Stripe phase: analytical results for weakly coupled repulsive Hubbard model

TL;DR

This paper provides analytical insights into stripe phases in weakly coupled Hubbard models, revealing how charge and spin density modulations interact and lead to stripe order, with implications for high-temperature cuprate superconductors.

Contribution

It offers a microscopic derivation of the spin-charge coupling and analyzes the stripe phase formation using renormalization group and self-consistent methods.

Findings

Charge density fluctuations favor specific wave vectors near half filling.

Quantum interference couples CDW and SDW phases at low temperatures.

Stripe order vanishes when the lattice potential is turned off.

Abstract

Motivated by the stripe developments in cuprates, we review some analytical results of our studies of the charge- and spin density modulations (CDW and SDW) in a weakly coupled one dimensional repulsive electron system on a lattice. It is shown that close to half filling, in the high temperature regime above the mean field transition temperature, short range repulsions favor charge density fluctuations with wave vectors bearing special relations with those of the spin density fluctuations. In the low temperature regime, not only the wave vectors, but also the mutual phases of the CDW and SDW become coupled due to a quantum interference phenomenon, leading to the stripe phase instability in a quasi one-dimensional repulsive electron system. It is shown that away from half filling periodic lattice potential causes cooperative condensation of the spin and charge superlattices. "Switching off" this potential causes 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, which indicate transient-scale correlations resembling the mean-field pattern. Farther, the self-consistent solution for the spin-charge solitonic superstructure in a quasi-one-dimensional electron system is obtained in the framework of the Hubbard model as a function of hole doping and temperature. Possible relationship with the stripe phase correlations observed in high T_c cuprates is discussed.