2013/01/31 by Aavishkar A. Patel, Shraddha Sharma, Amit Dutta · 1 citation
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #quant-ph
paper · pdf · doi:10.1209/0295-5075/102/46001
published as EPL, 102 (2013) 46001 · 6 pages, 3 figures
arxiv created 2013/04/08 · openalex publication_date 2013/05/01 · arxiv updated 2013/06/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.