Entropy accumulation near quantum critical points: effects beyond hyperscaling

Abstract

Entropy accumulation near a quantum critical point was expected based on\ngeneral scaling arguments, and has recently been explicitly observed. We\nexplore this issue further in two canonical models for quantum criticality,\nwith particular attention paid to the potential effects beyond hyperscaling. In\nthe case of a one-dimensional transverse field Ising model, we derive the\nspecific scaling form of the free energy. It follows from this scaling form\nthat the singular temperature dependence at the critical field has a vanishing\nprefactor but the singular field dependence at zero temperature is realized.\nFor the spin-density-wave model above its upper critical dimension, we show\nthat the dangerously irrelevant quartic coupling comes into the free energy in\na delicate way but in the end yields only subleading contributions beyond\nhyperscaling. We conclude that entropy accumulation near quantum critical point\nis a robust property of both models.\n