Brane parity orders in the insulating state of Hubbard ladders

TL;DR

This paper introduces a new definition of parity brane correlators in Hubbard ladders that remain finite with interchain coupling, revealing different insulating phases related to spin and charge properties.

Contribution

It proposes a modified parity brane correlator that stays non-zero in higher dimensions and analyzes its behavior in Hubbard ladders using DMRG simulations.

Findings

Charge parity brane remains non-zero at all repulsive interactions.

Spin parity brane is non-zero in even-leg ladders, indicating a spin gapped phase.

Numerical DMRG confirms the theoretical predictions.

Abstract

The Mott insulating state of the Hubbard model at half-filling could be depicted as a spin liquid of singly occupied sites with holon-doublon quantum fluctuations localized in pairs. In one dimension the behavior is captured by a finite value of the charge parity string correlator, which fails to remain finite when generalized to higher dimensions. We recover a definition of parity brane correlator which may remain nonvanishing in presence of interchain coupling, by assigning an appropriate fractional phase to the parity breaking fluctuations. In case of Hubbard ladders at half-filling, we find that the charge parity brane is non-zero at any repulsive value of interaction. The spin parity brane instead becomes nonvanishing in the even-leg case, in correspondence to the onset of the spin gapped D-Mott phase, which is absent in the odd-leg case. The behavior of the parity correlators is also analyzed by means of a numerical DMRG analysis of the one- and two-leg ladder.