Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation

TL;DR

This paper introduces a novel spin-orbital entangled RVB state on a square lattice, represented as a PEPS, revealing a striped critical spin liquid with topological properties and proposing a supporting Hamiltonian.

Contribution

It presents the first PEPS representation of a spin-orbital entangled RVB state with striped critical spin liquid characteristics.

Findings

State is a superposition of striped coverings with a topological quantum number.

The PEPS representation has bond dimension D=4.

The state supports a specific spin-orbital Hamiltonian.

Abstract

We introduce a spin-orbital entangled (SOE) resonating valence bond (RVB) state on a square lattice of spins-$\frac12$ and orbitals represented by pseudospins-$\frac12$. Like the standard RVB state, it is a superposition of nearest-neighbor hard-core coverings of the lattice by spin singlets, but adjacent singlets are favoured to have perpendicular orientations and, more importantly, an orientation of each singlet is entangled with orbitals' state on its two lattice sites. The SOE-RVB state can be represented by a projected entangled pair state (PEPS) with a bond dimension $D=4$. This representation helps to reveal that the state is a superposition of striped coverings conserving a topological quantum number. The stripes are a critical quantum spin liquid. We propose a spin-orbital Hamiltonian supporting a SOE-RVB ground state.