Different types of the dimensional crossover in the quasi-one-dimensional spinless fermion systems

Abstract

It is known that many-body correlations qualitatively modify the properties of a one-dimensional metal. However, for a quasi-one-dimensional metal these correlations are suppressed, at least partially. We study conditions under which the one-dimensional effects significantly influence the dimensional crossover of a quasi-one-dimensional metal. It is proved (i) that even a system with very high anisotropy of the single-particle hopping might behave on both sides of the crossover as an ordinary weakly non-ideal Fermi gas. Further, (ii) to demonstrate well-developed signatures of one-dimensional correlations the system must have extremely (exponentially) high anisotropy. Between cases (i) and (ii) an intermediate regime lies: (iii) the one-dimensional phenomena affect the two-particle susceptibilities, but do not reveal themselves in single-particle quantities. Unlike the normal state properties, (iv) the ordering transition is always very sensitive to the anisotropy: the mean field theory quickly becomes invalid as the anisotropy increases. An expression for the transition temperature is derived. The attributes (i-iv) are used to classify the weakly interacting quasi-one-dimensional fermion systems.

8 pages, 1 eps figure, accepted to Physical Review B

References in corpus (9)

• Universal theory of nonlinear Luttinger liquids
• Quasi-one-dimensional polarized Fermi superfluids
• Triplet superconducting pairing and density-wave instabilities in organic conductors
• 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
• Hidden Reentrant and Larkin-Ovchinnikov-Fulde-Ferrell Superconducting Phases in a Magnetic Field in (TMTSF)${}_2$ClO${}_4$
• Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
• Role of Interchain Hopping in the Magnetic Susceptibility of Quasi-One-Dimensional Electron Systems
• Increase of Superconducting Correlation due to Dimensionality Change in Quasi-One-Dimensional Conductors

Cited by in corpus (2)

• One-Dimensional Fermions with neither Luttinger-Liquid nor Fermi-Liquid Behavior
• Generation of localized magnetic moments in the charge-density-wave state