Role of marginality in quantum fidelity and Loschmidt echo: Dirac points in 2-D
Department of Physics, Indian Institute of Technology Kanpur - Kanpur 208016, India
Received: 6 March 2013
Accepted: 3 May 2013
We investigate the effect of marginality on the ground-state fidelity and Loschmidt echo. For this purpose, we study the above quantities near the quantum critical point (QCP) of the two-dimensional (2-D) Dirac Hamiltonian in the presence of a mass term which is tuned to zero at the Dirac point. An ideal example would be that of the low-energy carriers in graphene in which a mass term opens up a band gap. This happens to be a marginal situation where the behavior of the fidelity and the echo is markedly different as compared to that in the one-dimensional case. We encounter this marginal behavior near the Dirac point, which is displayed in the absence of a sharp dip in the ground-state fidelity (or equivalently in the logarithmic scaling of the fidelity susceptibility). Most importantly, there is also a logarithmic correction to the proposed scaling of the fidelity in the thermodynamic limit which cannot be a priori anticipated from the predicted scaling form. Interestingly, a sharp dip in the ground-state Loschmidt echo is also found to be absent near this QCP, which is again a consequence of the marginality. We also explain the absence of a sharp dip in both the fidelity and the Loschmidt echo close to the QCP in dimensions greater than two.
PACS: 64.70.Tg – Quantum phase transitions / 03.65.Pm – Relativistic wave equations
© EPLA, 2013