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The 6s2 lone-pair electrons (Pb2+, Bi3+) and 5s2 lone-pair electrons (Sn2+, Sb3+) show different responses to birefringence than they do to second harmonic generation (SHG). In the current work, different mechanisms of birefringence and SHG responses induced by Pb2+/Sn2+ cations were investigated using the first-principles method on AB2O3F2 (A = Ba, Sn, Pb). The obtained birefringence and SHG coefficients were in good agreement with the experimental values. The anisotropic lone-pair electron distribution was found at the states near the Fermi level containing cation sp-oxygen p states. Our analyses showed the birefringences of the AB2O3F2 (A = Ba, Sn, Pb) compounds to be directly affected by the anisotropic lone-pair electron distribution, however, the SHG responses of these three compounds have a more complicated relationship with the hybrid cation-oxygen states. The expanded hybrid cation-oxygen states including the lone-pair states were concluded to endow the PbB2O3F2 compound with a stronger SHG response than those displayed by the other compounds. [ABSTRACT FROM AUTHOR]

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction. • We extend 1D Penson-Kolb model where the one-electron hopping is modified. • The phase diagram is analytically obtained at weak coupling and at half filling. • The occupation-dependent hopping induces additional instabilities. • The relevant backward scatter processes drive a spin-gap transition. • The triplet superconducting instability dominates for positively small pair-hopping. [ABSTRACT FROM AUTHOR]

Highlights • We extend the 1D t – U – J x y model up to NNN easy-plane anisotropy. • We derive quantum phase diagram at weak coupling and at half filling. • The effects of the frustration on the phase diagram is highlighted. • The mechanism for the realization of two spin-gapped phases is clarified. Abstract At weak coupling, we investigate the frustrated Hubbard chain including nearest-neighbor and next-nearest-neighbor antiferromagnetic exchange with easy-plane anisotropy J 1 x y and J 2 x y. At half filling, we obtain three different phases in the J 1 x y – J 2 x y plane: a transverse spin density wave phase, a bond order wave phase and a Luther–Emery metallic phase characterized by the coexistence of singlet superconductivity and charge density wave correlations. The frustrating exchange J 2 x y accounts for the spin-gapped phases. [ABSTRACT FROM AUTHOR]

The experimental advances in cold fermion gases motivates the investigation of a one-dimensional (1D) correlated electronic system by incorporating a four-body coupling. Using the low-energy field theory scheme and focusing on the weak-coupling regime, we extend the 1D Penson–Kolb–Hubbard (PKH) model at half filling. It is found that the additional four-body interaction may significantly modify the quantum phase diagram, favoring the presence of the superconducting phase even in the case of two-body repulsions. [ABSTRACT FROM AUTHOR]

Applying the bosonization and renormalization group techniques, we study a generalized Hubbard chain incorporating extra off-diagonal hopping processes in the weak regime, and determine rich ground-state phase diagrams. At half filling, in addition to the insulating phases (HI, MI and DI), there exist the superconducting phases (LE and LL). The off-diagonal hopping accounts for the occurrence of insulator-superconductor transition. Away from half filling, the transition from the LL to LE phase takes place, and the insulating phases disappear. The result provides an insignificant insight into unconventional scenarios for Cooper pairing and insulator-superconductor transition. [ABSTRACT FROM AUTHOR]

We study a one-dimensional anisotropic extended Hubbard model, where the inter-site density ( V ) and exchange ( J ) interactions are spin-dependent. Use of bosonization and renormalization helps investigate phase diagram. At half filling, the ground state characterizes insulating phases. The spin-dependent repulsion leads to a bond-spin-density-wave (BSDW) phase. The antiferromagnetic exchange enhances the bond-order-wave (BOW) phase while weakens the charge-density-wave (CDW) phase. When J > 4 V , the BSDW and CDW phases disappear. Away from half filling, the ground state exhibits superconducting behavior. The anisotropic interactions have an important effect on the phase structures. [ABSTRACT FROM AUTHOR]

