Moir\'{e} pattern of spin liquid and Neel magnet in a Kitaev chain

TL;DR

This paper explores moiré patterns in a dimerized Kitaev spin chain with a periodic transverse field, revealing alternating magnetic and spin liquid phases and proposing a method to detect these patterns via Loschmidt echo measurements.

Contribution

It provides an exact solution for the ground states of a dimerized Kitaev chain with a periodic field and introduces a dynamic detection scheme for moiré fringes.

Findings

Alternating Neel and spin liquid phases along the chain.

Long beat period of phase alternation due to slight period mismatch.

Proposed detection method using Loschmidt echo measurements.

Abstract

A moir\'{e} pattern occurs when two periodic structures in a system have a slight mismatch period, resulting the coexistence of distinct phases in different large-scale spacial regions of the same system. Two periodic structures can arise from periodic electric and magnetic fields, respectively. We investigated the moir\'{e} pattern via a dimerized Kitaev spin chain with a periodic transverse field, which can be mapped onto the system of dimerized spinless fermions with p-wave superconductivity. The exact solution for staggered field demonstrated that the ground state has two distinct phases: (i) Neel magnetic phase for nonzero field, (ii) Spin liquid phase due to the emergence of isolated flat Bogoliubov--de Gennes band for vanishing field. We computed the staggered magnetization and local density of states (\textrm{LDOS}) for the field with a slight difference period to the chain lattice. Numerical simulation demonstrated that such two phases appear alternatively along the chain with a long beat period. Additionally, we proposed a dynamic scheme to detect the Moir\'{e} fringes based on the measurement of Loschmidt echo (\textrm{LE}) in the presence of local perturbation.