Quantum Critical Lines in the Ground State Phase Diagram of Spin‐1/2 Frustrated Transverse‐Field Ising Chains

Abstract

This paper focuses on the ground state phase diagram of a 1D spin‐1/2 quantum Ising model with competing first and second nearest neighbour interactions known as the axial next nearest neighbour Ising model in the presence of a transverse magnetic field. Here, using quantum correlations, both numerically and analytically, some evidence is provided to clarify the identification of the ground state phase diagram. Local quantum correlations play a crucial role in detecting the critical lines either revealed or hidden by symmetry‐breaking. A non‐symmetry‐breaking disorder transition line can be identified by the first derivative of both entanglement of formation and quantum discord between nearest neighbour spins. In addition, the quantum correlations between the second neighbour spins can also be used to reveal Kosterlitz–Thouless phase transition when their interaction strength grows and becomes closer to the first nearest neighbour one. The results obtained using the Jordan–Wigner transformation confirm the accuracy of the numerical case.

Entanglement and quantum correlations in the XX spin-1/2 honeycomb lattice

“…In recent years, powerful approaches based on the concepts borrowed from the quantum information theory 27 have been developed and intensively used to identify quantum critical points in different complex many-body systems 28 . In particular, the detailed analysis of various bipartite quantum correlations as the entanglement and the QD, has been successfully exploited to tackle many complicated problems 29 – 53 .…”

The Investigation of a Temperature and Field Characteristics of the One-dimensional Ising Model with Competing Exchange Interactions

“…Низкоразмерные магнитные системы привлекают к себе внимание ученых достаточно давно [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Модель Изинга имеет точное решение в одномерном и двумерном случае.…”