One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior

Abstract

It is well-known that, generically, the one-dimensional interacting fermions cannot be described in terms of the Fermi liquid. Instead, they present different phenomenology, that of the Tomonaga-Luttinger liquid: the Landau quasiparticles are ill-defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine-tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both the Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaking, such liquid exists only when the fermion interaction is irrelevant (in the renormalization group sense). The quasi-Fermi liquid exhibits the properties of both the Tomonaga-Luttinger liquid and the Fermi liquid. Similar to the Tomonaga-Luttinger liquid, no finite-momentum quasiparticles are supported by the quasi-Fermi liquid; on the other hand, its fermion occupation number demonstrates finite discontinuity at the Fermi energy, which is a hallmark feature of the Fermi liquid. Possible realization of the quasi-Fermi liquid with the help of cold atoms in an optical trap is discussed.

5 pages of the main tex, 4 pages of Supplemental Material, 2 eps figures

References in corpus (18)

• Many-Body Physics with Ultracold Gases
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Theory of ultracold Fermi gases
• Topological response in Weyl semimetals and the chiral anomaly
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Universal theory of nonlinear Luttinger liquids
• From high temperature supercondutivity to quantum spin liquid: progress in strong correlation physics
• Dynamic response of one-dimensional interacting fermions
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Coulomb drag by small momentum transfer between quantum wires
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion
• Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
• Dynamic structure factor of Luttinger liquids with quadratic energy dispersion and long-range interactions

Cited by in corpus (5)

• Real-time dynamics in the one-dimensional Hubbard model
• Spin-charge separated quasiparticles in one dimensional quantum fluids
• Strongly correlated Fermi systems as a new state of matter
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions
• Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions