Magnetic response and quantum critical behavior in the doped two-leg extended Hubbard ladder

TL;DR

This study explores quantum critical behavior in doped two-leg extended Hubbard ladders, revealing a transition from superconducting to density-wave states and unusual magnetic responses at criticality, relevant to ladder compounds.

Contribution

It introduces a bosonization analysis of magnetic and density-wave fluctuations, identifying critical points and calculating temperature-dependent magnetic responses with Majorana fermions.

Findings

Transition from SCd to density-wave states with increased repulsion or decreased doping

Magnetic excitations vanish at the critical point, indicating quantum criticality

Unusual temperature dependence of spin susceptibility and NMR relaxation rate

Abstract

We have investigated quantum critical behavior in the doped two-leg extended Hubbard ladder, by using a weak-coupling bosonization method. In the ground state, the dominant fluctuation changes from the conventional d-wave-like superconducting (SCd) state into density-wave states, with increasing nearest-neighbor repulsions and/or decreasing doping rate. The competition between the SCd state and the charge-density-wave state coexisting with the p-density-wave state becomes noticeable on the critical point, at which the gap for magnetic excitations vanishes. Based on the Majorana-fermion description of the effective theory, we calculate the temperature dependence of the magnetic response such as the spin susceptibility and the NMR relaxation rate, which exhibit unusual properties due to two kinds of spin excitation modes. On the quantum critical point, the spin susceptibility shows paramagnetic behavior with logarithmic corrections and the NMR relaxation rate also exhibits anomalous power-law behavior. We discuss the commensurability effect due to the umklapp scattering and relevance to the two-leg ladder compounds Sr_{14-x}Ca_xCu_{24}O_{41}.