Level statistics of XXZ spin chains with a random magnetic field

Abstract

The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude of the random magnetic field h. In the energy spectrum, quantum integrability competes with nonintegrability derived from the randomness, where the XXZ interaction is modified by the parameter $\Delta$. When $\Delta \ne 0$, the level-spacing distribution mostly shows Wigner-like behavior, while when $\Delta$=0, Poisson-like behavior appears although the system is nonintegrable due to randomness. Poisson-like behavior also appears for $\Delta \ne 0$ in the large h limit. Furthermore, the level-spacing distribution depends on the lattice size L, particularly when the random field is weak.

arXiv comment4 pages, 3 figures, to be published in Phys. Rev. B

References in corpus (4)

• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian
• Integrability and Quantum Chaos in Spin Glass Shards
• Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
• Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled XXZ spin chains

Cited by in corpus (21)

• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Quantum Quenches, Thermalization and Many-Body Localization
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• Local quenches with global effects in interacting quantum systems
• Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
• Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
• Level Statistics of XXZ Spin Chains with Discrete Symmetries: Analysis through Finite-size Effects
• Relaxation and Thermalization of Isolated Many-Body Quantum Systems
• Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems
• Many-body localization and thermalization in the full probability distribution function of observables
• Many-body localization phase in a spin-driven chiral multiferroic chain
• Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition
• Entanglement and localization transitions in eigenstates of interacting chaotic systems
• Universal scaling of spectral fluctuation transitions for interacting chaotic systems
• Hayden-Preskill Recovery in Hamiltonian Systems
• Learning What a Machine Learns in a Many-Body Localization Transition
• Exact solution of the minimalist Stark many body localization problem in terms of spin pair hopping
• Quantum chaos and fluctuations in isolated nuclear spin systems
• Level dynamics and avoided level crossings in driven disordered quantum dots
• Fock-space geometry and strong correlations in many-body localized systems
• Dynamical stability for finite quantum spin chains against a time-periodic inhomogeneous perturbation