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Phase String Effect in the t-J Model: General Theory

Z. Y. Weng·D. N. Sheng·Y. -C. Chen·C. S. Ting
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Abstract

We reexamine the problem of a hole moving in an antiferromagnetic spin background and find that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom. Previously unnoticed, such a string-like phase originates from the hidden Marshall signs which are scrambled by the hopping of the hole. We can rigorously show that this phase string is non-repairable at low energy and give a general proof that the spectral weight Z must vanish at the ground-state energy due to the phase string effect. Thus, the quasiparticle description fails here and the quantum interference effect of the phase string dramatically affects the long-distance behavior of the injected hole. We introduce a so-called phase-string formulation of the t-J model for a general number of holes in which the phase string effect can be explicitly tracked. As an example, by applying this new mathematical formulation in one dimension, we reproduce the well-known Luttinger-liquid behaviors of the asymptotic single-electron Green's function and the spin-spin correlation function. We can also use the present phase string theory to justify previously developed spin-charge separation theory in two dimensions, which offers a systematic explanation for the transport and magnetic anomalies in the high-T_c cuprates.

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Z. Y. Weng, D. N. Sheng, Y. -C. Chen, C. S. Ting. 1996-12-03. Phase String Effect in the t-J Model: General Theory. https://doi.org/10.1103/physrevb.55.3894

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