Energy-level statistics in strongly disordered systems with power-law hopping

Abstract

Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian $\propto 1/r^{\alpha }$ in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function $R_2(\omega )$ in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by $R_2(\omega ,V)=A_3\frac{\omega }{{\omega }_V}$ for small frequencies $\omega \ll {\omega }_V$ and $R_2(\omega ,V)=1-(\alpha -d)A_1{\left(\frac{{\omega }_V}{\omega }\right)}^{\frac{d}{\alpha }}-A_2{\left(\frac{{\omega }_V}{\omega }\right)}^2$ for large frequencies $\omega \gg {\omega }_V$, where ${\omega }_V\propto V^{-\frac{\alpha }{d}}$ is the characteristic matrix element of excitation hopping in a system of volume $V$, and $A_1$, $A_2$ and $A_3$ are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.

References in corpus (27)

• Quantum information with Rydberg atoms
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• The many-body localization phase transition
• The physics of dipolar bosonic quantum gases
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Realizing a lattice spin model with polar molecules
• Observation of entanglement propagation in a quantum many-body system
• Non-local propagation of correlations in long-range interacting quantum systems
• Statistics of energy levels and eigenfunctions in disordered systems
• Scalable quantum register based on coupled electron spins in a room temperature solid
• Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
• Fluctuations of the inverse participation ratio at the Anderson transition
• Many-body Localization with Dipoles
• Multifractality and critical fluctuations at the Anderson transition
• Spectral statistics across the many-body localization transition
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Duality in power-law localization in disordered one-dimensional systems
• Spectroscopy of interacting quasiparticles in trapped ions
• Critical Hamiltonians with long range hopping
• Quantum Levy flights and multifractality of dipolar excitations in a random system
• Superconductor-insulator quantum phase transition
• Localization and critical diffusion of quantum dipoles in two dimensions
• Strong quantum interference in strongly disordered bosonic insulators
• Mesoscopic fluctuations of the local density of states in interacting electron systems
• Fermionic and bosonic ac conductivities at strong disorder

Cited by in corpus (1)

• Duality between disordered nodal semimetals and systems with power-law hopping