Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1011.0684 · AIP conference proceedings

Fidelity decay of the two-level bosonic embedded ensembles of random matrices

Luis Benet, Saúl Hernández-Quiroz, T. H. Seligman, Kurt B. Wolf, Luis Benet, Juan Mauricio Torres, Peter Oto Hess

Published Jan 1, 2010• 1 citation
arXivHTMLPDF

Abstract

We study the fidelity decay of the k‐body embedded ensembles of random matrices for bosons distributed over two single‐particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one‐body term and includes the diagonal of the perturbing k‐body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off‐diagonal elements of the k‐body interaction. This choice mimics the typical mean‐field basis used in many calculations. We study separately the cases k = 2 and 3. We compute the ensemble‐averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, t = tH = 1, and a freeze in the fidelity decay, during which periodic revivals of period tH are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of tH. These fractional periodic revivals are related to the dominance of specific k‐body terms in the perturbation.

DOI
10.1063/1.3537867

Related papers

Fidelity decay in interacting two-level boson systems: Freezing and revivals

Luis Benet, Saúl Hernández-Quiroz, T. H. Seligman

We study the fidelity decay in the k-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the k-body embedded ensemble of random matrices and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time t(H). By selecting specific k-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of t(H), thus relating the period of the revivals with the range of the interaction k of the perturbing terms. Numerical calculations confirm the analytical results.

arXiv:1103.3167•Physical Review E•May 31, 2011•5 citations

Loschmidt echoes in two-body random matrix ensembles

Iztok Pižorn, Tomaž Prosen, T. H. Seligman

Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting, e.g., from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as ``freeze.'' Numerical calculations confirm this result and show that the ground state even on average displays the freeze. This may contribute to explanation of the ``unreasonable'' success of mean field theories.

arXiv:cond-mat/0702079•Physical Review B•Jul 27, 2007•9 citations

Fidelity freeze for a random matrix model with off-diagonal perturbation

H.‐J. Stöckmann, Heiner Kohler

The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Znidaric in the linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Znidaric are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely imaginary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.

Physical Review E•Jun 8, 2006•11 citations

Fidelity freeze for a random matrix model with off--diagonal perturbation

Heiner Kohler

The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Znidaric in the linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Znidaric are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely unitary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.

arXiv:nlin/0601037•Jan 16, 2006•0 citations

Fidelity decay and entropy production in many-particle systems after random interaction quench

Sudip Kumar Haldar, N D Chavda, Manan Vyas +1 more

Abstract We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic (bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin S . The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving S for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time ( t sat ) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.

arXiv:1509.01392•Journal of Statistical Mechanics Theory and Experiment•Apr 1, 2016•10 citations

Fidelity of the diagonal ensemble signals the many-body localization transition

Taotao Hu, Kang Xue, Xiaodan Li +2 more

In this work, we use exact matrix diagonalization to explore the many-body localization (MBL) transition in a random-field Heisenberg chain. We demonstrate that the fidelity and fidelity susceptibility can be utilized to characterize the interaction-driven many-body localization transition in this closed spin system which is in agreement with previous analytical and numerical results [S. Garnerone, N. T. Jacobson, S. Haas, and P. Zanardi, Phys. Rev. Lett. 102, 057205 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.057205; P. Zanardi and N. Paunkovic, Phys. Rev. E 74, 031123 (2006)PLEEE81539-375510.1103/PhysRevE.74.031123]. In particular, instead of ground-state fidelity, we test the fidelity between two diagonal ensembles related by a small parameter perturbation δh, it is special that here the parameter perturbation δh_{i} for each site are random variables like h_{i}. It shows that fidelity of the diagonal ensemble develop a pronounced drop at the transition. We utilize fidelity to estimate the critical disorder strength h_{c} for different system size, we get h_{c}∈ [2.5,3.9] and get a power-law decay with an exponent of roughly -1.49(2) for system size N, and can extrapolate h_{c}^{inf} of the infinite system is about 2.07 which all agree with a recent work by Huse and Pal, in which the MBL transition in the same model was predicted to be hc [2,4]. We also estimate the scaling of maximum of averaged fidelity susceptibility as a function of system size N, it shows a power law increase with an exponent of about 5.05(1).

