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

TL;DR

This paper investigates the phase string effect in the t-J model, revealing its fundamental impact on the behavior of holes in antiferromagnetic backgrounds and challenging quasiparticle descriptions, with implications for high-Tc superconductivity.

Contribution

It introduces a phase-string formulation for the t-J model that explicitly tracks the phase string effect and applies it to reproduce known behaviors and justify spin-charge separation in high dimensions.

Findings

The phase string effect causes the spectral weight Z to vanish at the ground state.

The phase string effect leads to non-quasiparticle behavior of holes.

The formulation reproduces Luttinger-liquid behavior in 1D and supports spin-charge separation in 2D.

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.