arXiv subjects

Syed Tahir Amin

Publications and source records attributed to Syed Tahir Amin.

4 recordsLinked to original sources

arXiv2022

Information geometry of quantum critical submanifolds: relevant, marginal and irrelevant operators

We analyze the thermodynamical limit of the quantum metric along critical submanifolds of theory space. Building upon various results previously known in the literature, we relate its singular behavior to normal directions, which are naturally associated with relevant operators in the renormalization group sense. We formulate these results in the language of information theory and differential geometry. We exemplify our theory through the paradigmatic examples of the XY and Haldane models, where the normal directions to the critical submanifolds are seen to be precisely those along which the metric has singular behavior, while for the tangent ones it vanishes -- these directions lie in the kernel of the metric.

cond-mat.mes-hall↗

arXiv2021

Probing Band-center Anomaly with the Kernel Polynomial Method

We investigate the anomalous behavior of localization length of a non-interacting one-dimensional Anderson model at zero temperature. We report numerical calculations of the Thouless expression of localization length, based on the Kernel polynomial method (KPM), which has an O(N ) computational complexity, where N is the system size. The KPM results show an excellent agreement with perturbative result in large system size limit, confirming the validity of Thouless formula. Thus, contrary to the previous numerical results, the KPM approximation of the Thouless expression produce the correct localization length at the band center. The Thouless expression relates localization length in terms of density of states in a one-dimensional disordered system. By calculating the KPM estimates of density of states, we find a cusp-like behavior around the band center in the perturbative regime. This cusp-like singularity can not be obtained by an approximate analytical calculations with in the second-order approximations, reflects the band-center anomaly.

cond-mat.dis-nn↗

arXiv2019

Information geometric analysis of long range topological superconductors

The Uhlmann connection is a mixed state generalisation of the Berry connection. The latter has a very important role in the study of topological phases at zero temperature. Closely related, the quantum fidelity is an information theoretical quantity which is a measure of distinguishability of quantum states. Moreover, it has been extensively used in the analysis of quantum phase transitions. In this work, we study topological phase transitions in 1D and 2D topological superconductors with long-range hopping and pairing amplitudes, using the fidelity and the quantity $Δ$ closely related to the Uhlmann connection. The drop in the fidelity and the departure of $Δ$ from zero signal the topological phase transitions in the models considered. The analysis of the ground state fidelity susceptibility and its associated critical exponents are also applied to the study of the aforementioned topological phase transitions.

cond-mat.supr-con↗

arXiv2015

Practical Quantum Teleportation of an Unknown Quantum State

We develop a theory to teleport an unknown quantum state using entanglement between two distant parties. Our theory takes into account experimental limitations due to contribution of multi-photon pair production of parametric down conversion source, inefficiency and dark counts of detectors and channel losses. We use a linear optics setup for quantum teleportation of an unknown quantum state by performing Bell state measurement by the sender. Our theory successfully provides a model for experimentalists to optimize the fidelity by adjusting the experimental parameters. We apply our model to a recent experiment on quantum teleportation and the results obtained by our model are in good agreement with the experiment results.

quant-ph↗