We construct a one-dimensional (1D) theoretical model to clarify the occurrence of superconductivity. The weak-coupling (WC) theory allows a determination of the phase diagram. The constrained hopping induces additional two-body and three-body interactions. At half-filling, the three-body interaction is responsible for the triplet superconducting (TS) correlation. Away from half-filling, the two-body interaction works, favoring the singlet superconducting (SS) correlation. The results are expected to provide an insignificant insight into the superconductivity mechanism. [ABSTRACT FROM AUTHOR]

At half filling, we study analytically a one-dimensional correlated electronic system modeled by an extended Penson–Kolb–Hubbard (PKH) chain with the occupation-dependent hopping. The modification of the electron hopping amplitude is exhibited to induce the additional correlated-hopping interactions. At weak coupling, we use the field theory to obtain ground-state phase diagram, including the SDW, BCDW, BSDW, SS and TS phases for U > 0. The induced three-body attractive interaction accounts for the superconductivity absent in the usual PKH model. • We study a 1D extended PKH model with the occupation-dependent hopping. • The modified one-electron hopping leads to the correlated-hopping interactions. • The induced three-body attraction accounts for the superconducting phases. • The study supplements the understanding of quantum properties of the 1D physics. [ABSTRACT FROM AUTHOR]

By introducing a modulation parameter ( ξ ), we study the one-dimensional correlated system with modulated hopping, on-site ( U ) and nearest-neighbor ( V ) repulsions in the weak-coupling regime. The induced three-body attraction changes topology of the conventional phase diagram. Besides the usual CDW and SDW phases, a BSDW phase exists for | U − 2 V | < 8 t ξ 2 / π . In the absence of V , an insulator–metal transition takes place, and the TS phase is realized for ξ > π U / 8 t . Phenomenologically, the general quantum phase diagram including insulating and superconducting phases is discussed. [ABSTRACT FROM AUTHOR]

The ground-state properties of a 1D modified Penson–Kolb–Hubbard model characterized by alternating Hubbard interaction at odd and even sites are discussed by the bosonization scheme and the renormalization group analysis. At quarter filling, the quantum phase diagram consists of the charge-density-wave, spin-density-wave and singlet-superconductivity instabilities. The insulating phases come from the relevant umklapp process induced by the unequal on-site repulsion. The results provide a further understanding of occurrence of the umklapp process in 1D correlated electron systems. • We study the 1D modified PKH model with unequal on-site interactions. • The alternating on-site repulsion induces relevant umklapp process at quarter filling. • The study supplements understanding of quantum properties of 1D correlated systems. [ABSTRACT FROM AUTHOR]

Using the low-energy effective field theory scenario combined Abelian bosonization and renormalization-group techniques, we study the Hubbard chain with additional anisotropic nearest-neighbor and isotropic next-nearest-neighbor spin exchanges J and J′ in the weak-coupling regime. The spin correlations are non-critical due to the anisotropic J (Jxy ≠ Jz). The frustrating antiferromagnetic exchange J′ leads to an enhancement of the dimerized phase and induces a long-range charge-density-wave (CDW) phase. For smaller values of J′ (J′ < 2U/3), the quantum phase diagram consists of the insulating spin-density-wave (xy, z) and bond-charge-density-wave (BCDW) phases and the triplet superconducting (0, ±) phase. For larger J′ (J′ ≥ 2U/3), a finite CDW phase appears. The result shows that the frustrated spin exchange J′ changes the topological structure of the usual t-U-J chain. [ABSTRACT FROM AUTHOR]

In this paper, we study analytically a one-dimensional half-filled Hubbard model with nearest-neighbor Coulomb repulsion (V) and anisotropic spin exchange (J⊥ ≠ Jz) via the bosonization and renormalization-group (RG) techniques, and establish the rich phase diagrams based on the charge-spin separation hypothesis in the weak-coupling regime. The spin exchange anisotropy induces a non-critical behavior of spin correlations. The result indicates that the spin exchange anisotropy has an important impact on the topological phase diagram of the 1D extended Hubbard model. [ABSTRACT FROM AUTHOR]

