Ground State Entanglement in Spin Systems

Yano, H.; Nishimori, Hidetoshi

doi:10.1143/ptps.157.164

Cited by 8 publications

(10 citation statements)

References 2 publications

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“…In [48] a relation between the critical field h E c for entanglement creation and the critical field h E d at which entanglement dies was proposed. A relation that is in agreement with the results from the finite size systems [49]. For quantum discord however, the comportment is different.…”

Section: Entanglement and Quantum Discordsupporting

confidence: 86%

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

Mzaouali

Baz

2019

Physica A: Statistical Mechanics and its Applications

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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...

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Section: Entanglement and Quantum Discordsupporting

confidence: 86%

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

Mzaouali

Baz

2019

Physica A: Statistical Mechanics and its Applications

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“…It is notable that there is a relationship between h E c and h c . Our results show that the critical entangled-field is and was reported in finite size systems for the first time 36 . Here we explicitly showed that this phenomenon is also observed in the thermodynamic limit.…”

Section: The Modelsupporting

confidence: 69%

“…It has been shown that at zero temperature, the entanglement between the non-nearest neighbor spins becomes finite around the quantum critical field. The entanglement remains finite even if the distance between the spin pair reaches the system size 36 . The concurrence and the quantum discord for the 2N spins were also studied in the Ising and the XXZ spin chains 38 .…”

Section: Introductionmentioning

confidence: 99%

Magnetic entanglement in spin-1/2 XY chains

Fumani

Nemati

Mahdavifar

et al. 2016

Physica A: Statistical Mechanics and its Applications

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In the study of entanglement in a spin chain, people often consider the nearest-neighbor spins. The motivation is the prevailing role of the short range interactions in creating quantum correlation between the 1st neighbor (1N) spins. Here, we address the same question between farther neighbor spins. We consider the one-dimensional (1D) spin-1/2 XY model in a magnetic field. Using the fermionization approach, we diagonalize the Hamiltonian of the system. Then, we provide the analytical results for entanglement between the 2nd, 3rd and 4th neighbor (denoted as 2N, 3N, and 4N respectively) spins. We find a magnetic entanglement that starts from a critical entangled-field (h E c ) at zero temperature. The critical entangled-field depends on the distance between the spins. In addition to the analytical results, the mentioned phenomenon is confirmed by the numerical Lanczos calculations. By adding the temperature to the model, the magnetic entanglement remains stable up to a critical temperature, Tc. Our results show that entanglement spreads step by step to farther neighbors in the spin chain by reducing temperature. At first, the 1N spins are entangled and then further neighbors will be entangled respectively. Tc depends on the value of the magnetic field and will be maximized at the quantum critical field.

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“…In other words, there is a threshold transverse field h E c above which the 2nd neighbor spins become entangled at zero temperature. The entanglement which induced by an external magnetic field is known as the "magnetic entanglement" where reported for longitudinal magnetic fields [13,28,[59][60][61]. It is worthwhile to mention that, the phase transition at T = 0 is pinpointed by a global maximum of entanglement between both first and second neighbor spin pairs at the critical point ∆ c = 1.…”

Section: Resultsmentioning

confidence: 99%

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

Mahdavifar¹,

Jafari²

2017

Phys. Rev. A

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One-dimensional spin-1/2 systems are well-known candidates to study the quantum correlations between particles. In the condensed matter physics, studies often are restricted to the 1st neighbor particles. In this work, we consider the 1D XXZ model in a transverse magnetic field (TF) which is not integrable except at specific points. Analytical expressions for quantum correlations (entanglement and quantum discord) between spin pairs at any distance are obtained for both zero and finite temperature, using an analytical approach proposed by Caux et al. [PRB 68, 134431 (2003)]. We compare the efficiency of the QD with respect to the entanglement in the detection of critical points (CPs) as the neighboring spin pairs go farther than the next nearest neighbors. In the absence of the TF and at zero temperature, we show that the QD for spin pairs farther than the 2nd neighbors is able to capture the critical points while the pairwise entanglement is absent. In contrast to the pairwise entanglement, two-site quantum discord is effectively long-range in the critical regimes where it decays algebraically with the distance between pairs. We also show that the thermal quantum discord between neighbor spins possesses strong distinctive behavior at the critical point that can be seen at finite temperature and, therefore, spotlights the critical point while the entanglement fails in this task.

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Ground State Entanglement in Spin Systems

Cited by 8 publications

References 2 publications

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

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

Magnetic entanglement in spin-1/2 XY chains

Magnetic quantum correlations in the one-dimensional transverse-field XXZ model

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