Ground-state phase diagram of the two-dimensional t-J model

TL;DR

This study maps the ground-state phase diagram of the 2D t-J model using tensor network algorithms, revealing multiple competing phases including various superconducting and magnetic states.

Contribution

It introduces a systematic tensor network approach to identify all ground states of the 2D t-J model across different dopings and interaction strengths.

Findings

Identification of phase separation between antiferromagnetic and hole-rich states.

Discovery of four distinct homogeneous phases with different superconducting and magnetic orders.

Observation of coexistence and symmetry mixing in superconducting states.

Abstract

The ground-state phase diagram of the two-dimensional t-J model is investigated in the context of the tensor network algorithm in terms of the graded Projected Entangled-Pair State representation of the ground-state wave functions. There is a line of phase separation between the Heisenberg anti-ferromagnetic state without hole and a hole-rich state. For both J=0.4t and J=0.8t, a systematic computation is performed to identify all the competing ground states for various dopings. It is found that, besides a possible Nagaoka's ferromagnetic state, the homogeneous regime consists of four different phases: one phase with charge and spin density wave order coexisting with a p_x (p_y)-wave superconducting state, one phase with the symmetry mixing of d+s-wave superconductivity in the spin-singlet channel and p_x (p_y)-wave superconductivity in the spin-triplet channel in the presence of an anti-ferromagnetic background, one superconducting phase with extended s-wave symmetry, and one superconducting phase with p_x (p_y)-wave symmetry in a ferromagnetic background.