Competing pair density wave orders in the square lattice $t$-$J$ model

TL;DR

This paper uses advanced numerical methods to identify new pair density wave states in the $t$-$J$ model, shedding light on the complex competing orders in high-temperature superconductors and their relation to the pseudogap phase.

Contribution

The study introduces new types of PDW states within the $t$-$J$ model using fermionic tensor product states, providing evidence for a fluctuating quantum liquid of PDW states.

Findings

Discovery of new PDW states in the $t$-$J$ model.

Evidence for a fluctuating quantum liquid of PDW states.

Implications for understanding the pseudogap phase in cuprates.

Abstract

Over the last two decades, the competing orders in high-$T_{c}$ cuprates have been intensely studied, such as pseudogap phase, charge density waves (CDW), and pair density waves (PDW), which are thought to play a crucial role in high-temperature superconductivity. Using the $t$-$J$ model on a square lattice as the simplest model for high-$T_{c}$ cuprates, we employed the fermionic tensor product state (fTPS) method for numerical investigations. Our study revealed new types of PDW states alongside the well-known $d$-wave state and the recently discovered fluctuating PDW state within the low-energy subspace of the $t$-$J$ model. We believe that the competition among these states in the underdoped region suggests the potential existence of a fluctuating quantum liquid of PDW states, providing direct evidence for the pseudogap phase's "cheap vortex" scenario. Furthermore, we discuss the potential experimental implication of our discovery.