Ground state fidelity and quantum phase transitions in free Fermi systems

Zanardi, Paolo; Cozzini, Marco; Giorda, Paolo

doi:10.1088/1742-5468/2007/02/l02002

Cited by 102 publications

(139 citation statements)

References 14 publications

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“…The GS fidelity is defined as the overlap between two ground states with only slightly different values of the external parameters [8] and thus is a pure geometrical quantity. Since no a priori knowledge of the order parameter is needed, the fidelity might be a potential universal criteria for characterizing the QPTs [8,9,10,11,12,13,14,15]. An increasing interest has been drawn in the role of GS fidelity in detecting QPTs for various many-body systems [9,10,11,12,13,14,15], since Zanardi and Paunkovic first exploited it to identify QPTs in the XY spin chain [8] where the fidelity shows a narrow drop at the transition point.…”

Section: Introductionmentioning

confidence: 99%

“…Since no a priori knowledge of the order parameter is needed, the fidelity might be a potential universal criteria for characterizing the QPTs [8,9,10,11,12,13,14,15]. An increasing interest has been drawn in the role of GS fidelity in detecting QPTs for various many-body systems [9,10,11,12,13,14,15], since Zanardi and Paunkovic first exploited it to identify QPTs in the XY spin chain [8] where the fidelity shows a narrow drop at the transition point. Remarkably, the success of fidelity analysis in dealing with the Bose-Hubbard model [9] and spin systems [14,15] implies that it may have practical relevance even for more complicate strongly interacting systems where no a simple description is possible.…”

Section: Introductionmentioning

confidence: 99%

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Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition

et al. 2008

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The notion of fidelity in quantum information science has been recently applied to analyze quantum phase transitions from the viewpoint of the ground-state (GS) overlap for various many-body systems. In this work, we unveil the intrinsic relation between the GS fidelity and the derivatives of GS energy and find that they play equivalent role in identifying the quantum phase transition. The general connection between the two approaches enables us to understand the different singularity and scaling behaviors of fidelity exhibited in various systems on general grounds. Our general conclusions are illustrated via several quantum spin models which exhibit different kinds of QPTs.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition

et al. 2008

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“…It was studied conventionally by Landau paradigm with order parameter in the frame of statistics and condensed matter physics. Recently, two quantuminformation [2] concepts, entanglement [3,4,5,6,7,8,9,10,11,12,13] and fidelity [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] have been investigated extensively in QPTs and are recognized to be effective and powerful in detecting the critical point. The former measures quantum correlations between partitions, while the latter measures the distance in quantum state space.…”

Section: Introductionmentioning

confidence: 99%

Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model

Wang

2009

Phys. Rev. E

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We study the reduced fidelity susceptibility χr for an M -body subsystem of an N -body LipkinMeshkov-Glick model with τ = M/N fixed. The reduced fidelity susceptibility can be viewed as the response of subsystem to a certain parameter. In noncritical region, the inner correlation of the system is weak, and χr behaves similar with the global fidelity susceptibility χg, the ratio η = χr/χg depends on τ but not N . However, at the critical point, the inner correlation tends to be divergent, then we find χr approaches χg with the increasing the N , and η = 1 in the thermodynamic limit. The analytical predictions are perfect agreement with the numerical results.

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“…A generalization of this result, valid for the so-called geometric tensor, has been given in [4]. Previous works have characterized the pure XY spin chain using the fidelity approach [2,3,19,20] and the quantum Chernoff bound [21]. The mapping of the spin model onto the quasi-free fermion Hamiltonian [13],…”

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confidence: 99%

Fidelity Approach to the Disordered QuantumXYModel

et al. 2009

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We study the random XY spin chain in a transverse field by analyzing the susceptibility of the ground state fidelity, numerically evaluated through a standard mapping of the model onto quasifree fermions. It is found that the fidelity susceptibility and its scaling properties provide useful information about the phase diagram. In particular it is possible to determine the Ising critical line and the Griffiths phase regions, in agreement with previous analytical and numerical results.Introduction.-In the last few years concepts borrowed from quantum information theory have proven useful in characterizing the critical behavior of quantum manybody systems [1]. In particular, a geometric approach to the study of quantum phase transitions (QPTs), i.e. the fidelity analysis, has been shown to be an effective way of characterizing distinct phases of quantum systems [2,3,4,5,6,7,8]. Previously, the fidelity approach has been applied to a variety of homogeneous systems. In this work we extend these studies to disordered quantum systems. Specifically, we investigate the behavior of the fidelity susceptibility of the disordered XY model in a transverse field. It is well known that the presence of quenched disorder can have drastic effects on critical properties. The appearance of new universality classes and novel states of matter such as the Griffiths phase are two important examples [9,10,11,12]. The aim of the present work is to show what can be inferred about the physics of the disordered quantum system from the properties of the fidelity susceptibility.

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Ground state fidelity and quantum phase transitions in free Fermi systems

Cited by 102 publications

References 14 publications

Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition

Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition

Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model

Fidelity Approach to the Disordered QuantumXYModel

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