The paper proves, with one explicit assumption in the intermediate regime, that prethermal Floquet phases exist for power-law interacting systems with exponent alpha > d, and predicts a disorder-free one-dimensional prethermal discrete time crystal for 1 < alpha < 2.
Nearly-linear light cones in long-range interacting quantum systems
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abstract
In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems.
fields
cond-mat.stat-mech 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Long-Range Prethermal Phases of Nonequilibrium Matter
The paper proves, with one explicit assumption in the intermediate regime, that prethermal Floquet phases exist for power-law interacting systems with exponent alpha > d, and predicts a disorder-free one-dimensional prethermal discrete time crystal for 1 < alpha < 2.