In this paper, we study analytically a half-filled generalized Hubbard chain with a quite general nearest-neighbor interaction, parametrized by diagonal repulsion V, off-diagonal pair-hopping and correlated-hopping repulsions W, X and antiferromagnetic spin exchange J for small values of the interactions. The ground state phase diagram is obtained in the weak-coupling regime. Besides the charge-density-wave (CDW) and spin-density-wave (SDW) phases for large 2V/U and U/2V, respectively, we identify a bond-spin-density-wave (BSDW) for J/W < 2, 3J/2 - 2W < 2V - U < 2W - J/2 and bond-charge-density-wave (BCDW) phase for J/W > 2, 2W - J/2 < 2V - U < 3J/2 - 2W. The modulating effect of W and J is responsible for the emergence of BSDW and BCDW phases, which, however, are decreased weakly by the Umklapp scattering of parallel-spin electrons. [ABSTRACT FROM AUTHOR]

By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree-Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically. [ABSTRACT FROM AUTHOR]

Using the field theoretical bosonization and renormalization group techniques, we analytically study quantum phase diagram of a one-dimensional half-filled extended Hubbard model with on-site (U) and spin-dependent nearest-neighbor interactions (V⊥, V|) in the weak coupling regime. In the case of easy-plane anisotropy (V⊥ > V|) and at V| < U/2, the existence of bond-ordered spin-density-wave phase, corresponding to spin gapless transverse magnetization located on bonds (BSDW±) is shown. [ABSTRACT FROM AUTHOR]

In this paper, we study the phase diagram of the one-dimensional deformed t-J1-J2 model with frustrated exchange interaction. The introduction of the deformed parameter ζ softens the strength of the induced four- and six-electron interactions caused by the no-double occupancy constraint. For the small ζ and in the weak-coupling regime, we use the bosonization approach and the renormalization group techniques to obtain the phase diagram, which is characterized by the singlet-(SS) and triplet-superconducting (TS), spin-density-wave (SDW) as well as bond-charge-density wave (BCDW) instabilities. The TS and BCDW phases are realized in the whole regime while the SDW and SS correlations depend on J2/J1 < (J2/J1)c or J2/J1 > (J2/J1)c, where (J2/J1)c = 1/3. Furthermore, the deformed model with ζ ≪ 1 is expected to adiabatically connect to the conventional t-J1-J2 model with ζ = 1. [ABSTRACT FROM AUTHOR]

Abstract: The one-dimensional half-filled extended Hubbard model with on-site repulsion (U) and nearest-neighbor interactions including Coulomb repulsion (V) and exchange (J) is studied in the weak-coupling regime. We present a theoretical argument for the occurrence of bond-located phases. The bond–charge–density–wave (BCDW) is realized for and bond–spin–density–wave (BSDW) occurs for . [Copyright &y& Elsevier]

By using the bosonization approach and the renormalization group (RG) technique, we study the half-filled band one-dimensional t-U-J model with additional on-bond repulsion (W>0) in the weak-coupling regime. The presence of on-bond repulsion is responsible for realization of a metallic phase in the system, and the phase diagram is strongly controlled by the symmetry of the model. By analyzing the RG flow diagram and comparing order parameters, the phase boundaries are determined and the structure of the phase diagram is clarified. In the case of SU(2) ⊗ SU(2) symmetry, the phase diagram consists of a metallic phase characterized by a Luttinger liquid (LL) and two insulting phases characterized by the degenerate spin-density-wave (SDW) and the bond-charge-density-wave (BCDW). In the SU(2) ⊗ U(1)-symmetric case, the phase diagram contains two metallic phases: a LL and a Luther-Emery phase, and three insulating phases: the transverse SDW (SDW±), the longitudinal SDW (SDWz) and the dimerized BCDW. The insulating charge-density-wave and bond-spin-density-wave (BSDW) phases are always suppressed in the ground state. In addition, the system show a long-ranged order in the BCDW and SDWz phases. [ABSTRACT FROM AUTHOR]