We analyze effective $d$ -wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive $d$ -wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the $d$ -wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enhanced by the nearest-neighbor interaction in the extended Hubbard model, but they always remain smaller than the dominant antiferromagnetic, pairing, or charge density wave fluctuations.We analyze effective $d$-wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive $d$-wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the $d$-wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enhanced by the nearest-neighbor interaction in the extended Hubbard model, but they always remain smaller than the dominant antiferromagnetic, pairing, or charge density wave fluctuations.

arXiv:1203.2887Physical Review BAug 10, 201252 citations

Spin waves in antiferromagnetic phase in the (t-J)-model

Yu. A. Izyumov, B. M. Letfulov

Journal of Magnetism and Magnetic MaterialsFeb 1, 19950 citations

Vertex Corrections near the Stripe Phase

S. Caprara, C. Di Castro, Philipp Werner +1 more

We calculate the vertex corrections within a model for fermion quasiparticles coupled with charge and spin fluctuations, which provide the relevant scattering mechanism near the stripe instability in high- T(c) cuprates. The logarithmic divergence of the vertex, which characterizes the spin-fermion model near the antiferromagnetic instability, is ruled out, due to the incommensuration of the charge and spin modulation within the stripe phase, as revealed by neutron scattering. This simplifies the skeleton structure of the problem. The vertex is negative in the relevant kinematical regime, effectively reducing the interaction strength. Our results apply to generic incommensurate instabilities of electronic origin.We calculate the vertex corrections within a model for fermion quasiparticles coupled with charge and spin fluctuations, which provide the relevant scattering mechanism near the stripe instability in high- T(c) cuprates. The logarithmic divergence of the vertex, which characterizes the spin-fermion model near the antiferromagnetic instability, is ruled out, due to the incommensuration of the charge and spin modulation within the stripe phase, as revealed by neutron scattering. This simplifies the skeleton structure of the problem. The vertex is negative in the relevant kinematical regime, effectively reducing the interaction strength. Our results apply to generic incommensurate instabilities of electronic origin.

Physical Review LettersJan 25, 20023 citations

Spin and charge fluctuations in the t–J model

George Jackeli, Nikolay M. Plakida

Physica B Condensed MatterJan 1, 19991 citation

Mean-field ground-state phase diagram of the ${t-t^\prime}$ ionic-Hubbard chainMean-field ground-state phase diagram of the ${t-t^\prime}$ ionic-Hubbard chain

