Quantum coherence and quantum phase transitions

Li, Yanchao; Lin, Hai‐Qing

doi:10.1038/srep26365

Cited by 83 publications

(36 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This indicates that the DWF could be a good alternative to correlation measures that involve extremization procedures due to the comparative simplicity in its calculation and its easy physical interpretation following Eq. (13). Looking at ∂ 2 ∆ W M of the DWF in the inset of Fig.…”

Section: B the Xxz Modelmentioning

confidence: 98%

Discrete and generalized phase space techniques in critical quantum spin chains

2019

View full text Add to dashboard Cite

We apply the Wigner function formalism from quantum optics via two approaches, Wootters' discrete Wigner function and the generalized Wigner function, to detect quantum phase transitions in critical spin-1 2 systems. We develop a general formula relating the phase space techniques and the thermodynamical quantities of spin models, which we apply to single, bipartite and multi-partite systems governed by the XY and the XXZ models. Our approach allows us to introduce a novel way to represent, detect, and distinguish first-, second-and infiniteorder quantum phase transitions. Furthermore, we show that the factorization phenomena of the XY model is only directly detectable by quantities based on the square root of the bipartite reduced density matrix. We establish that phase space techniques provide a simple, experimentally promising tool in the study of many-body systems and we discuss their relation with measures of quantum correlations and quantum coherence.

show abstract

Section: B the Xxz Modelmentioning

confidence: 98%

Discrete and generalized phase space techniques in critical quantum spin chains

2019

View full text Add to dashboard Cite

show abstract

“…Such developments led to number of applications using coherence as a basic ingredient in various fields such as quantum communication [30] and in farther other arenas, such as thermodynamics [31] and even certain branches of biology [32]. Few works were dedicated to study quantum coherence in condensed matter systems [33,34,35,36]. In fact, the investigations that were carried out in spin chains like the XY model had the sole purpose of revealing the connection between quantum coherence and quantum phase transitions.…”

mentioning

confidence: 99%

Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain

Mzaouali

Baz

2019

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin-1 2 XX chain. Following the Jordan-Wigner mapping, we diagonalise the hamiltonian of the chain and we check this procedure numerically as well. Using the "Pauli basis expansion" formalism we get the pairwise quantities studied in this work at any distance. We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing.plays an important role in identifying quantum phase transitions [8,20], quantum discord has received much attention in this regard as well [21,22]. Moreover, it was applied in several contexts like open quantum systems [23], quantum dynamics [24] and even biophysics [25].Recently, the concept of quantum coherence has received much attention in the quantum information community as it plays an essential role in phenomena like quantum interference, bipartite and multipartite entanglement [26]. Various schemes were proposed for detecting coherence [27,28], but it was never quantified in the language of quantum information theory until the seminal work of Baumgratz, Cramer and Plenio [29] in which they constructed a quantitative theory that captures the resource character of coherence in a mathematically rigorous fashion. Such developments led to number of applications using coherence as a basic ingredient in various fields such as quantum communication [30] and in farther other arenas, such as thermodynamics [31] and even certain branches of biology [32]. Few works were dedicated to study quantum coherence in condensed matter systems [33,34,35,36]. In fact, the investigations that were carried out in spin chains like the XY model had the sole purpose of revealing the connection between quantum coherence and quantum phase transitions. These studies has shown the role played by coherence in detecting important features like critical points, but it is still early to say how efficient quantum coherence is in detecting quantum phase transitions as the field needs more models and measures to investigate these connections.Motivated by these developments, the aim of this paper is to study and compare the behavior of non-nearest quantum coherence, quantum and classical correlations in an infinite 1D spin-1 2 XX chain in the presence of a magnetic field. This is an analytically solvable model by means of the Jordan-Wigner transformation which we check numeric...

show abstract

“…Investigations on the role of quantum coherence in thermodynamic processes [24][25][26], assisted subspace discrimination [27], quantum state merging [28] and in the generation of gaussian entanglement [29] have been carried out. Currently there is a lot of interest in applying the procedure of quantifying coherence and relating them to experimental quantities in feasible systems like Bose-Einstein condensates [30,31], cavity optomechanical system [32,33] and spin systems [34][35][36][37][38][39].In Ref.[4] the set of properties a functional should satisfy in order to be considered as a coherence measure were proposed. Based on these developments several functions were introduced to serve as measures of coherence [4,[40][41][42][43][44][45][46][47].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions

Radhakrishnan

Parthasarathy

Jambulingam

et al. 2017

Sci Rep

View full text Add to dashboard Cite

We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The σ z σ z interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and find similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.Quantum coherence is one of the central concepts in quantum physics, and hence its detection and quantification is a fundamental task. Traditionally, the distinction between quantum and classical coherence is made using phase space distributions 1,2 and higher order correlation functions 3 . While this gives some insight into the nature of coherence, these techniques do not quantify coherence in a rigorous sense. Recently a scheme for measuring coherence was developed by Baumgratz and co-workers in ref. 4 based on the framework of quantum information theory. Fundamental quantities such as incoherent states, maximally coherent states and incoherent operations which are needed for the development of the procedure were introduced and analyzed. Rapid developments have been made in understanding the theory of quantum coherence through numerous works 5-16 and in using it as a resource in quantum information theory [17][18][19][20][21][22][23] . Investigations on the role of quantum coherence in thermodynamic processes [24][25][26] , assisted subspace discrimination 27 , quantum state merging 28 and in the generation of gaussian entanglement 29 have been carried out. Currently there is a lot of interest in applying the procedure of quantifying coherence and relating them to experimental quantities in feasible systems like Bose-Einstein condensates 30,31 , cavity optomechanical system 32,33 and spin systems [34][35][36][37][38][39] .In ref. 4 the set of properties a functional should satisfy in order to be considered as a coherence measure were proposed. Based on these developments several functions were introduced to serve as measures of coherence 4,40-47 . All these measures of coherence can be broadly classified into either the entropic or the geometric class of measures. This depends on whether the measure is based on the entropy functional or has a metric nature which can give rise to a geometric structure. A mathematical functional is deemed to be a metric if it obeys the axioms of distance and satisfies the triangle inequality. In ref. 47 we introduced a new...

show abstract

Quantum coherence and quantum phase transitions

Cited by 83 publications

References 46 publications

Discrete and generalized phase space techniques in critical quantum spin chains

Discrete and generalized phase space techniques in critical quantum spin chains

Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain

Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions

Contact Info

Product

Resources

About