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arXiv:1108.2272 · Physical Review B

Phase diagram of the half-filled one-dimensional t - V - V ′ model

Tapan Mishra, Juan Carrasquilla, Marcos Rigol

Published Sep 23, 2011• 59 citations
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Abstract

We study the phase diagram of spinless fermions with nearest- and next-nearest-neighbor interactions in one dimension utilizing the (finite-size) density-matrix renormalization group method. The competition between nearest- and next-nearest-neighbor interactions and nearest-neighbor hopping generates four phases in this model: two charge-density-wave insulators, a Luttinger-liquid phase, and a bond-order phase. We use finite-size scaling of the gap and various structure factors to determine the phase diagram.

DOI
10.1103/physrevb.84.115135

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We study the phase diagram of spinless fermions with nearest- and next-nearest-neighbor interactions in one dimension utilizing the (finite-size) density-matrix renormalization group method. The competition between nearest- and next-nearest-neighbor interactions and nearest-neighbor hopping generates four phases in this model: two charge-density-wave insulators, a Luttinger-liquid phase, and a bond-order phase. We use finite-size scaling of the gap and various structure factors to determine the phase diagram.
We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest-neighbor range.In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor interactions.Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations.The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles.In relation with recent studies, we show several emergent transition lines with a central charge c = 3/2 between the Luttinger liquid and the cluster Luttinger liquid phases.These results could be experimentally investigated using highly tunable quantum simulators.
We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).
We establish the ground-state phase diagram of a spinless fermion model with the nearest and next-nearest-neighbor repulsions via the density-matrix-renormalization-group method. The bond-order (BO) correlation function and its static structure factor can be employed to accurately determine the BO phase boundaries. The first derivative of the charge-density wave (CDW) structure factor and the second derivative of the energy are expect to diverge at the 2k(F)-CDW-BO transition point, which indicates that a second-order transition occurs. We determine the metallic-4k(F)-CDW boundary by analyzing the decay behavior of the charge correlation function near the transition point.
We study the one-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hopping integrals by using the density-matrix renormalization group method and Hartree-Fock approximation. Based on the calculated results for the spin gap, total-spin quantum number, and Tomonaga-Luttinger-liquid parameter, we determine the ground-state phase diagram of the model in the entire filling and wide parameter region. We show that, in contrast to the weak-coupling regime where a spin-gapped liquid phase is predicted in the region with four Fermi points, the spin gap vanishes in a substantial region in the strong-coupling regime. It is remarkable that a large variety of phases, such as the paramagnetic metallic phase, spin-gapped liquid phase, singlet and triplet superconducting phases, and fully polarized ferromagnetic phase, appear in such a simple model in the strong-coupling regime.
We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudosite density-matrix renormalization group technique. Performing a careful finite-size scaling analysis, we determine the ground-state phase diagram and convincingly prove that the model exhibits a metal-insulator quantum phase transition for the half-filled band case. In order to characterize the metallic and insulating regimes we calculate, besides the local particle densities and fermion-boson correlation functions, the kinetic energy, the charge-structure factor, the Luttinger liquid charge exponent, and the single-particle excitation gap for a one-dimensional infinite system.
We examine the ground-state properties of the one-dimensional Hubbard model at quarter filling with Coulomb interactions between nearest-neighbors V1{V}_{1}V1​ and next-nearest neighbors V2{V}_{2}V2​. Using the density-matrix renormalization group and exact diagonalization methods, we obtain for U=10tU=10tU=10t three different phases in the ${V}_{1}\text{\ensuremath{-}}{V}_{2}$ plane: 2kF2{k}_{\mathrm{F}}2kF​- and 4kF4{k}_{\mathrm{F}}4kF​-charge-density-wave (CDW) and a broad metallic phase in between. Assuming that the metal is a Tomonaga-Luttinger liquid (TLL), we calculate the TLL parameter ${K}_{\ensuremath{\rho}}$. It is largest when V1{V}_{1}V1​ and V2{V}_{2}V2​ are frustrated, and ${K}_{\ensuremath{\rho}}=0.25$ at the boundaries between the metallic phase and each of the two CDW phases.