Masaki Tezuka

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.

In a one-dimensional (1D) superconductor, zero temperature quantum fluctuations destroy phase coherence. Here we put forward a mechanism which can restore phase coherence: power-law hopping. We study a 1D attractive-U Hubbard model with power-law hopping by Abelian bosonization and density-matrix renormalization group (DMRG) techniques. The parameter that controls the hopping decay acts as the effective, non-integer spatial dimensionality $d_{eff}$. For real-valued hopping amplitudes we identify analytically a range of parameters for which power-law hopping suppress fluctuations and restore superconducting long-range order for any $d_{eff} > 1$. A detailed DMRG analysis fully supports these findings. These results are also of direct relevance to quantum magnetism as our model can be mapped onto a S=1/2 XXZ spin-chain with power-law decaying couplings, which can be studied experimentally by cold ion-trap techniques.