Transport through a quantum critical system: A thermodynamically consistent approach

Currents through quantum systems may probe non-analyticities in quantum-critical many-body ground states. For a large class of dissipative quantum critical systems we show that it is possible to obtain the reduced system dynamics in the vicinity of quantum critical points in a thermodynamically consistent way, while capturing non-Markovian effects. We achieve this by combining reaction coordinate mappings with polaron transforms. Exemplarily, we consider the Lipkin-Meshkov-Glick model in a transport setup, where the quantum phase transition manifests itself in the heat transfer statistics.