Kinetic-to-magnetic frustration crossover and linear confinement in the doped triangular $t-J$ model

TL;DR

This study explores the complex interplay of kinetic and magnetic frustrations in the doped triangular $t-J$ model, revealing temperature-dependent magnetic correlations and evidence of linear confinement of dopants, advancing understanding of strongly correlated systems.

Contribution

It provides the first detailed analysis of magnetic frustration crossover and linear confinement phenomena in the doped triangular $t-J$ model, highlighting temperature effects and dopant behavior.

Findings

High-temperature Nagaoka ferromagnetism in doublon doping

Low-temperature antiferromagnetic order around doublons

Evidence of linear confinement of dopants via energy scaling

Abstract

Microscopically understanding competing orders in strongly correlated systems is a key challenge in modern quantum many-body physics. For example, the study of magnetic polarons and their relation to pairing in the Fermi-Hubbard model in different geometries remains one of the central questions, and may help to understand the mechanism underlying unconventional superconductivity in cuprates or transition metal dichalcogenides. With recent advances in analog quantum simulation of the Fermi-Hubbard model on non-bipartite lattices, frustrated physics can now be explored experimentally in systems lacking particle-hole symmetry. Here, we study the singly doped $t-J$ model on the triangular lattice, focusing on the competition between kinetic and magnetic frustration as a function of temperature. In doublon doped systems, we uncover a crossover between Nagaoka-type ferromagnetic (FM) correlations at high temperature and exchange mediated antiferromagnetic (AFM) order around the doublon at low temperature. For hole doped systems, kinetic Haerter-Shastry-type AFM at high temperature as well as exchange interactions at low temperature favor $120^{\circ}$ order, strengthening magnetic correlations compared to the undoped system. In the ground state, the presence of AFM correlations throughout a wide range of interactions indicates confinement of both types of dopants. In this regime we firmly establish the presence of linear confining potentials via energy scaling arguments, supporting the picture of geometric strings in the frustrated triangular $t-J$ model.