Diagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains

TL;DR

This paper demonstrates that diagonal entropy effectively detects topological phase transitions in extended Kitaev chains, offering a basis-independent quantum-informatic method to characterize topological order.

Contribution

It introduces the use of diagonal entropy density and block scaling law to identify topological phase transitions, even with higher winding numbers, in extended Kitaev chains.

Findings

Diagonal entropy shows volume effect and can identify critical points.

Diagonal entropy density is basis-independent and detects topological transitions.

Global entanglement fails to clearly indicate topological phase transitions.

Abstract

We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and Majorana zero modes. Both the finite size scaling law and block scaling law of the diagonal entropy are studied, which indicates that the diagonal entropy demonstrates volume effect. The parameter of volume term is regarded as the diagonal entropy density, which can identify the critical points of symmetry-protected topological phase transitions efficiently in the studied models, even for those with higher winding numbers. The formulation of block scaling law and the capability of diagonal entropy density in detecting topological phase transitions are independent of the chosen bases. In order to manifest the advantage of diagonal entropy, we also calculate the global entanglement, which can not show clear signatures of the topological phase transitions. This work provides a new quantum-informatic approach to characterize the feature of the topologically ordered states and may motivate a deep understanding of the quantum coherence and diagonal entropy in various condensed matter systems.