Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition

Abstract

We show that short-range interactions are irrelevant around gapless ground-state delocalization-localization transitions driven by quasiperiodicity in interacting fermionic chains. In the presence of interactions, these transitions separate Luttinger Liquid and Anderson glass phases. Remarkably, close to criticality, we find that excitations become effectively non-interacting. By formulating a many-body generalization of a recently developed method to obtain single-particle localization phase diagrams, we carry out precise calculations of critical points between Luttinger Liquid and Anderson glass phases and find that the correlation length critical exponent takes the value $\nu =1.001\pm 0.007$, compatible with $\nu =1$ known exactly at the non-interacting critical point. We also show that other critical exponents, such as the dynamical exponent $z$ and a many-body analog of the fractal dimension are compatible with the exponents obtained at the non-interacting critical point. Noteworthy, we find that the transitions are accompanied by the emergence of a many-body generalization of previously found single-particle hidden dualities. Finally, we show that in the limit of vanishing interaction strength, all finite range interactions are irrelevant at the non-interacting critical point.

References in corpus (18)

• Anderson Transitions
• Many-Body Localization in a Quasiperiodic System
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Flat Bands Under Correlated Perturbations
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Tomonaga-Luttinger parameters for doped Mott insulators
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• Phase diagram and momentum distribution of an interacting Bose gas in a bichromatic lattice
• Entanglement entropy of aperiodic quantum spin chains
• Phase transition of interacting disordered bosons in one dimension
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Many-body localization of spinless fermions with attractive interactions in one dimension
• Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid

Cited by in corpus (8)

• Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
• Interaction-induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices
• Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems
• Anderson localization: a density matrix approach
• Fractal Quasicondensation in One Dimension
• One-dimensional interacting Su-Schrieffer-Heeger model at quarter filling: An exact diagonalization study