Energy transport between critical one-dimensional systems with different central charges

Abstract

Energy transport can reveal information about interacting many-body systems beyond other transport probes.In particular, in one dimension it has been shown that the energy current is directly proportional to the central charge, thus revealing information about the degrees of freedom of critical systems. In this paper, we explicitly verify this result in two cases for translationally invariant systems based on explicit microscopic calculations. More importantly, we generalize the result to nontranslation invariant setups and use this to study a composite system of two subsystems possessing different central charges. We find a bottleneck effect, meaning the smaller central charge limits the energy transport.

On the hydrodynamics of unstable excitations

“…Our numerical results suggest 1) and T is the largest temperature. This is different from any of the formulae found in [73][74][75] and likely due to our special set-up. A better understanding of the conditions under which each behaviour is to be expected is still needed.…”

“…However, none of these works has considered a situation that is directly comparable to ours and indeed they all predict a different behaviour of the current. For instance in [73,74] the connection of two free CFTs of different central charges was considered, whereas in [75] two different critical models are connected by a defect which breaks conformal invariance. However, the argument put forward in [74] about a possible "bottleneck" effect whereby the smallest central charge limits the growth of the currents, seems rather plausible and yet does not hold here.…”

“…For instance in [73,74] the connection of two free CFTs of different central charges was considered, whereas in [75] two different critical models are connected by a defect which breaks conformal invariance. However, the argument put forward in [74] about a possible "bottleneck" effect whereby the smallest central charge limits the growth of the currents, seems rather plausible and yet does not hold here. A potential explanation is that with an actual, localised impurity in the dynamics, a true bottleneck effect may arise where the impurity is unable to carry more degrees of freedom through it than those supported by the theory with the smallest central charge.…”

On the Hydrodynamics of Unstable Excitations

“…However, none of these works has considered a situation that is directly comparable to ours and indeed they all predict a different behaviour of the current. For instance in [71,72] the connection of two free CFTs of different central charges was considered, whereas in [73] two different critical models are connected by a defect which breaks conformal invariance. However, the argument put forward in [72] about a possible "bottleneck" effect whereby the smallest central charge limits the growth of the currents, seems rather plausible and yet does not hold here.…”

“…For instance in [71,72] the connection of two free CFTs of different central charges was considered, whereas in [73] two different critical models are connected by a defect which breaks conformal invariance. However, the argument put forward in [72] about a possible "bottleneck" effect whereby the smallest central charge limits the growth of the currents, seems rather plausible and yet does not hold here. A potential explanation is that with an actual, localised impurity in the dynamics, a true bottleneck effect may arise where the impurity is unable to carry more degrees of freedom through it than those supported by the theory with the smallest central charge.…”