Fidelity susceptibility approach to quantum phase transitions in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="italic">XY</mml:mi></mml:mrow></mml:math>spin chain with multisite interactions

Cheng, Wei‐Wen; Liu, J.-M.

doi:10.1103/physreva.82.012308

Cited by 32 publications

(12 citation statements)

References 40 publications

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“…2, in which we find that at some "magic point" when k = 2πn/N → k 0 , a "pulse" in these two quantities can be found. The analogous features can also be found in other extended models [58,[62][63][64]. The breakdown of this scaling also indicates the failure of Eq.…”

Section: Thus We Have ξsupporting

confidence: 70%

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Scaling of geometric phase and fidelity susceptibility across the critical points and their relations

et al. 2017

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It was shown via numerical simulations that geometric phase (GP) and fidelity susceptibility (FS) in some quantum models exhibit universal scaling laws across phase transition points. Here we propose a singular function expansion method to determine their exact form across the critical points as well as their corresponding constants. For the models such as anisotropic XY model where the energy gap is closed and reopened at the special points (k0 = 0, π), scaling laws can be found as a function of system length N and parameter deviation λ − λc (where λc is the critical parameter). Intimate relations for the coefficients in GP and FS have also been determined. However in the extended models where the gap is not closed and reopened at these special points, the scaling as a function of system length N breaks down. We also show that the second order derivative of GP also exhibits some intriguing scaling laws across the critical points. These exact results can greatly enrich our understanding of GP and FS in the characterization of quantum phase transitions. [14][15][16]. GP has become a central concept in amounts of investigations in recent decades as an important tool to study the geometric feature of Hamiltonians [17][18][19]; especially, it can even be used to characterize topological phase transitions [20][21][22], which are beyond the accessibility of Landau theory of phase transition. This phase can also be directly measured in experiments [3,[23][24][25][26]. Across the critical points the derivative of GP exhibits universal scaling laws [27][28][29].Fidelity susceptibility (FS) based on the overlap of ground state functions is another way beyond the Landau paradigm to characterize quantum phase transitions [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. The FS is not defined along a closed trajectory in parameter space, thus it is not directly related to the global geometric feature of the ground state. However since the structure of wave functions in two different phases are different, we see that FS also exhibits some scaling laws across critical points; see reviews in Refs. [29,32].In previous literatures all these scaling laws are exploited by numerical simulations, thus our understanding of these laws are limited although they have been widely investigated [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Here in this work these scaling laws are obtained exactly using a singular function expansion method, in which all coefficients are also determined exactly. We show that these two measurements are essentially determined by the same physics across the critical points, thus their coefficients also have some intimate relations. The coefficients of the divergent terms only reflect how and in which way the energy gap is closed and reopened during phase transition, thus do not carry information about the topological properties of ground state wave functions. We also find that the constant term in FS is accompanied by a discontinuous jump across the critical points, thus does not...

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Section: Thus We Have ξsupporting

confidence: 70%

“…Extended Ising model. We next show that these scaling laws depend strongly on at which point the gap is closed and reopened and they may break down when the gap is not closed at the special points, which can be captured by the following extended Ising model [58,[61][62][63][64],…”

Section: Thus We Have ξmentioning

confidence: 96%

Scaling of geometric phase and fidelity susceptibility across the critical points and their relations

et al. 2017

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“…Different measures, such as entanglement, quantum discord (QD) and violation of Bell inequalities, have been introduced to account for the "quantumness" of a given state and it was shown that such measures can be used as a fundamental resource in the protocols of quantum informational and computational tasks [6]. Several attempts have been made to find a universal quantum correlation measure that can unambiguously signal all the QPTs and to search for a relation between QPTs and quantum correlation measures [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Indeed, different measures of quantum correlations, such as entanglement [7][8][9][10][11], quantum discord [12][13][14][15][16][17][18][19][20], fidelity [21,22] and Bell inequalities [23][24][25] have been shown to provide the signatures of QPTs.…”

Section: Introductionmentioning

confidence: 99%

“…Several attempts have been made to find a universal quantum correlation measure that can unambiguously signal all the QPTs and to search for a relation between QPTs and quantum correlation measures [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Indeed, different measures of quantum correlations, such as entanglement [7][8][9][10][11], quantum discord [12][13][14][15][16][17][18][19][20], fidelity [21,22] and Bell inequalities [23][24][25] have been shown to provide the signatures of QPTs. Although not always, the extremal points (minimums or maximums) as well as the behavior of the derivatives of the correlation measures can signal the existence of a critical point (CP).…”

Section: Introductionmentioning

confidence: 99%

Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems

Altintas¹,

Eryiğit²

2012

Annals of Physics

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We have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system Lipkin-Meshkov-Glick models, by using different quantumness measures, such as entanglement of formation, quantum discord, as well as its classical counterpart, measurement-induced disturbance and the Clauser-Horne-Shimony-Holt-Bell function. Measurement-induced disturbance is found to detect the first and second order phase transitions present in these critical systems, while, surprisingly, it is found to fail to signal the infinite-order phase transition present in the XXZ model. Remarkably, the Clauser-Horne-Shimony-Holt-Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.

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“…the x and y direction. Both Ising and anisotropy transitions share the same critical exponent ν = 1 [45,46], and we intend to calculate it analytically according to the expressions Eq. (3) and Eq.…”

Section: Modelmentioning

confidence: 99%

Fidelity susceptibility of the anisotropic XY model: The exact solution

2018

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We derive several closed-form expressions for the fidelity susceptibility (FS) of the anisotropic XY model in the transverse field. The basic idea lies in a partial fraction expansion of the expression so that all the terms are related to a simple fraction or its derivative. The critical points of the model are reiterated by the FS, demonstrating its validity for characterizing the phase transitions. Moreover, the critical exponents ν associated with the correlation length in both critical regions are successfully extracted by the standard finite-size scaling analysis.

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Fidelity susceptibility approach to quantum phase transitions in theXYspin chain with multisite interactions

Cited by 32 publications

References 40 publications

Scaling of geometric phase and fidelity susceptibility across the critical points and their relations

Scaling of geometric phase and fidelity susceptibility across the critical points and their relations

Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems

Fidelity susceptibility of the anisotropic XY model: The exact solution

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