Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0512546

Modulation of Luttinger liquid exponents in multi-walled carbon nanotubes

S. Bellucci·J. Gonzalez·P. Onorato·E. Perfetto
View original source ↗Read source document ↗Export metadata ↓

Abstract

We develop in this paper a theoretical framework that applies to the intermediate regime between the Coulomb blockade and the Luttinger liquid behavior in multi-walled carbon nanotubes. Our main goal is to confront the experimental observations of transport properties, under conditions in which the thermal energy is comparable to the spacing between the single-particle levels. For this purpose we have devised a many-body approach to the one-dimensional electron system, incorporating the effects of a discrete spectrum. We show that, in the crossover regime, the tunneling conductance follows a power-law behavior as a function of the temperature, with an exponent that oscillates with the gate voltage as observed in the experiments. Also in agreement with the experimental observations, a distinctive feature of our approach is the existence of an inflection point in the log-log plots of the conductance vs temperature, at gate voltages corresponding to peaks in the oscillation of the exponent. Moreover, we evaluate the effects of a transverse magnetic field on the transport properties of the multi-walled nanotubes. For fields of the order of 4 T, we find changes in the band structure that may be already significant for the outer shells, leading to an appreciable variation in the power-law behavior of the conductance. We then foresee the appearance of sensible modulations in the exponent of the conductance for higher magnetic fields, as the different subbands are shifted towards the development of flat Landau levels.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. Bellucci, J. Gonzalez, P. Onorato, E. Perfetto. 2005-12-21. Modulation of Luttinger liquid exponents in multi-walled carbon nanotubes. https://doi.org/10.1103/physrevb.74.045427

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An Exact Conjugation Identity for the Many-Body Wilson Loop Beyond Quantization

Constraints on unquantized many-body holonomies, such as Wilson loops (or their Berry phases), are less explored than those on their quantized counterparts. Here, we realize an unquantized regime by tuning the bond dimerization $δ$ and the staggered potential $Δ$ in a half-filled dimerized staggered Hubbard ring. For the tuned parameter sets, a finite excitation gap persists along the $U(1)$ twist cycle $θ\in[0,2π]$, so that the ground state $|ψ_δ(θ)\rangle$ remains separated from the excited states. The many-body Wilson loop is therefore well defined from the ground-state family $\{|ψ_δ(θ)\rangle;\,θ\in[0,2π]\}$. In this setup, we show an exact many-body Wilson loop conjugation identity, $W(-δ)=W(δ)^*$, accumulated along a cycle parametrized by $θ$. Importantly, the identity persists in regimes where the Berry phase $γ\equiv-\arg W$ varies continuously. We demonstrate the identity numerically using the density-matrix renormalization group (DMRG) method. The identity extends to other models where the flux-threaded ground-state family along the closed $θ$-cycle is mapped to the reversed cycle. Beyond its conceptual content, the identity provides a symmetry-based consistency check for numerical evaluations of Berry phases in interacting systems. It also justifies the signal-to-noise ratio improvement in Monte Carlo simulations by performing simulations at both $δ$ and $-δ$ and averaging $W(δ)$ with $W(-δ)^{*}$.

cond-mat.str-el↗
arXiv2026

Torus Berry Data Determine All-Genus Abelian Topological Orders

We show that for Abelian Chern-Simons topological orders, torus Berry matrices determine the all-genus extended TQFT. We identify the topological part of the projective Berry holonomy under metric deformations with the mapping-class-group representation of the Abelian Chern-Simons TQFT and prove that the normalized torus data reconstruct its finite quadratic module (G,q). Recent work showed that (G,q) classifies the extended theory up to symmetric monoidal natural isomorphism, and that the associated Abelian defect extension is determined by the pointed modular category C(G,q) arising from the same finite quadratic-module data. Therefore genus-one Berry data determine not only the all-genus bulk theory but also its associated defect structures without choosing a K-matrix presentation. We also prove that, for normalized character row errors $δ$<21.96%, nearest-row decoding recovers the Abelian fusion algebra independently of the number of anyons. The result applies to Abelian fractional quantum Hall and spin-liquid phases described by even-lattice Chern-Simons theories.

cond-mat.str-el↗
arXiv2026

Accidental accuracy and vertex corrections in $GW$: Exact benchmarks for the extended Hubbard model

The $GW$ approximation is the standard tool for quasiparticle predictions in materials, yet its regime of validity in correlated systems remains poorly quantified, because \textit{ab initio} vertex corrections are computationally prohibitive. Using exact diagonalization of the half-filled extended Hubbard model on finite rings as a numerically exact reference, we construct the corresponding model-space $GW$ theory on the identical Hilbert space and quantify its error as a function of local ($U$) and non-local ($V$) interaction strength. We find that the required vertex correction changes character across the phase diagram: in the weak-coupling regime the effective vertex $Γ_{\rm eff} < 1$, reflecting the suppression of RPA charge fluctuations by exact short-range correlations, whereas in the Mott regime $Γ_{\rm eff}$ grows monotonically (to $\sim 3$ at $U=8t$ for $N=6$), reflecting the local dynamical self-energy structure required to open the Hubbard gap. Vertex corrections in the electron-hole (polarizability) channel are shown to \emph{worsen} the gap error, indicating that reproducing the Mott gap requires dynamical self-energy structure rather than improved screening. For $V=0$, static COHSEX is accidentally exact at a single crossover $U^* \approx 3.5\,t$; finite $V$, through non-local Fock exchange, splits this point into a double-crossover window that collapses toward weak coupling. Even at the crossover, however, the exact spectral function retains Hubbard-band structure that no static functional reproduces, so gap agreement does not imply functional accuracy. These results yield quantitative diagnostics for the reliability of $GW$ in correlated materials.

cond-mat.str-el↗