Quantum critical scaling of fidelity susceptibility

Albuquerque, A. Fabricio; Alet, Fabien; Sire, Clément; Capponi, Sylvain

doi:10.1103/physrevb.81.064418

Cited by 211 publications

(329 citation statements)

References 40 publications

(91 reference statements)

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“…with the peak height χ F (γ c2 (N )) [44], we extrapolate the data of γ c2 (N ) to the thermodynamic limit, obtaining γ c2 ≈ −0.11π [inset of Fig. 4(a)].…”

Section: Determination Of the Parameter Ranges Of Qsh Statesmentioning

confidence: 99%

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Furukawa

Ueda

2014

Phys. Rev. A

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We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-1 2 ) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling g ↑↓ to the intracomponent one g > 0. This time-reversalinvariant setting represents a bosonic analogue of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for g ↑↓ up to as large as g. For g ↑↓ = −g, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses.

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“…with the peak height χ F (γ c2 (N )) [44], we extrapolate the data of γ c2 (N ) to the thermodynamic limit, obtaining γ c2 ≈ −0.11π [inset of Fig. 4(a)].…”

Section: Determination Of the Parameter Ranges Of Qsh Statesmentioning

confidence: 99%

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Furukawa

Ueda

2014

Phys. Rev. A

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“…(14) in ref. [36]. It is simply to check that, in our notations, it emerges exactly as the quantum Chernoff metric d 2 QC , Eq.(34).…”

Section: Chernoff/wigner-yanase Metricmentioning

confidence: 96%

“…Here, the following comment is in order. In terms of Green's functions a finite-temperature generalization of the fidelity susceptibility was proposed in [36]. This quantity is quite different from the Bures-Uhlmann fidelity susceptibility (i.e.…”

Section: Chernoff/wigner-yanase Metricmentioning

confidence: 99%

“…It is simply to check that, in our notations, it emerges exactly as the quantum Chernoff metric d 2 QC , Eq.(34). Since, the computational problems in studying χ T F can be efficiently tackled by the quantum Monte Carlo approach [36] this fact transfers new computational possibilities in the field concerning the quantum Chernoff metric.…”

Section: Chernoff/wigner-yanase Metricmentioning

confidence: 99%

“…[6,10,[36][37][38] and references therein. The Bures metric d 2 B appears under different names: quantum Fisher information (apart from a numerical factor), SLD metric, fidelity susceptibility, etc [4,6,18,19].…”

Section: Introductionmentioning

confidence: 99%

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Monotone Riemannian metrics and dynamic structure factor in condensed matter physics

Tonchev

2016

Journal of Mathematical Physics

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An analytical approach is developed to the problem of computation of monotone Riemannian metrics (e.g. Bogoliubov-Kubo-Mori, Bures, Chernoff, etc.) on the set of quantum states. The obtained expressions originate from the Morozova,Cencov and Petz correspondence of monotone metrics to operator monotone functions. The used mathematical technique provides analytical expansions in terms of the thermodynamic mean values of iterated (nested) commutators of a model Hamiltonian T with the operator S involved through the control parameter h. Due to the sum rules for the frequency moments of the dynamic structure factor new presentations for the monotone Riemannian metrics are obtained. Particularly, relations between any monotone Riemannian metric and the usual thermodynamic susceptibility or the variance of the operator S are discussed. If the symmetry properties of the Hamiltonian are given in terms of generators of some Lie algebra, the obtained expansions may be evaluated in a closed form. These issues are tested on a class of model systems studied in condensed matter physics.2

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Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method

Yang

2021

Annalen der Physik

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The fidelity susceptibility and trace distance in the valence‐bond‐solid (VBS) transition of a quantum mixed spin chain is investigated, which consists of unit cells arrayed as 1/2‐1/2‐1‐1 with alternating Heisenberg antiferromagnetic exchange couplings, by using the density matrix renormalization group (DMRG) method in the matrix product state (MPS) form. It is observed that the fidelity susceptibility and the first derivative of the trace distance display explicit divergence near the quantum critical point. The information about the quantum criticality, such as the quantum critical point and correlation length critical exponent, is extracted from the finite size scaling behaviors. The obtained quantum critical point is more accurate than previous work, and the existence of the scaling function of the trace distance near the critical point is observed numerically for the first time. In addition, it is also found that the trace distance between two sites can supplement the VBS picture for describing the change of the ground state as the control parameter is varied through the quantum critical point.

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Quantum critical scaling of fidelity susceptibility

Cited by 211 publications

References 40 publications

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Global phase diagram of two-component Bose gases in antiparallel magnetic fields

Monotone Riemannian metrics and dynamic structure factor in condensed matter physics

Quantum Phase Transition of a Quantum Mixed Spin Chain by Employing Density Matrix Renormalization Group Method

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