Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians

• URL: http://arxiv.org/abs/2109.06895v2
• Date: Tue, 14 Dec 2021 17:25:43 GMT
• Title: Single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians
• Authors: Patrycja {\L}yd\.zba, Yicheng Zhang, Marcos Rigol, Lev Vidmar
• Abstract summary: We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians. We show that the diagonal matrix elements exhibit vanishing eigenstate-to-eigenstate fluctuations, and a variance proportional to the inverse Hilbert space dimension.
• Score: 4.557919434849493
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson model below the localization transition. We show that they display eigenstate thermalization for normalized observables. Specifically, we show that the diagonal matrix elements exhibit vanishing eigenstate-to-eigenstate fluctuations, and a variance proportional to the inverse Hilbert space dimension. We also demonstrate that the ratio between the variance of the diagonal and the off-diagonal matrix elements is $2$, as predicted by the random matrix theory. We study distributions of matrix elements of observables and establish that they need not be Gaussian. We identify the class of observables for which the distributions are Gaussian.

Related papers

• Simulating NMR Spectra with a Quantum Computer [49.1574468325115]
  This paper provides a formalization of the complete procedure of the simulation of a spin system's NMR spectrum. We also explain how to diagonalize the Hamiltonian matrix with a quantum computer, thus enhancing the overall process's performance.
  arXiv  Detail & Related papers  (2024-10-28T08:43:40Z)
• Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
  We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems. The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
  arXiv  Detail & Related papers  (2024-08-02T10:15:26Z)
• Scattering Neutrinos, Spin Models, and Permutations [42.642008092347986]
  We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with $N$ degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to $N$, non-trivial eigenvalues.
  arXiv  Detail & Related papers  (2024-06-26T18:27:15Z)
• A Result About the Classification of Quantum Covariance Matrices Based on Their Eigenspectra [0.0]
  We find a non-trivial class of eigenspectra with the property that the set of quantum covariance matrices corresponding to any eigenspectrum in this class are related by symplectic transformations. We show that all non-degenerate eigenspectra with this property must belong to this class, and that the set of such eigenspectra coincides with the class of non-degenerate eigenspectra.
  arXiv  Detail & Related papers  (2023-08-07T09:40:09Z)
• A class of 2 X 2 correlated random-matrix models with Brody spacing distribution [0.0]
  A class of 2 X 2 random-matrix models is introduced for which the Brody distribution is the eigenvalue spacing distribution. The random matrices introduced here differ from those of the Gaussian Orthogonal Ensemble (GOE) in three important ways.
  arXiv  Detail & Related papers  (2023-08-03T03:11:54Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Re-Analyze Gauss: Bounds for Private Matrix Approximation via Dyson Brownian Motion [28.431572772564518]
  Given a symmetric matrix $M$ and a vector $lambda$, we present new bounds on the Frobenius-distance utility of the Gaussian mechanism for approximating $M$ by a matrix. Our bounds depend on both $lambda$ and the gaps in the eigenvalues of $M$, and hold whenever the top $k+1$ eigenvalues of $M$ have sufficiently large gaps.
  arXiv  Detail & Related papers  (2022-11-11T18:54:01Z)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• Localization in quantum walks with periodically arranged coin matrices [0.0]
  The occurrence of localization is known to be equivalent to the existence of eigenvalues of the time evolution operators. This study shows that the method can be applied to extended models with periodically arranged coin matrices.
  arXiv  Detail & Related papers  (2021-11-30T05:22:28Z)
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions [0.0]
  Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz. We study a quantum chaotic spin-fermion model in a one-dimensional lattice.
  arXiv  Detail & Related papers  (2020-11-27T19:05:32Z)
• Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems [0.0]
  We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum.
  arXiv  Detail & Related papers  (2020-08-03T18:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.