Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems.

  title={Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems.},
  author={Yicheng Zhang and Lev Vidmar and Marcos Rigol},
  journal={Physical review. E},
  volume={106 1-1},
We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in noninteracting systems. We focus on the quasimomentum occupation of hard-core bosons in one dimension and show that the distributions of the off-diagonal matrix elements are well described by generalized Gamma distributions, in both the presence and absence of… 

Effect of symmetries in out-of-time ordered correlators in interacting integrable and nonintegrable many-body quantum systems

Out-of-time ordered correlators (OTOCs) help characterize the scrambling of quantum information and are usually studied in the context of nonintegrable systems. We compare the relaxation dynamics of

Tight-binding billiards.

Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common

Off-diagonal matrix elements of local operators in many-body quantum systems.

This work shows that, for generic nonintegrable systems, the distribution of off-diagonal matrix elements is a Gaussian centered at zero, and describes the proximity to integrability through the deviation of this distribution from a Gaussians shape.

Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems.

In the quantum-chaotic model the behavior of the variance is qualitatively similar for matrix elements that connect eigenstates from the same versus different quasimomentum sectors, and this is not the case in the interacting integrable model for observables whose translationally invariant counterpart does not break integrability if added as a perturbation to the Hamiltonian.

Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain

We study the matrix elements of local operators in the eigenstates of the integrable XXZ chain and of the quantum-chaotic model obtained by locally perturbing the XXZ chain with a magnetic impurity.

Entanglement and matrix elements of observables in interacting integrable systems.

The bipartite von Neumann entanglement entropy and matrix elements of local operators in the eigenstates of an interacting integrable Hamiltonian (the paradigmatic spin-1/2 XXZ chain) are studied, and it is found that the leading term of the average eigenstate entanglements has a volume-law coefficient that is smaller than the universal one in quantum chaotic systems.

Eigenstate thermalization hypothesis through the lens of autocorrelation functions

Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz within the eigenstate thermalization hypothesis (ETH). We study a quantum chaotic

Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems.

  • L. F. SantosM. Rigol
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
The results for the complexity of the eigenvectors and for the expectation values of few-body observables confirm the validity of the Eigenstate thermalization hypothesis in the chaotic regime, and therefore the occurrence of thermalization.

Quantitative Impact of Integrals of Motion on the Eigenstate Thermalization Hypothesis.

A generic protocol is introduced to construct observables, subtracted by their projections on LIoms as well as products of LIOMs, and systematically reduces fluctuations and/or the structure of the diagonal matrix elements of local observables.

Eigenstate Thermalization in a Locally Perturbed Integrable System.

It is shown that the diagonal matrix elements of observables in the perturbed eigenstates follow the microcanonical predictions for the integrable model, and that the ballistic character of spin transport in the integRable model is manifest in the behavior of the off-diagonal matrix element of the current operator in the probabilistic eigenstate.

Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: complete relaxation of one-body observables.

It is demonstrated that, in the presence of interactions, correlations between particles in the many-body wave function provide the effective dissipation required to drive the relaxation of all one-body observables to the GGE.

Quantum quenches and thermalization in one-dimensional fermionic systems

We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We