Block entropy and quantum phase transition in the anisotropic Kondo necklace model

Mendoza‐Arenas, J. J.; Franco, R.; Silva–Valencia, J.

doi:10.1103/physreva.81.062310

Cited by 15 publications

(11 citation statements)

References 35 publications

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“…Besides the determination of order parameters, quantities such as gaps, spatial correlation functions, and structure factors are commonly used to determine the quantum critical points of several models. Remarkably, a few years ago it was realized that entanglement plays a fundamental role in critical phenomena and that different measures of entanglement can be used to determine the location of several types of QPTs [9][10][11][12][13][14][15][16][17][18][19][20][21]. Furthermore, the relation of Bell inequalities and criticality has been recently explored [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

et al. 2016

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In the present paper we introduce a way of identifying quantum phase transitions of many-body systems by means of local time correlations and Leggett-Garg inequalities. This procedure allows us to experimentally determine the quantum critical points not only of finite-order transitions but also those of infinite order, as the Kosterlitz-Thouless transition that is not always easy to detect with current methods. By means of simple analytical arguments for a general spin-1/2 Hamiltonian, and matrix product simulations of one-dimensional XXZ and anisotropic XY models, we argue that finite-order quantum phase transitions can be determined by singularities of the time correlations or their derivatives at criticality. The same features are exhibited by corresponding Leggett-Garg functions, which noticeably indicate violation of the Leggett-Garg inequalities for early times and all the Hamiltonian parameters considered. In addition, we find that the infinite-order transition of the XXZ model at the isotropic point can be revealed by the maximal violation of the Leggett-Garg inequalities. We thus show that quantum phase transitions can be identified by purely local measurements and that many-body systems constitute important candidates to observe experimentally the violation of Leggett-Garg inequalities.

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Section: Introductionmentioning

confidence: 99%

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

et al. 2016

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“…Based on many analytical and numerical studies, it is well established that for the 1D Kondo necklace model, its ground-state is a gapped Kondo spin singlet state for all value of J/t except for J = 0. [21][22][23][24]32,33 However, we should remind the reader that the Kondo necklace model cannot be derived from the original Kondo lattice model at half-filling but could only be considered as a phenomenological model devised for studying the low-lying spin excitations.…”

Section: Three Limit Situationsmentioning

confidence: 99%

Kondo spin liquid in the Kondo necklace model: Classical disordered phase versus symmetry-protected topological state

Zhong

Wang

et al. 2014

Physica B: Condensed Matter

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We study possible topological features of Kondo spin liquid phase in terms of the one-and twodimensional Kondo necklace models within the frame work of quantum O(N) non-liner sigma model (NLSM). In the one-dimensional case, it is found that the bulk properties of the Kodno spin liquid phase are similar to the well-known Haldane phase at strong coupling fixed point. The difference between them mainly comes from their boundaries due to the effect of the topological term. In the two-dimensional case, the system can be mapped onto an O(4)-like NLSM with some O(3) anisotropy. Interestingly, we find that if hedgehog-like point defects are included together with the restoration of the full O(4) symmetry, our model is identical to a kind of SU(2) symmetryprotected topological (SPT) state. Additionally, if the system has the O(5) symmetry instead, the effective NLSM with Wess-Zumino-Witten term is just a description of the surface modes of a threedimensional SPT state, though such O(5) NLSM could not be a proper description of Kondo spin liquid phase due to its gaplessness. We expect that the discussions might provide useful threads to identify certain microscopic bilayer antiferromagnet models (and related materials), which can support the desirable SPT states.

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“…In recent years, many efforts have been made to comprehend the relation between entanglement and quantum phase transitions [1][2][3][4]. An obvious advantage in determining quantum critical points using measures of entanglement is that we do not require a priori knowledge of the order parameter and the symmetries of the system.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

Solano-Carrillo

Franco

Silva–Valencia

2011

Physica A: Statistical Mechanics and its Applications

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Block entropy and quantum phase transition in the anisotropic Kondo necklace model

Cited by 15 publications

References 35 publications

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

Kondo spin liquid in the Kondo necklace model: Classical disordered phase versus symmetry-protected topological state

Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

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