Three-Body Problem of
 H
 +
 2
 Ion

Lin, Qi-Hu; Ren, Zhongzhou

doi:10.1088/0253-6102/57/2/09

Cited by 3 publications

(5 citation statements)

References 19 publications

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“…Then the parameter b qe expresses the effect of "quantum entanglement". This quantum fluctuation appears only in quantum systems, and it is used as an order parameter of quantum systems at zero temperature in many cases [17][18][19][20][21][22]. The temperature dependences of b d1 , b cf , b qe and b d2 are shown in Fig.2.…”

Section: Equilibrium Systems Without External Fields (Hmentioning

confidence: 99%

“…From the definition of the entanglement entropy (6), it is easily understood that S A includes the original fluctuation of the partial system A. The above studies [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] do not separate the fluctuations, namely the original fluctuations and the entanglement fluctuations. In addition, the entanglement entropy is not a physical parameter defined by eigenvalues of unitary operators, such as magnetization, but a status of states.…”

Section: Quantum Entanglementmentioning

confidence: 99%

“…The quantum entanglement plays an important role in quantum computations [9,10], and it is useful in applications of the AdS/CFT correspondence [12][13][14][15][16]. On the other hand, in some statistical studies of quantum spin systems, the entanglement entropy is used as an order parameter [17][18][19][20][21][22][23]. In addition, how the entanglement entropy corresponds to the classical one has been studied [24] using the Suzuki-Trotter transformation [25].…”

Section: Quantum Entanglementmentioning

confidence: 99%

“…On the other hand, the symbol |+ +|| − −| means that the spin A takes the state |+ +| in the original space different from the state | − −| in the tilde space.Then the parameter b qe expresses the effect of "quantum entanglement". This quantum fluctuation appears only in quantum systems, and it is used as an order parameter of quantum systems at zero temperature in many cases[17][18][19][20][21][22]. The temperature dependences of b d1 , b cf , b qe and b d2 are shown in Fig.2.…”

mentioning

confidence: 99%

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Understanding quantum entanglement by thermo field dynamics

Hashizume

Suzuki

2013

Physica A: Statistical Mechanics and its Applications

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We propose a new method to understand quantum entanglement using the thermo field dynamics (TFD) described by a double Hilbert space. The entanglement states show a quantum-mechanically complicated behavior. Our new method using TFD makes it easy to understand the entanglement states, because the states in the tilde space in TFD play a role of tracer of the initial states. For our new treatment, we define an extended density matrix on the double Hilbert space. From this study, we make a general formulation of this extended density matrix and examine some simple cases using this formulation. Consequently, we have found that we can distinguish intrinsic quantum entanglement from the thermal fluctuations included in the definition of the ordinary quantum entanglement at finite temperatures. Through the above examination, our method using TFD can be applied not only to equilibrium states but also to non-equilibrium states. This is shown using some simple finite systems in the present paper.Comment: 24 pages, 6 figures accepted by Physica A (in press

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Section: Equilibrium Systems Without External Fields (Hmentioning

confidence: 99%

Section: Quantum Entanglementmentioning

confidence: 99%

Section: Quantum Entanglementmentioning

confidence: 99%

mentioning

confidence: 99%

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Understanding quantum entanglement by thermo field dynamics

Hashizume

Suzuki

2013

Physica A: Statistical Mechanics and its Applications

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“…A quench scenario is considered thereafter, where we couple our model to a spin half system, and compute the LE. Thereafter, using the density matrix renormalisation group methods [2,[30][31][32], we compute the entanglement entropy, and find sharp jumps across both first order and second order phase transitions, a result that is in contradiction to the ones known in the literature, namely that the EE shows discontinuity at a first-order QPT, while a cusp or a kink in the EE indicates the second-order QPT [33,34]. Finally, we also consider multiple global quench scenarios in the model and contrast this with such quenches in the transverse XY model.…”

Section: Introductionmentioning

confidence: 99%

Complexity and quenches in models with three and four spin interactions

Gautam¹,

Jaiswal²,

Gill³

et al. 2022

Preprint

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We study information theoretic quantities in models with three and four spin interactions. These models show distinctive characteristics compared to their nearest neighbour counterparts. Here, we quantify these in terms of the Nielsen complexity in static and quench scenarios, the Fubini-Study complexity, and the entanglement entropy. The models that we study have a rich phase structure, and we show how the difference in the nature of phase transitions in these, compared to ones with nearest neighbour interactions, result in different behaviour of information theoretic quantities, from ones known in the literature. For example, the derivative of the Nielsen complexity does not diverge but shows a discontinuity near continuous phase transitions, and the Fubini-Study complexity may be regular and continuous across such transitions. The entanglement entropy shows a novel discontinuity both at first and second order quantum phase transitions. We also study multiple quench scenarios in these models and contrast these with quenches in the transverse XY model.

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