Conductivity of hard core bosons: A paradigm of a bad metal

Two-dimensional hard core bosons suffer strong scattering in the high-temperature resistive state at half filling. The dynamical conductivity σ(ω) is calculated using nonperturbative tools such as continued fractions, series expansions, and exact diagonalization. We find a large temperature range with linearly increasing resistivity and broad dynamical conductivity, signaling a breakdown of Boltzmann-Drude quasiparticle transport theory. At zero temperature, a high-frequency peak in σ(ω) appears above a ``Higgs mass'' gap and corresponds to order-parameter magnitude fluctuations. We discuss the apparent similarity between conductivity of hard core bosons and phenomenological characteristics of cuprates, including the universal scaling of Homes et al. [Nature (London) 430, 539 (2004)].