We explore the behavior of the disconnected entanglement entropy (DEE) across the topological phases of a long-range interacting Kitaev chain where the long-range interactions decay as a power law with an exponent $\ensuremath{\alpha}$. We show that while the DEE may not remain invariant deep within the topologically nontrivial phase when $\ensuremath{\alpha}<1$, it nevertheless shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition. We also study the time evolution of the DEE after a sudden quench of the chemical potential within the same phase. In the short-range limit of a finite chain, the DEE is expected to remain constant up to a critical time after the quench, which diverges in the thermodynamic limit. However, no such critical time is found to exist when the long-range interactions dominate (i.e., $\ensuremath{\alpha}<1$).We explore the behavior of the disconnected entanglement entropy (DEE) across the topological phases of a long-range interacting Kitaev chain where the long-range interactions decay as a power law with an exponent $\ensuremath{\alpha}$. We show that while the DEE may not remain invariant deep within the topologically nontrivial phase when $\ensuremath{\alpha}<1$, it nevertheless shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition. We also study the time evolution of the DEE after a sudden quench of the chemical potential within the same phase. In the short-range limit of a finite chain, the DEE is expected to remain constant up to a critical time after the quench, which diverges in the thermodynamic limit. However, no such critical time is found to exist when the long-range interactions dominate (i.e., $\ensuremath{\alpha}<1$).

arXiv:2111.03506Physical review. B./Physical review. BFeb 4, 202218 citations

Detecting topological phase transitions in long range interacting Kitaev chain through the entanglement between disconnected partitions

Saikat Mondal, Souvik Kumar Bandyopadhyay, Sourav Bhattacharjee +1 more

We explore the behavior of the disconnected entanglement entropy (DEE) across the topological phases of a long range interacting Kitaev chain where the long range interactions decay as a power law with an exponent $\alpha$ . We show that while the DEE may not remain invariant deep within the topologically non-trivial phase when $\alpha<1$ , it still shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition for the long range interacting systems. We also study the time evolution of the disconnected entanglement entropy after a sudden quench of chemical potential within same phase. In the short range limit of a finite chain, the DEE is expected to remain constant upto a critical time which diverges in the thermodynamic limit. However, we find that no such critical time exists in the presence of long range interactions ( $\alpha<1$ ).We explore the behavior of the disconnected entanglement entropy (DEE) across the topological phases of a long range interacting Kitaev chain where the long range interactions decay as a power law with an exponent $\alpha$. We show that while the DEE may not remain invariant deep within the topologically non-trivial phase when $\alpha<1$, it still shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition for the long range interacting systems. We also study the time evolution of the disconnected entanglement entropy after a sudden quench of chemical potential within same phase. In the short range limit of a finite chain, the DEE is expected to remain constant upto a critical time which diverges in the thermodynamic limit. However, we find that no such critical time exists in the presence of long range interactions ($\alpha<1$).

Nov 5, 20211 citation

One-dimensional p-wave superconductivity with long-range hopping and pairing

Ansari, S, Rouhollah Jafari

In this paper, we have considered the extended version of the Kitaev model in one dimension, i.e., a long-range p-wave superconducting wire. In the long-range Kitaev chain, the superconducting hopping and pairing terms in the Hamiltonian decay, independently, in a power-law fashion , where l is the distance between the two sites and x is some positive constant. We have studied the appearance of Majorana zero-energy edge modes and also, massive Dirac edge modes by exact diagonalization, as well as analytical computations. Exact diagonalization indicates the existence of both kinds of massless and massive edge modes in the energy spectrum. Furthermore, we obtain the phase diagram and the topological phase transitions by calculating the winding number, which is the topological invariant.In this paper, we have considered the extended version of the Kitaev model in one dimension, i.e., a long-range p-wave superconducting wire. In the long-range Kitaev chain, the superconducting hopping and pairing terms in the Hamiltonian decay, independently, in a power-law fashion , where l is the distance between the two sites and x is some positive constant. We have studied the appearance of Majorana zero-energy edge modes and also, massive Dirac edge modes by exact diagonalization, as well as analytical computations. Exact diagonalization indicates the existence of both kinds of massless and massive edge modes in the energy spectrum. Furthermore, we obtain the phase diagram and the topological phase transitions by calculating the winding number, which is the topological invariant.

Iranian Journal of Physics ResearchJul 1, 20200 citations

\alpha

. We show that while the DEE may not remain invariant deep within the topologically non-trivial phase when

\alpha<1

, it still shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition for the long range interacting systems. We also study the time evolution of the disconnected entanglement entropy after a sudden quench of chemical potential within same phase. In the short range limit of a finite chain, the DEE is expected to remain constant upto a critical time which diverges in the thermodynamic limit. However, we find that no such critical time exists in the presence of long range interactions (

\alpha<1