Impurity in a Luttinger liquid away from half-filling : a numerical study

Conformal field theory gives quite detailed predictions for the low-energy spectrum and scaling exponents of a massless Luttinger liquid at generic filling in the presence of an impurity. While these predictions were verified for half-filled systems, there was until now no analysis away from this particular filling. Here, we fill in this gap by numerically investigating a quarter-filled system using the density-matrix renormalization-group technique. Our results confirm conformal-field-theory predictions, and suggest that they are indeed valid for arbitrary fillings.Conformal field theory gives quite detailed predictions for the low-energy spectrum and scaling exponents of a massless Luttinger liquid at generic filling in the presence of an impurity. While these predictions were verified for half-filled systems, there was until now no analysis away from this particular filling. Here, we fill in this gap by numerically investigating a quarter-filled system using the density-matrix renormalization-group technique. Our results confirm conformal-field-theory predictions, and suggest that they are indeed valid for arbitrary fillings.

arXiv:cond-mat/9705269Physical review. B, Condensed matterOct 15, 199749 citations

Doped AB2 Hubbard chain: Spiral, Nagaoka and resonating-valence-bond states, phase separation, and Luttinger-liquid behavior

R. R. Montenegro-Filho, Mauricio D. Coutinho-Filho

We present an extensive numerical study of the Hubbard model on the doped $A{B}_{2}$ chain, both in the weak coupling and the infinite- $U$ limit. Due to the special unit-cell topology, this system displays a rich variety of phases as a function of hole doping $(\ensuremath{\delta})$ away from half-filling. Near half-filling spiral states develop in the weak-coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite- $U$ limit. For higher doping, the system phase-separates before reaching a Mott insulating phase of short-range resonating-valence-bond states at $\ensuremath{\delta}=1∕3$. Moreover, for $\ensuremath{\delta}>1∕3$ we observe a crossover, which anticipates the Luttinger-liquid behavior for $\ensuremath{\delta}>2∕3$.We present an extensive numerical study of the Hubbard model on the doped $A{B}_{2}$ chain, both in the weak coupling and the infinite-$U$ limit. Due to the special unit-cell topology, this system displays a rich variety of phases as a function of hole doping $(\ensuremath{\delta})$ away from half-filling. Near half-filling spiral states develop in the weak-coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite-$U$ limit. For higher doping, the system phase-separates before reaching a Mott insulating phase of short-range resonating-valence-bond states at $\ensuremath{\delta}=1∕3$. Moreover, for $\ensuremath{\delta}>1∕3$ we observe a crossover, which anticipates the Luttinger-liquid behavior for $\ensuremath{\delta}>2∕3$.

arXiv:0802.3880Physical Review BSep 28, 200623 citations

Transport properties of a Luttinger liquid with a cluster of impurities

Joy Prakash Das, Girish S. Setlur

arXiv:1811.08175Physica E Low-dimensional Systems and NanostructuresFeb 10, 20194 citations

Transport in a spin-polarized Luttinger liquid in the presence of a single impurity

Hsuan-Yeh Chang, D. Schmeltzer

arXiv:cond-mat/0212262Physics Letters AJul 7, 20056 citations

Luttinger liquid phase in the Aubry-André Hubbard chain

Runze Chi, Josephine J. Yu, Chaitanya Murthy +1 more

We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.

arXiv:2401.08980Physical review. B./Physical review. BOct 8, 20240 citations

We present an extensive numerical study of the Hubbard model on the doped

A{B}_{2}

chain, both in the weak coupling and the infinite-

U

limit. Due to the special unit-cell topology, this system displays a rich variety of phases as a function of hole doping $(\ensuremath{\delta})$ away from half-filling. Near half-filling spiral states develop in the weak-coupling regime, while Nagaoka itinerant ferromagnetism is observed in the infinite-

U

limit. For higher doping, the system phase-separates before reaching a Mott insulating phase of short-range resonating-valence-bond states at $\ensuremath{\delta}=1∕3$. Moreover, for $\ensuremath{\delta}>1∕3$ we observe a crossover, which anticipates the Luttinger-liquid behavior for $\ensuremath{\delta}>2∕3$.