Physical review. E•Nov 11, 2016•12 citations
We study the fidelity decay of the k‐body embedded ensembles of random matrices for bosons distributed over two single‐particle states. Fidelity is defined in terms of a reference Hamiltonian, which is a purely diagonal matrix consisting of a fixed one‐body term and includes the diagonal of the perturbing k‐body embedded ensemble matrix, and the perturbed Hamiltonian which includes the residual off‐diagonal elements of the k‐body interaction. This choice mimics the typical mean‐field basis used in many calculations. We study separately the cases k = 2 and 3. We compute the ensemble‐averaged fidelity decay as well as the fidelity of typical members with respect to an initial random state. Average fidelity displays a revival at the Heisenberg time, t = tH = 1, and a freeze in the fidelity decay, during which periodic revivals of period tH are observed. We obtain the relevant scaling properties with respect to the number of bosons and the strength of the perturbation. For certain members of the ensemble, we find that the period of the revivals during the freeze of fidelity occurs at fractional times of tH. These fractional periodic revivals are related to the dominance of specific k‐body terms in the perturbation.
We study the fidelity decay in the k-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the k-body embedded ensemble of random matrices and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time t(H). By selecting specific k-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of t(H), thus relating the period of the revivals with the range of the interaction k of the perturbing terms. Numerical calculations confirm the analytical results.
Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting, e.g., from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as ``freeze.'' Numerical calculations confirm this result and show that the ground state even on average displays the freeze. This may contribute to explanation of the ``unreasonable'' success of mean field theories.
The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Znidaric in the linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Znidaric are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely imaginary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.
The concept of fidelity has been introduced to characterize the stability of a quantum-mechanical system against perturbations. The fidelity amplitude is defined as the overlap integral of a wave packet with itself after the development forth and back under the influence of two slightly different Hamiltonians. It was shown by Prosen and Znidaric in the linear-response approximation that the decay of the fidelity is frozen if the Hamiltonian of the perturbation contains off-diagonal elements only. In the present work the results of Prosen and Znidaric are extended by a supersymmetry calculation to arbitrary strengths of the perturbation for the case of an unperturbed Hamiltonian taken from the Gaussian orthogonal ensemble and a purely unitary antisymmetric perturbation. It is found that for the exact calculation the freeze of fidelity is only slightly reduced as compared to the linear-response approximation. This may have important consequences for the design of quantum computers.
Abstract We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic (bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin S . The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving S for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time ( t sat ) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.
In this work, we use exact matrix diagonalization to explore the many-body localization (MBL) transition in a random-field Heisenberg chain. We demonstrate that the fidelity and fidelity susceptibility can be utilized to characterize the interaction-driven many-body localization transition in this closed spin system which is in agreement with previous analytical and numerical results [S. Garnerone, N. T. Jacobson, S. Haas, and P. Zanardi, Phys. Rev. Lett. 102, 057205 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.057205; P. Zanardi and N. Paunkovic, Phys. Rev. E 74, 031123 (2006)PLEEE81539-375510.1103/PhysRevE.74.031123]. In particular, instead of ground-state fidelity, we test the fidelity between two diagonal ensembles related by a small parameter perturbation δh, it is special that here the parameter perturbation δh_{i} for each site are random variables like h_{i}. It shows that fidelity of the diagonal ensemble develop a pronounced drop at the transition. We utilize fidelity to estimate the critical disorder strength h_{c} for different system size, we get h_{c}∈ [2.5,3.9] and get a power-law decay with an exponent of roughly -1.49(2) for system size N, and can extrapolate h_{c}^{inf} of the infinite system is about 2.07 which all agree with a recent work by Huse and Pal, in which the MBL transition in the same model was predicted to be hc [2,4]. We also estimate the scaling of maximum of averaged fidelity susceptibility as a function of system size N, it shows a power law increase with an exponent of about 5.05(1).