Calculation of multifractal dimensions in spin chains

Abstract

It was demonstrated in [Phys. Rev. E 86, 021104, (2012)], that the ground-state wave functions for a large variety of one-dimensional spin-1/2 models are multifractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of these results.

25 pages

References in corpus (2)

• Phase transition in the Rényi-Shannon entropy of Luttinger liquids
• Rényi entropy of a line in two-dimensional Ising models

Cited by in corpus (29)

• Extended nonergodic states in disordered many-body quantum systems
• Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
• Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential
• Chaos and ergodicity across the energy spectrum of interacting bosons
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Chaos and quantum scars in Bose-Josephson junction coupled to a bosonic mode
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Dynamics of quasiperiodically driven spin systems
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Multifractality in quasienergy space of coherent states as a signature of quantum chaos
• Chaos in the Bose-Hubbard model and random two-body Hamiltonians
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Optimal route to quantum chaos in the Bose-Hubbard model
• Identification of quantum scars via phase-space localization measures
• Spectral statistics of Toeplitz matrices
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization
• Coherent Forward Scattering Peak and Multifractality
• Generalized Survival Probability
• Exact phase diagram and topological phase transitions of the XYZ spin chain
• Star junctions and watermelons of pure or random quantum Ising chains : finite-size properties of the energy gap at criticality
• Fractal states of the Schwinger model
• Multifractality in aperiodic quantum spin chains
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Characterization of the chaotic phase in the tilted Bose-Hubbard model
• On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain
• Quantum transitions, ergodicity, and quantum scars in the coupled top model
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold