Phase String Effect in a Doped Antiferromagnet

Abstract

Based on the t-J model, it is shown that a hole moving on an antiferromagnetic spin background always induces a phase-string effect. Such a previously unnoticed phase string is revealed by explicitly tracking the Marshall sign and can be rigorously shown to be nonrepairable at low energy. Its quantum interference can drastically modify the long-wavelength behavior of the doped hole, leading to a vanishing spectral weight Z at the ground-state energy. Implication for finite doping is also discussed.[ S0031-9007(96) PACS numbers: 71.27.+a, 74.20.Mn, 75.10.Jm A hole injected into a two-dimensional (2D) antiferromagnet has been studied extensively [1][2][3] based on the t-J model. It is well known that a string of spin mismatches left by the hopping of the injected hole on the spin background can be repaired through the spin flip process. Consequently the hole is believed to be mobile without a confining potential linearly proportional to the length of the path. However, whether such a mobile hole can be described as a quasiparticle is still controversial.The key issue [4] involves the spectral weight Z at the ground-state energy E G . Z͑E G ͒ fi 0 means a finite overlap of the "bare" hole state with the true ground state. It implies that the real hole in the ground state behaves like a spin polaron with the bare hole carrying a spin distortion around it. If Z͑E G ͒ 0, then each injected hole will cause a global adjustment in the original ground state with a breakdown of the perturbatively treatable quasiparticle picture. The main difficulty in this problem arises from the fact that as different from the usual phonon-polaron picture, SU(2) spins are involved here and a U(1) phase plays an important role in shaping the long-distance part of a spin polaron with little energy cost. The spectral weight Z͑E G ͒ at the ground-state energy is particularly sensitive to such long-wavelength, lowenergy correlations in the system. Even though exact diagonalization calculations on small lattices [2,3] have indicated a quasiparticle peak at the energy bottom of the spectral function, when the lattice size goes to infinity it is hard to tell whether such a quasiparticle peak would still stay at the lower end of the spectra or there could be some weight (e.g., a tail) emerging below the peak which vanishes at the ground-state energy [such that Z͑E G ͒ 0]. Therefore, a more accurate approach would be desirable in order to get access to this long-distance regime. In this Letter, by explicitly tracking the Marshall sign, we show that the injected hole always has to pick up a sequence of signs (phases) from the quantum spin background. In contrast to the well-known repairable string defect of spin mismatches, we find that the phase string revealed here cannot be dynamically "eliminated" through the low-lying spin dynamics. Consequently, it dramatically modifies the long-wavelength behaviors of the doped hole. In particular, the spectral weight Z͑E G ͒ has to vanish due to such a nonrepairable phase-string effect.Let us start with ...

Mean-field description of the phase string effect in thet−Jmodel

“…Due to such a sign, a hole moving from a site a to an another site b will acquire a sequence of signs, i.e., a phase string as shown in Fig. 1, which has been shown [16,17] to be nonrepairable by the spin flip process governed by H J . It implies that the slave-fermion formalism of the t − J model cannot be treated in a perturbative way in doped case.…”

“…A sign σ = ±1 then appears in the hopping term (2.3) which is the origin of the phase string effect [16,17] mentioned in the Introduction. Due to such a sign, a hole moving from a site a to an another site b will acquire a sequence of signs, i.e., a phase string as shown in Fig.…”

“…[14] This implies that doped holes may have introduced some singular doping effect which has been mistreated in the mean-field approximations. Such a singular doping effect has been recently identified [16,17] by reexamining the motion of doped holes in the AF background. It has been found that spin-mismatches caused by the hopping of doped holes cannot be completely "repaired" through spin flips at low energy.…”

“…Such a residual nonrepairable effect can be expressed by a path-dependent phase product known as phase string. [16] Due to the phase string effect, a hole slowly moves through a closed path will acquire a nontrivial Berry's phase. As this phase string effect is very singular locally at a lattice constant scale, its topological effect can be easily lost if a conventional mean-field average is involved -a reason causing the aforementioned spiral instability.…”

Excitonic quasiparticles in a spin–orbit Mott insulator

“…This spin-polaron picture is supported by numerical approaches, such as quantum Monte Carlo 4 , exact diagonalization 5 and self-consistent Born approximation (SCBA) 2 . In a contrasting picture, the notion of QP can break down due to various mechanism such as orthogonality catastrophe 6 , spin-charge separation 7 and/or localization effects 8 , reflecting the unconventional nature of two-dimensional (2D), strongly interacting fermions. To date, no evidence for a QP has been found in experiments [9][10][11][12] that probe the dynamics of a single hole doped into a 2D spin-1/2 quantum AFs.…”