Sekania, Mikheil, Shota Garuchava, Jamal Berakdar +1 more

Ground state (GS) phase diagram of the one dimensional repulsive Hubbard model with both nearest neighbor ( $t$ ) and next-nearest-neighbor ( $t^{\prime}$ ) hopping and a staggered potential ( $Δ$ ) is determined in the case of half-filled band and zero net magnetization within the mean-field theory. The model may be realized by cold atoms in engineered optical lattices. Connection between the peculiarities of the GS phase diagram of the interacting system and the topological Lifshitz transition in GS of free particle chain is discussed. The mean-field Hamiltonian is given by six order parameters, which are determined self-consistently. It is shown that the GS phase diagram {\em predominantly} consists of insulating phases characterized by coexistence of the long-range ordered modulations of the charge- (I) and antiferromagnetic (AF) spin-density with wavelengths equal to two and/or four lattice units. Below the Lifshitz transition, the GS phase diagram is qualitatively similar to that of the standard ( ${t^{\prime}=0}$ ) ionic Hubbard model. After the Lifshitz transition, charge- and spin-density modulations emerge within the sublattices and have wavelengths equal to four lattice units. For moderate values of the on-site repulsion the insulating phases are characterized by the presence of I and AF modulations coexisting with ferrimagnetic spin- and charge-density modulations within the one sublattice, or by the coexistence of I order and additional AF spin density modulation only within the sublattice with high ionic potential. At large repulsion the insulating phase with AF order inside both sublattices and remaining small ionicity left between the sublattices is realized.Ground state (GS) phase diagram of the one dimensional repulsive Hubbard model with both nearest neighbor ($t$) and next-nearest-neighbor ($t^{\prime}$) hopping and a staggered potential ($Δ$) is determined in the case of half-filled band and zero net magnetization within the mean-field theory. The model may be realized by cold atoms in engineered optical lattices. Connection between the peculiarities of the GS phase diagram of the interacting system and the topological Lifshitz transition in GS of free particle chain is discussed. The mean-field Hamiltonian is given by six order parameters, which are determined self-consistently. It is shown that the GS phase diagram {\em predominantly} consists of insulating phases characterized by coexistence of the long-range ordered modulations of the charge- (I) and antiferromagnetic (AF) spin-density with wavelengths equal to two and/or four lattice units. Below the Lifshitz transition, the GS phase diagram is qualitatively similar to that of the standard (${t^{\prime}=0}$) ionic Hubbard model. After the Lifshitz transition, charge- and spin-density modulations emerge within the sublattices and have wavelengths equal to four lattice units. For moderate values of the on-site repulsion the insulating phases are characterized by the presence of I and AF modulations coexisting with ferrimagnetic spin- and charge-density modulations within the one sublattice, or by the coexistence of I order and additional AF spin density modulation only within the sublattice with high ionic potential. At large repulsion the insulating phase with AF order inside both sublattices and remaining small ionicity left between the sublattices is realized.

arXiv:2211.10543Nov 19, 20220 citations

Fluctuations of the two-dimensional quantum antiferromagnet in a disordered phase

V. I. Belinicher, João da Providência

May 11, 19990 citations

We analyze effective

d

-wave interactions in the two-dimensional extended Hubbard model at weak coupling and small to moderate doping. The interactions are computed from a renormalization group flow. Attractive

d

-wave interactions are generated via antiferromagnetic spin fluctuations in the pairing and charge channels. Above Van Hove filling, the

d

-wave charge interaction is maximal at incommensurate diagonal wave vectors, corresponding to nematic fluctuations with a diagonal modulation. Below Van Hove filling a modulation along the crystal axes can be favored. The nematic fluctuations are enhanced by the nearest-neighbor interaction in the extended Hubbard model, but they always remain smaller than the dominant antiferromagnetic, pairing, or charge density wave fluctuations.

Mean-field ground-state phase diagram of the

{t-t^\prime}

ionic-Hubbard chain

Ground state (GS) phase diagram of the one dimensional repulsive Hubbard model with both nearest neighbor (

t

) and next-nearest-neighbor (

t^{\prime}

) hopping and a staggered potential (

Δ

) is determined in the case of half-filled band and zero net magnetization within the mean-field theory. The model may be realized by cold atoms in engineered optical lattices. Connection between the peculiarities of the GS phase diagram of the interacting system and the topological Lifshitz transition in GS of free particle chain is discussed. The mean-field Hamiltonian is given by six order parameters, which are determined self-consistently. It is shown that the GS phase diagram {\em predominantly} consists of insulating phases characterized by coexistence of the long-range ordered modulations of the charge- (I) and antiferromagnetic (AF) spin-density with wavelengths equal to two and/or four lattice units. Below the Lifshitz transition, the GS phase diagram is qualitatively similar to that of the standard (

{t^{\prime}=0}

) ionic Hubbard model. After the Lifshitz transition, charge- and spin-density modulations emerge within the sublattices and have wavelengths equal to four lattice units. For moderate values of the on-site repulsion the insulating phases are characterized by the presence of I and AF modulations coexisting with ferrimagnetic spin- and charge-density modulations within the one sublattice, or by the coexistence of I order and additional AF spin density modulation only within the sublattice with high ionic potential. At large repulsion the insulating phase with AF order inside both sublattices and remaining small ionicity left between the sublattices is realized.