Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions

Schwandt, David; Alet, Fabien; Capponi, Sylvain

doi:10.1103/physrevlett.103.170501

Cited by 130 publications

(186 citation statements)

References 37 publications

(32 reference statements)

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“…These approaches provide crucial insight into models that are not exactly solvable (e.g. [11]), and shall be especially useful for studies of systems with unknown order parameters, critical points and critical exponents.…”

Section: Basics Of Fidelitymentioning

confidence: 99%

“…It is caused by discontinuity of f k at zero momentum when |c| = 1. Indeed, from (11,23,24) it is easy to calculate the limits…”

Section: Xy Modelmentioning

confidence: 99%

“…First, powerful numerical techniques have been deployed including tensor networks [31] and Quantum Monte Carlo [11,12] simulations. These approaches provide crucial insight into models that are not exactly solvable (e.g.…”

Section: Basics Of Fidelitymentioning

confidence: 99%

“…This has been worked out independently in the "small system" [10][11][12][13][14][15][16] and in the thermodynamic [17] limits. Broadly speaking the former corresponds to δ → 0 at fixed system size N , while the latter corresponds to N → ∞ at small, fixed δ.…”

Section: Introductionmentioning

confidence: 99%

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Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Rams

Damski

2011

Phys. Rev. A

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We study ground state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe in detail cases when fidelity is dominated by the universal contribution reflecting quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting from the change of either the system size or the parameters of the Hamiltonian. Moreover, we show when fidelity is dominated by non-universal contributions, study fidelity in the extended Ising model, and illustrate how our results provide additional insight into dynamics of quantum phase transitions. Special attention is put to studies of fidelity from the momentum space perspective. All our main results are obtained analytically. They are in excellent agreement with numerics.

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Section: Basics Of Fidelitymentioning

confidence: 99%

“…It is caused by discontinuity of f k at zero momentum when |c| = 1. Indeed, from (11,23,24) it is easy to calculate the limits…”

Section: Xy Modelmentioning

confidence: 99%

Section: Basics Of Fidelitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Rams

Damski

2011

Phys. Rev. A

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“…In the last few years, there have been many studies of the phase diagrams for various quantum models in the aid of the fidelity [13][14][15][16][17][18][19] or mixed-state fidelity [2,[20][21][22]. All the investigations are performed for Hermitian Hamiltonians, where the probability is preserving in the context of standard Dirac inner product.…”

Section: Model and Solutionmentioning

confidence: 99%

Finite-temperature quantum criticality in a complex-parameter plane

Song

2015

Phys. Rev. A

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A conventional quantum phase transition (QPT) occurs not only at zero temperature, but also exhibits finite-temperature quantum criticality. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the finite-temperature quantum criticality in a non-Hermitian PT -symmetric Ising model. We present the complete set of exact eigenstates of the non-Hermitian Hamiltonian, based on which the mixed-state fidelity in the context of biorthogonal bases is calculated. Analytical and numerical results show that the fidelity approach to finite-temperature QPT can be extended to the non-Hermitian Ising model. This paves the way for experimental detection of quantum criticality in a complex-parameter plane.

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Biorthogonal quantum criticality in non-Hermitian many-body systems

2021

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We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a secondorder phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.

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Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions

Cited by 130 publications

References 37 publications

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Finite-temperature quantum criticality in a complex-parameter plane

Biorthogonal quantum criticality in non-Hermitian many-body systems

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