Renormalization Group Approach to Quasi-One-Dimensional Conductors

Abstract

We review the recent progress made in the application of the renormalization group method to the interacting quasi-one-dimensional electron gas. From the functional integral formulation of the partition function as expressed in terms of anticommuting Grassmann variables, the effects of single-electron interchain hopping on the mechanisms of propagation of correlations leading to long range ordering is analyzed in full details for the non-half-filled band case. Within a unified formalism, the scaling features of the purely one-dimensional correlations, the dimensionality crossover of both single and composite particles, the critical temperatures, and the responses functions are described.

Magnetic response and quantum critical behavior in the doped two-leg extended Hubbard ladder

“…(4.18b). As is known in the single-chain case, 55 both the spin and charge degrees of freedom contribute to (T −1 1 ) stag . The critical charge mode in our theory is the total sector φ ρ+ , whose Hamiltonian is given by…”

“…In this section we study the uniform spin susceptibility and the NMR relaxation rate at finite temperature from two different approaches by extending previous calculations on the single chain 55,56 or on the undoped Heisenberg ladder. 57,58,59,60 One approach is the random-phase approximation (RPA) combined with the renormalization group method and another is direct calculation in terms of the low-energy effective Hamiltonian (3.7).…”

Numerical studies of the two-leg Hubbard ladder

“…Earlier work, in this context, had considered a 2-dimensional system of weakly coupled chains [6]. Further work [7,8], using bosonization techniques, valid for weak interchain coupling, has identified a number of possible phases which the 2-leg Hubbard ladder may exhibit.…”

( Sr / Ca ) 14 Cu 24 O 41 spin ladders studied by NMR under pressure

“…63 Cu(I = 3/2) NMR measurements have been performed at a fixed magnetic field of 9.3 Tesla (B b) via a Fourier transform of the spin echo on the central transition (1/2, −1/2) using phase alternation techniques. The echo signal was obtained after the pulse sequence (τ p ) x − t del − (τ p ) y − t − echo with τ p ≤ 1.5 µs.…”

“…However, as for undoped ladder compounds, a spin gap is still observed in the ladder plane and a smaller spin gap (≈ 140K) is also present in the chain sublattice. The existence of a spin gap on ladders was demonstrated by 63 Cu-NMR measurements which can easily separate the contributions coming from copper nuclei belonging to chains and ladders. The spin part of the NMR shift, which is directly proportional to the spin susceptibility, allows an accurate determination of these gaps.…”