Entanglement in a simple quantum phase transition

Osborne, Tobias J.; Nielsen, Michael A.

doi:10.1103/physreva.66.032110

Cited by 1,489 publications

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References 53 publications

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“…1. From the equations (7,8) we can determine there are fixed point bifurcations for certain choices of the coupling parameters. These bifurcations allow us to divide the coupling parameter space into different regions.…”

Section: Casementioning

confidence: 99%

“…ground-state) phases in manybody quantum systems, due largely to a cross fertilisation of ideas between the condensed matter theory and the quantum information theory communities. Much of this study has explored the relationship between entanglement and quantum criticality [7][8][9]. However other characterisations of quantum criticality have been sought too [10,11].…”

Section: Introductionmentioning

confidence: 99%

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Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

et al. 2007

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We study a three-mode Hamiltonian modelling a heteronuclear molecular BoseEinstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classical analogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wavefunction overlaps to clarify the nature of the ground-state phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance.

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Section: Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

et al. 2007

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“…Traditionally such a problem is addressed by resorting to notions like order-parameter and symmetry breaking i.e., the Landau-Ginzburg paradigm [2]. In the last few years a big effort has been devoted to the analysis of QPTs from the perspective of Quantum Information [3] the main tool being the study of different entanglement measures [4].…”

mentioning

confidence: 99%

Quantum Critical Scaling of the Geometric Tensors

2007

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Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a suffcient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analisys is further checked by exact diagonalisation of the spin-1/2 XXZ Heisenberg chain.

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“…Also, the study of entanglement has attracted much attention within the last few years, as entangled systems play an important role in many different research areas such as quantum information technology [15] and quantum phase transitions [16]. Particularly the research activity has expanded towards investigating the entanglement properties in various systems composed of interacting particles.…”

Section: Introductionmentioning

confidence: 99%

Quantum Entanglement of Two Harmonically Trapped Dipolar Particles

Kościk

2015

Few-Body Syst

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We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other in regard to aspects of their entanglement.

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Entanglement in a simple quantum phase transition

Cited by 1,489 publications

References 53 publications

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

Emergent quantum phases in a heteronuclear molecular Bose–Einstein condensate model

Quantum Critical Scaling of the Geometric Tensors

Quantum Entanglement of Two Harmonically Trapped Dipolar Particles

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