Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems

Abstract

The ground states of interacting one-dimensional metals are generically Luttinger liquids. Luttinger liquid theory is usually considered for translation invariant systems. The Luttinger liquid description remains valid for weak quasiperiodic modulations; however, as the quasiperiodic modulation gets increasingly strong, it is increasingly renormalized and eventually fails, as the system becomes localized. We explore how quasiperiodic modulation renormalizes the Luttinger parameter characterizing this emergent Luttinger liquid, using the renormalization of transmission coefficients across a barrier as a proxy that remains valid for general quasiperiodic modulation. We find, unexpectedly, that quasiperiodic modulation weakens the effects of short-range interactions, but enhances those of long-range interactions. We support the former finding with matrix-product numerics. We also discuss how interactions affect the localization phase boundary.

References in corpus (39)

• The density-matrix renormalization group in the age of matrix product states
• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Disordered quantum gases under control
• Time-evolving a matrix product state with long-ranged interactions
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
• Anomalous metals -- failed superconductors
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Observing localisation in a 2D quasicrystalline optical lattice
• Disorder in quantum many-body systems
• Correlated Fermions in a one-dimensional quasiperiodic potential
• Anderson localization transitions with and without random potentials
• Localization of interacting fermions in the Aubry-Andre' model
• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• Detecting a many-body mobility edge with quantum quenches
• Magic-angle semimetals
• The insulating phases and superfluid-insulator transition of disordered boson chains
• Weyl semimetal to metal phase transitions driven by quasiperiodic potentials
• Universality and Quantum Criticality in Quasiperiodic Spin Chains
• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• Localization and symmetry breaking in the quantum quasiperiodic Ising glass
• Interacting particles at a metal-insulator transition
• Weak Versus Strong Disorder Superfluid-Bose Glass Transition in One Dimension
• The quasi-periodic quantum Ising transition in 1D
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• Non-equilibrium steady state phases of the interacting Aubry-Andre-Harper model
• Moiré versus Mott: Incommensuration and Interaction in One-Dimensional Bichromatic Lattices
• Asymptotically Exact Scenario of Strong-Disorder Criticality in One-Dimensional Superfluids
• Quantum criticality in Ising chains with random hyperuniform couplings
• Enhanced compressibility due to repulsive interaction in the Harper model
• Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition
• Critical behavior of the quasi-periodic quantum Ising chain
• The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum
• Fractal x-ray edge problem at the critical point of the Aubry-André model