arXiv subjects

Atanu Rajak

Publications and source records attributed to Atanu Rajak.

23 records · Page 2Linked to original sources

arXiv2015

Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model

We study the critical behavior of Sherrington-Kirkpatrick model in transverse field (at finite temperature) using Monte Carlo simulation and exact diagonalization (at zero temperature). We determine the phase diagram of the model by estimating the Binder cumulant. We also determine the correlation length exponent from the collapse of the scaled data. Our numerical studies here indicate that critical Binder cumulant (indicating the universality class of the transition behavior) and the correlation length exponent cross over from their `classical' to `quantum' values at a finite temperature (unlike the cases of pure systems where such crossovers occur at zero temperature). We propose a qualitative argument supporting such an observation, employing a simple tunneling picture.

cond-mat.stat-mech↗

arXiv2015

Possibility of adiabatic transport of a Majorana edge state through an extended gapless region

In the context of slow quenching dynamics of a $p$-wave superconducting chain, it has been shown that a Majorana edge state can not be adiabatically transported from one topological phase to the other separated by a quantum critical line. On the other hand, the inclusion of a phase factor in the hopping term, that breaks the extended time reversal invariance, results in an extended gapless region between two topological phases. We show that for a finite chain with an open boundary condition there exists a non-zero probability that an edge Majorana can be adiabatically transported from one topological phase to the other across this gapless region following a slow quench of the superconducting term; this happens for an optimum transit time, that is proportional to the system size and diverges for a thermodynamically large chain. We attribute this phenomenon to the mixing of the Majorana only with low-lying inverted bulk states.

cond-mat.mes-hall↗

arXiv2014

Fidelity susceptibility and Loschmidt echo for generic paths in a three spin interacting transverse Ising model

We study the effect of presence of different types of critical points such as ordinary critical point, multicritical point and quasicritical point along different paths on the Fidelity susceptibility and Loschmidt echo of a three spin interacting transverse Ising chain using a method which does not involve the language of tensors. We find that the scaling of fidelity susceptibility and Loschmidt echo with the system size at these special critical points of the model studied, is in agreement with the known results, thus supporting our method.

cond-mat.stat-mech↗

arXiv2014

Survival probability of an edge Majorana in a 1-D p-wave superconducting chain under sudden quenching of parameters

We consider the temporal evolution of a zero energy edge Majorana of a spinless $p$-wave superconducting chain following a sudden change of a parameter of the Hamiltonian. Starting from one of the topological phases that has an edge Majorana, the system is suddenly driven to the other topological phase or to the (topologically) trivial phases and also to the quantum critical points (QCPs) separating these phases. The survival probability of the initial edge Majorana as a function of time is studied following the quench. Interestingly when the chain is quenched to the QCP, we find a nearly perfect oscillations of the survival probability, indicating that the Majorana travels back and forth between two ends, with a time period that scales with the system size. We also generalize to the situation when there is a next-nearest-neighbor hopping in superconducting chain and there resulting in a pair of edge Majorana at the each end of the chain in the topological phase. We show that the frequency of oscillation of the survival probability gets doubled in this case. We also perform an instantaneous quenching the Hamiltonian (with two Majorana modes at each end of the chain) to an another Hamiltonian which has only one Majorana mode in equilibrium; the MSP shows oscillations as a function of time with a noticeable decay in the amplitude. On the other hand for a quenching which is reverse to the previous one, the MSP decays rapidly and stays close to zero with fluctuations in amplitude.

cond-mat.mes-hall↗

arXiv2012

Study of Loschmidt Echo for two-dimensional Kitaev model

In this paper, we study the Loschmidt Echo (LE) of a two-dimensional Kitaev model residing on a honeycomb lattice which is chosen to be an environment that is coupled globally to a central spin. The decay of LE is highly influenced by the quantum criticality of the environmental spin model e.g., it shows a sharp dip close to the anisotropic quantum critical point (AQCP) of its phase diagram. The early time decay and the collapse and revival as a function of time at AQCP do also exhibit interesting scaling behavior with the system size which is verified numerically. It has also been observed that the LE stays vanishingly small throughout the gapless phase of the model. The above study has also been extended to the 1D Kitaev model i.e. when one of the interaction terms vanishes.

cond-mat.stat-mech↗