Destruction of Long-range Order by Quenching the Hopping Range in One Dimension

Abstract

We study the dynamics in a one dimensional hard-core Bose gas with power-law hopping after an abrupt reduction of the hopping range using the time-dependent density-matrix renormalization group (t-DMRG) and bosonization techniques. In particular, we focus on the destruction of the Bose-Einstein condensate (BEC), which is present in the initial state in the thermodynamic limit. We argue that this type of quench is akin to a sudden reduction in the effective dimensionality $d$ of the system (from $d>1$ to $d=1$). We identify two regimes in the evolution of the BEC fraction. For short times the decay of the BEC fraction is Gaussian while for intermediate to long times, it is well described by a stretched exponential with an exponent that depends on the initial effective dimensionality of the system. These results are potentially relevant for cold trapped-ion experiments which can simulate an equivalent of hard-core bosons, i.e. spins, with tunable long-range interactions.

8 pages, 7 figures, accepted for publication in Phys. Rev. A

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• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Quantum Quenches in the Luttinger model and its close relatives
• Quantum quench in long-range field theories
• Bloch dynamics in lattices with long range hoppings
• Entanglement entropy of the long-range Dyson hierarchical model
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface