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Journal of Physics Condensed Matter

Bond-order correlation and ground-state phase diagram of a one-dimensionalV1–V2spinless fermion model

Cheng-Bo Duan, Weizhong Wang

Published Aug 25, 2011• 10 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/23/36/365602

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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 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 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 reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.
The functional renormalization group (FRG) has been used widely to investigate phase diagrams, in particular the one of the two-dimensional Hubbard model. So far, the study of one-dimensional models has not attracted as much attention. We use the FRG to investigate the phases of a one-dimensional spinless tight-binding chain with nearest and next-nearest neighbor interactions at half filling. The phase diagram of this model has already been established with other methods, and phase transitions from a metallic phase to ordered phases take place at intermediate to strong interactions. The model is thus well suited to analyze the potential and the limitations of the FRG in this regime of interactions. We employ flow equations that are exact up to second order in the interaction, which implies that we take into account the frequency dependence of the two-particle vertex as well as the feedback of the dynamic self-energy. For intermediate nearest neighbor interactions, our scheme captures the phase transition from a metallic phase to a charge density wave with alternating occupation. The critical interaction, at which this transition occurs, is underestimated due to our approximations. Similarly, for intermediate next-nearest neighbor interactions, we observe a transition to a charge density wave with occupation pattern ...00110011......00110011......00110011.... We show that taking into account a feedback of the two-particle vertex in the flow equation is essential for the detection of those phases.
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.
The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.