Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagom\'e Lattice

TL;DR

This paper maps the complex phase diagram of a spin-1/2 Heisenberg model on the kagome lattice, revealing various quantum phases including spin liquids, magnetic orders, and phase transitions using advanced numerical methods.

Contribution

It provides the first comprehensive phase diagram of the kagome lattice Heisenberg model with multiple neighbor interactions, identifying new quantum spin liquid and magnetic phases.

Findings

Identification of a time-reversal invariant quantum spin liquid phase at small interactions.

Discovery of a chiral spin liquid and cuboc1 magnetic order with distinct time-reversal symmetry breaking.

Observation of both first-order and continuous quantum phase transitions between phases.

Abstract

We study the quantum phase diagram of the spin-$1/2$ Heisenberg model on the kagom\'e lattice with first-, second-, and third-neighbor interactions $J_1$, $J_2$, and $J_3$ by means of density matrix renormalization group. For small $J_2$ and $J_3$, this model sustains a time-reversal invariant quantum spin liquid phase. With increasing $J_2$ and $J_3$, we find in addition a $q=(0,0)$ N\'{e}el phase, a chiral spin liquid phase, a valence-bond crystal phase, and a complex non-coplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first order phase transition. The transitions from the chiral spin liquid to both the $q=(0,0)$ phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.