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arXiv:cond-mat/0311019 · International Journal of Modern Physics B

Stripe Phase: Analytical Results for Weakly Coupled Repulsive Hubbard Model

Sergei I. Mukhin, Sergey I. Matveenko

Published Aug 20, 2003• 4 citations
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Abstract

Motivated by the stripe developments in cuprates, we review analytical results for the spin-charge solitonic superstructures derived in the framework of the Hubbard model in our studies of weakly coupled (quasi) one-dimensional repulsive electron systems on a lattice. These results demonstrate that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wavevectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, besides the wavevectors, mutual phases of the charge and spin densities also become coupled due to a quantum interference phenomenon, leading to the stripe phase instability. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential leads to the vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group ("parquet") analysis away from half filling are also presented. They reveal transient-scale correlations resembling the mean-field pattern. Possible correspondence of our theory with the experimental data on stripe phase in high Tc cuprates is discussed.

DOI
10.1142/s0217979203022726

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Motivated by the stripe developments in cuprates, we review analytical results for the spin-charge solitonic superstructures derived in the framework of the Hubbard model in our studies of weakly coupled (quasi) one-dimensional repulsive electron systems on a lattice. These results demonstrate that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wavevectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, besides the wavevectors, mutual phases of the charge and spin densities also become coupled due to a quantum interference phenomenon, leading to the stripe phase instability. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential leads to the vanishing of the stripe order. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. Results of the 1D renormalization group ("parquet") analysis away from half filling are also presented. They reveal transient-scale correlations resembling the mean-field pattern. Possible correspondence of our theory with the experimental data on stripe phase in high Tc cuprates is discussed.
A quantum interference mechanism of the stripe-phase instability in quasi-one-dimensional (1D) repulsive electron system is proposed. It is shown that away from half-filling periodic lattice potential causes cooperative condensation of the spin and charge superlattices. The leading spin-charge coupling term in the effective Landau functional is derived microscopically. 1D renormalization-group analysis indicates transient-scale correlations resembling the mean-field pattern. These results reveal possible mechanism of the numerically predicted spin-charge coupling phenomenon, which was recently observed in doped cuprates and nickelates.
A quantum interference mechanism of the stripe phase instability in quasi one-dimensional (1D) repulsive electron system is proposed. The leading spin-charge coupling term in Landau functional is derived microscopically. It is shown that away from half filling, periodic lattice potential causes cooperative condensation of the spin and charge superlattices, which constitute a 1D analogue of the experimentally observed quasi 2D structures in lanthanum cuprates and nickelates. Renormalization group analysis qualitatively supports the Hartree-Fock picture.
Abstract. Magnetic and charge susceptibilities of the two-dimensional repulsive Hubbard model are investigated applying a strong coupling diagram technique in which the expansion in powers of the hopping constants is used. For small lattices and high temperatures results are in agreement with Monte Carlo simulations. With the departure from half-filling x the low-frequency magnetic susceptibility becomes incommensurate and the incommensurability parameter grows with x. The incommensurability, its dependence on frequency and on x resemble experimental results in lanthanum cuprates. Also for finite x sharp maxima appear in the static charge susceptibility. The maxima are finite which points to the absence of the long-range charge ordering (static stripes). However, for x ≈ 0.12 the maxima are located near the momenta (0, ±π/2), (±π/2, 0). In this case an interaction of carriers with tetragonal distortions can stabilize stripes with the wavelength of four lattice spacings, as observed in the low-temperature tetragonal phase of cuprates. As follows from the obtained results, the magnetic incommensurability is not a consequence of the stripes. The Hubbard model is thought to be appropriate to describe the main features of electron correlations in narrow energy bands, leading to collective effects such as magnetism and
Many strongly correlated materials are characterized by deeply intertwined charge and spin order. Besides their high superconducting transition temperatures, one of the central features of these complex patterns in cuprates is a phase shift which occurs across lines of decreased hole density. That is, when doped away from their antiferromagnetic phase, the additional charge is not distributed uniformly, but rather in ``stripes.'' The sublattices preferentially occupied by up and down spin are reversed across these stripes, a phenomenon referred to as a ``$\ensuremath{\pi}$ phase shift.'' Many of the spin-charge patterns, including the $\ensuremath{\pi}$ phase shift, are reproduced by density matrix renormalization group and quantum Monte Carlo calculations of simplified tight binding (repulsive Hubbard) models. In this paper we demonstrate that this sublattice reversal is generic by considering the corresponding phenomenon in the attractive Hubbard Hamiltonian, where a charge density wave phase forms at half filling. We introduce charge stripes via an appropriate local chemical potential; measurements of charge correlation across the resulting lines of lowered density reveal a clear $\ensuremath{\pi}$ phase.
We study a one-dimensional (1D) electron liquid embedded in a 2D antiferromagnetic insulator, and coupled to it via a weak antiferromagnetic spin-exchange interaction. We argue that this model may qualitatively capture the physics of a single charge stripe in the cuprates on length and time scales shorter than those set by its fluctuation dynamics. Using a local mean-field approach we identify the low-energy effective theory that describes the electronic-spin sector of the stripe as that of a sine-Gordon model. We determine its phases via a perturbative renormalization-group analysis. For realistic values of the model parameters we obtain a phase characterized by enhanced spin density and composite charge-density-wave correlations, coexisting with subleading triplet and composite singlet-pairing correlations. This result is shown to be independent of the spatial orientation of the stripe on the square lattice. We argue that slow transverse fluctuations of the stripes tend to suppress the density correlations, thus promoting the pairing instabilities. The largest amplitudes for the composite instabilities appear when the stripe forms an antiphase domain wall in the antiferromagnet. For twisted spin alignments the amplitudes decrease and leave room for a new type of composite pairing correlation, breaking parity but preserving time-reversal symmetry.
Abstract A microscopic understanding of the strongly correlated physics of the cuprates must account for the translational and rotational symmetry breaking that is present across all cuprate families, commonly in the form of stripes. Here we investigate emergence of stripes in the Hubbard model, a minimal model believed to be relevant to the cuprate superconductors, using determinant quantum Monte Carlo (DQMC) simulations at finite temperatures and density matrix renormalization group (DMRG) ground state calculations. By varying temperature, doping, and model parameters, we characterize the extent of stripes throughout the phase diagram of the Hubbard model. Our results show that including the often neglected next-nearest-neighbor hopping leads to the absence of spin incommensurability upon electron-doping and nearly half-filled stripes upon hole-doping. The similarities of these findings to experimental results on both electron and hole-doped cuprate families support a unified description across a large portion of the cuprate phase diagram.