Exact sign structure of the $t$-$J$ chain and the single hole ground state

TL;DR

This paper reveals the nontrivial sign structure, known as the phase string, in the single-hole $t$-$J$ chain, demonstrating its crucial role in Mott physics, and uses DMRG and variational methods to analyze its effects.

Contribution

It identifies and analyzes the exact sign structure in the $t$-$J$ chain, showing its impact on physical properties and providing a variational wave function that captures these effects.

Findings

Sign structure causes characteristic momentum and Luttinger liquid behavior.

DMRG simulations show differences with and without the sign structure.

Variational wave function reproduces key DMRG results with correct sign structure.

Abstract

Injecting a single hole into a one-dimensional Heisenberg spin chain is probably the simplest case of doping a Mott insulator. The motion of such a single hole will generally induce a many-body phase shift, which can be identified by an exact sign structure of the model known as the phase string. We show that the sign structure is nontrivial even in this simplest problem, which is responsible for the essential properties of Mott physics. We find that the characteristic momentum structure, the Luttinger liquid behavior, and the quantum phase interference of the hole under a periodic boundary condition, can all be attributed to it. We use the density matrix renormalization group (DMRG) numerical simulation to make a comparative study of the $t$-$J$ chain and a model in which the sign structure is switched off. We further show that the key DMRG results can be reproduced by a variational wave function with incorporating the correct sign structure. Physical implications of the sign structure for doped Mott insulators in general are also discussed.