Transport through a quantum critical system: A thermodynamically consistent approach

Quantum phase transitions are striking phenomena of many-body systems at low temperatures. The current experimental feasibilities enable us to bring such critical systems out of equilibrium in a controlled manner. Due to the vanishing energy gap above the ground state [1], appropriate methods have to be developed to study the dynamics and thermodynamical applications. We show for a class of critical systems connected to several non-Markovian heat baths that by combining the reaction coordinate mapping [2] and a polaron technique [3] it is possible to find analytic expressions of the reduced system dynamics in the vicinity of quantum critical points, which are consistent with the laws of thermodynamics. As an example we consider the Lipkin-Meshkov-Glick model in a transport setup, where the underlying phase transition manifests itself in the heat transfer statistics.
[1] S. Sachdev, Quantum Phase Transitions (Cambridge Univ. Press, Cambridge, 1999).
[2] P. Strasberg et. al, New J. Phys. 18, 073007 (2016).
[3] P. Kirton and J. Keeling, Phys. Rev. Lett. 111, 100404 (2013).