of the one-dimensional Bose-Hubbard model with a quasiperiodic superlattice potential. This system can be realized in interacting ultracold bosons in optical lattice in the presence of an incommensurate superlattice potential. We first analyze the quasiperiodic superlattice made by the cosine function, which we call Harper-like Bose-Hubbard model. We compute the Chern number and observe a gap-closing behavior as the interaction strength $U$ is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of $U$ and a continuous deformation parameter $β$ between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.We analyze topological properties of the one-dimensional Bose-Hubbard model with a quasiperiodic superlattice potential. This system can be realized in interacting ultracold bosons in optical lattice in the presence of an incommensurate superlattice potential. We first analyze the quasiperiodic superlattice made by the cosine function, which we call Harper-like Bose-Hubbard model. We compute the Chern number and observe a gap-closing behavior as the interaction strength $U$ is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of $U$ and a continuous deformation parameter $β$ between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.

arXiv:1404.6315Journal of the Physical Society of JapanJul 24, 201423 citations

Thermalization of interacting bosons in random potentials

Tobias Geiger, Thomas Wellens, Andreas Buchleitner

Mar 8, 20120 citations

Bosons in one-dimensional incommensurate superlattices

Tommaso Roscilde

We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices [L. Fallani et al., Phys. Rev. Lett. 98, 130404 (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasiperiod) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasiperiodic potential for both hard-core and soft-core bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover, we discuss the validity of the local-density approximation in the presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasiperiodic potential; and we discuss the ab initio derivation of the Bose-Hubbard Hamiltonian with quasiperiodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices [L. Fallani et al., Phys. Rev. Lett. 98, 130404 (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasiperiod) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasiperiodic potential for both hard-core and soft-core bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover, we discuss the validity of the local-density approximation in the presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasiperiodic potential; and we discuss the ab initio derivation of the Bose-Hubbard Hamiltonian with quasiperiodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.

arXiv:0712.2741Physical Review AJun 9, 2008111 citations

Condensation of interacting bosons in a random potential

Robert Seiringer, Jakob Yngvason, Valentin Anatol'evich Zagrebnov

The European Physical Journal Special TopicsFeb 1, 20130 citations

Stability of dipolar bosons in a quasiperiodic potential

Paolo Molignini, Barnali Chakrabarti

Quasiperiodic potentials and dipolar interactions each impose long-range order in quantum systems, but their interplay unlocks a rich landscape of unexplored quantum phases. In this work, we investigate how dipolar bosonic crystals respond to correlated disorder in the form of quasiperiodic potentials. Using exact numerical simulations and a suite of observables—including order parameters, energy, density distributions, and two-body coherence measures—we explore one-dimensional dipolar bosons in quasiperiodic lattices at both commensurate and incommensurate fillings. Our results reveal a complex competition between superfluid, Mott-insulator, density-wave, and crystalline phases, governed by the intricate balance of dipolar interactions, kinetic energy, and disorder strength. Crucially, we identify mechanisms that influence dipolar crystals, showing their surprising robustness even in the presence of strong quasiperiodic disorder. Strikingly, we challenge previous claims by demonstrating that a crystal phase—expected to precede full crystallization—does not emerge in the ground state. Instead, its traits appear only under moderate disorder, but never fully develop, giving way to a direct transition from a charge density wave to a crystal state. These findings provide new insights into the resilience of many-body quantum phases in complex environments and pave the way for engineering exotic quantum states in ultracold atomic systems.Quasiperiodic potentials and dipolar interactions each impose long-range order in quantum systems, but their interplay unlocks a rich landscape of unexplored quantum phases. In this work, we investigate how dipolar bosonic crystals respond to correlated disorder in the form of quasiperiodic potentials. Using exact numerical simulations and a suite of observables—including order parameters, energy, density distributions, and two-body coherence measures—we explore one-dimensional dipolar bosons in quasiperiodic lattices at both commensurate and incommensurate fillings. Our results reveal a complex competition between superfluid, Mott-insulator, density-wave, and crystalline phases, governed by the intricate balance of dipolar interactions, kinetic energy, and disorder strength. Crucially, we identify mechanisms that influence dipolar crystals, showing their surprising robustness even in the presence of strong quasiperiodic disorder. Strikingly, we challenge previous claims by demonstrating that a crystal phase—expected to precede full crystallization—does not emerge in the ground state. Instead, its traits appear only under moderate disorder, but never fully develop, giving way to a direct transition from a charge density wave to a crystal state. These findings provide new insights into the resilience of many-body quantum phases in complex environments and pave the way for engineering exotic quantum states in ultracold atomic systems.

arXiv:2502.04429Physical Review ResearchJun 9, 202510 citations

Stability of dipolar bosons in a quasiperiodic potential

Anonymous

Physical Review ResearchMay 15, 20250 citations

U

is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of

U

and a continuous deformation parameter

β

between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.