Quantum coherence of an XY spin chain with Dzyaloshinskii-Moriya interaction and quantum phase transition

Abstract

We investigate the quantum coherence of an XY spin chain with Dzyaloshinskii–Moriya interaction using a quantum renormalization group-based method, and show that the relative entropy of coherence increases with Dzyaloshinskii–Moriya interaction strength at zero temperature, as well as at finite temperature. We also study the quantum criticality of the system by making use of the relative entropy of coherence and violation of Bell inequality, and find that the first derivatives of the renormalized quantum coherence exhibit singularity near the critical point of the quantum phase transition. Finally, we explore the finite-size scaling behaviors of the derivatives of the quantum coherence at the critical point of the quantum phase transition, and obtain several universal finite-size scaling laws.

Correlation between quantum entanglement and quantum coherence in the case of XY spin chains with the Dzyaloshinskii-Moriya interaction

“…The type of connection between entanglement and coherence will be explored in the case of the XY Heisenberg model with two types of anisotropy. Both of the considered Hamiltonians will include the DM interaction, as it was already proven that it gives rise to coherence [43]. One may say that its presence is non-negligible in various systems, such as CsCuCl 3 and FeBO 3 [50,51] and it is thus frequently theoretically explored [52][53][54].…”

“…(the same Hamiltonian was previously used in [42,43]), where J is the nearest neighbour coupling constant, γ anisotropy parameter, D z-component of the strength of the DM interaction and σ α i (α = x, y) are Pauli matrices for the ith site defined as:…”

“…Since spin models are used to describe a variety of different physical problems, such as the properties of magnetic compounds [26][27][28][29][30], quantum Hall systems [31,32], Josephson junction arrays [33], quantum phase transitions [34][35][36][37][38] etc., it is clear that quantum information is no exception. Nowadays, XY and XYZ spin chains [39,40] are of significant interest, especially the ones frustrated with the Dzyaloshinskii-Moriya interaction (DM interaction) [41][42][43][44][45]. In this paper, the XY model with the DM interaction will be considered for systems based on three 1/2-spins.…”

“…In this paper, the XY model with the DM interaction will be considered for systems based on three 1/2-spins. Quantum renormalization group is a significant tool which helps one to observe the appearance of quantum phase transitions [42][43][44]. However, in this article it will be used to check the validity of the conclusions obtained in the case of larger systems (containing several spin-blocks).…”

Basis-independent quantum coherence and its distribution

“…In the seminal work of Baumgratz, Cramer, and Plenio [4], this was achieved by defining central concepts such as incoherent states, maximally coherent states and incoherent operations. In a short time rapid developments have been made in the basic theory of quantum coherence [5][6][7][8][9][10][11][12] and its applications [13][14][15][16][17]. On the application side the major focus has been on using quantum coherence for investigating quantum state merging [18], in assisted subspace discrimination [19] and identifying quantum phase transitions [20][21][22][23][24][25] in many body systems.…”