Charge modulation as fingerprints of phase-string triggered interference

Abstract

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high Tc cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock type mean field theory. Here we demonstrate a new mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite t − J ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This new form of charge modulation can be understood analytically in a path-integral language with a mean-field like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left-and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.

Spin and charge modulations in a single-hole-doped Hubbard ladder: Verification with optical lattice experiments

“…Our key results (i) to (iii) for the Hubbard model, however, were not contained in Ref. [14]. The fact that density modulations of bulk samples also occur in small samples means that strong correlations operate within a relatively short range.…”

“…and Z.W.) in a two-leg ladder of the t-J model [14]. Our key results (i) to (iii) for the Hubbard model, however, were not contained in Ref.…”

“…As a hole moves from point a to point b and back, different loops connecting a and b contain different phase-string factors τ ps C , leading to an oscillator in spatial density [14].…”

“…We have studied the case of a single hole injected into the half-filled two-leg ladder using density matrix renormalization group (DMRG) with the numerical details similar to those used in Ref. [14] for the t-J case. Without doping the hole, the density profiles of both spin and charge are simply flat as all the charge and spin fluctuations are gapped in the Mott regime when U is big enough and spins are short-range singlet paired.…”

“…) created by removing a down-spin away from the half-filling spin ladder, a total spin S z = 1/2 is found in a spin gapped background in the large U/t (Mott) regime. Such a total S z = 1/2 is found to distribute around the hole at a given site with an alternative distribution of up (red circle) and down (blue circle) spins (with the magnitude represented by the size of each full circle as determined by the hole-spin correlation function [14]). At α = 0.4, the doped charge is tightly bound with a spin-1/2; in contrast, the hole and the spin-1/2 are loosely bound at α = 1, where the phase string becomes unscreened as previously discussed in the context of the t-J ladder [12] (see text).…”