Entropy Fluctuation Formulas of Fermionic Gaussian States

Huang, Youyi; Wei, Lu

doi:10.1007/s00023-023-01342-w

Cited by 3 publications

(8 citation statements)

References 40 publications

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“…where CF denotes the closed-form terms in the bracket of (B.12). The sum in (29) may not be summable into a closed-form expression and is referred to as an unsimplifiable basis [6,8,10,11,21,23,29]. However, in the special cases of a given integer d, it permits closed-form representation as a result of the identity (B.3).…”

Section: Resultsmentioning

confidence: 99%

“…It has been introduced in [23] that the joint probability densities ( 10) and ( 15) can be compactly represented by a single joint density as…”

Section: Entanglement Capacity Over Fermionic Gaussian States With Pa...mentioning

confidence: 99%

“…In the past decades, there has been considerable progress in estimating the degree of entanglement over different models of generic states, where one of the most extensively studied area is the entropy based estimations using, for example, von Neumann entropy [1][2][3][4][5][6][7][8][9][10][11], quantum purity [7,[12][13][14][15][16], and Tsallis entropy [17,18] as entanglement indicators. These results mainly focus on the statistical behavior of entanglement entropies over generic state models, such as the well-known Hilbert-Schmidt ensemble [1-6, 8, 11, 12, 15, 17, 18], the Bures-Hall ensemble [7,9,10,13,14,16,19], and the fermionic Gaussian ensemble [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…For the fermionic Gaussian ensemble without particle number constraint, the average capacity of equal subsystem dimensions is derived in [21,30], whereas the corresponding finite-size formula in the general case of unequal dimensions remains open. Knowing the finite-size formula of average capacity allows the comparison to the finite-size results of entanglement entropy obtained recently in [20][21][22][23], leading to a more comprehensive understanding of the properties of entanglement capacity. For noisy intermediate-scale quantum systems [31], where the qubits number is limited to a few dozens, finite-size estimations of degree of entanglement including the finite-size average capacity become crucial.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we compute the exact average entanglement capacity valid for any subsystem dimensions of fermionic Gaussian states for the cases of with and without particle number constraints. A key ingredient in obtaining the results is the set of tools for simplifying finite summations developed very recently [23] in the study of von Neumann entropy of the fermionic Gaussian ensemble. Our exact results also lead to the limiting values of average capacity when the subsystem dimensions approach infinity with a fixed dimension difference.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement capacity of fermionic Gaussian states

Huang,

Wei

2023

J. Phys. A: Math. Theor.

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We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic formulas of average capacity of two different cases -- with and without particle number constraints. For the later case, the obtained formulas generalize some partial results of average capacity in the literature. The key ingredient in deriving the results is a set of new tools for simplifying finite summations developed very recently in the study of entanglement entropy of fermionic Gaussian states.

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Section: Resultsmentioning

confidence: 99%

“…It has been introduced in [23] that the joint probability densities ( 10) and ( 15) can be compactly represented by a single joint density as…”

Section: Entanglement Capacity Over Fermionic Gaussian States With Pa...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Entanglement capacity of fermionic Gaussian states

Huang,

Wei

2023

J. Phys. A: Math. Theor.

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Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble

Vinaixa,

Mula,

Deaño

et al. 2024

J. Stat. Mech.

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We characterize the long-term state of the 1D Dirac vacuum stirred by an impenetrable object, modeled as the ground state of a finite free-fermionic chain dynamically perturbed by a moving classical obstacle which suppresses the local hopping amplitudes. We find two different regimes, depending on the velocity of the obstacle. For a slow motion, the effective Floquet Hamiltonian presents features which are typical of the Gaussian orthogonal ensemble, and the occupation of the Floquet modes becomes roughly homogeneous. Moreover, the long term entanglement entropy of a contiguous block follows a Gaussian analogue of Page’s law, i.e. a volumetric behavior. Indeed, the statistical properties of the reduced density matrices correspond to those of a random Slater determinant, which can be described using the Jacobi ensemble from random matrix theory. On the other hand, if the obstacle moves fast enough, the effective Floquet Hamiltonian presents a Poissonian behavior. The nature of the transition is clarified by the entanglement links, which determine the effective geometry underlying the entanglement structure, showing that the one-dimensionality of the physical Hamiltonian dissolves into a random adjacency matrix as we slow down the obstacle motion.

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Entanglement Entropy of Free Fermions with a Random Matrix as a One-Body Hamiltonian

Pastur,

Slavin

2024

Entropy

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We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1≪L≲N. A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N→∞, then an asymptotic analysis of the entanglement entropy as L→∞. In this paper, we consider another version of the above inequality: the regime of asymptotically proportional L and N, i.e., the simultaneous limits L→∞,N→∞,L/N→λ>0. Specifically, we consider a system of free fermions that is in its ground state, and such that its one-body Hamiltonian is a large random matrix, which is often used to model long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-range hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give streamlined proof of Page’s formula for the entanglement entropy of black hole radiation for a wide class of typical ground states, thereby proving the universality and the typicality of the formula.

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Entropy Fluctuation Formulas of Fermionic Gaussian States

Cited by 3 publications

References 40 publications

Entanglement capacity of fermionic Gaussian states

Entanglement capacity of fermionic Gaussian states

Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble

Entanglement Entropy of Free Fermions with a Random Matrix as a One-Body Hamiltonian

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