Ground state overlap and quantum phase transitions

Zanardi, Paolo; Paunković, Nikola

doi:10.1103/physreve.74.031123

Cited by 794 publications

(1,037 citation statements)

References 27 publications

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“…This sort of behavior has been observed in all the systems analyzed in Refs [5]- [9] and does amount to the critical fidelity drop at the QPTs. As we will show in the next section, in general the converse result i.e., QPT→ super-extensive growth of ds 2 (L) does not hold true: Q µν /L d can be finite in the thermodynamic limit even for gapless systems.…”

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confidence: 56%

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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confidence: 56%

Quantum Critical Scaling of the Geometric Tensors

2007

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“…In order to gain a better insight into the effect of the threshold couplings for the quantum system, in our final analysis we adopt the method of wavefunction overlaps [12,13]. If a system admits a quantum phase transition, then two states belonging to different phases of the same system are distinguishable.…”

Section: Wavefunction Overlapsmentioning

confidence: 99%

“…However other characterisations of quantum criticality have been sought too [10,11]. Recently the notion of wavefunction overlaps (also known as the fidelity), which is again common in quantum information theory, has been applied to the study of quantum phase transitions [12,13]. An advantage of this approach is its universality, as it can be applied to any system independent of the choice of decomposition into subsystems.…”

Section: Introductionmentioning

confidence: 99%

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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“…In another direction, one should use dcq Turing machines for developing the theory and applications of prefix-free quantum Kolomogorov complexity, possibly with bounded resources (including space), and comparing these notions with physical measures of the complexity of quantum states, like fidelity [21]. In due course, one should extend our approach to dcq machines acting on density operators instead of pure quantum states.…”

Section: Discussionmentioning

confidence: 99%

Universality of quantum Turing machines with deterministic control

Mateus

Sernadas

Souto

2015

J Logic Computation

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A simple notion of quantum Turing machine with deterministic, classical control is proposed and shown to be powerful enough to compute any unitary transformation which is computable by a finitely generated quantum circuit. An efficient universal machine with the s-m-n property is presented. The BQP class is recovered. A robust notion of plain Kolmogorov complexity of quantum states is proposed and compared with those previously reported in the literature.

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Ground state overlap and quantum phase transitions

Cited by 794 publications

References 27 publications

Quantum Critical Scaling of the Geometric Tensors

Quantum Critical Scaling of the Geometric Tensors

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

Universality of quantum Turing machines with deterministic control

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