# Nature of the randomness-induced quantum spin liquids in two dimensions

## TL;DR

This paper investigates the properties and excitations of the randomness-induced quantum spin liquid state, known as the random-singlet state, in two-dimensional frustrated lattices using exact-diagonalization and Hams-de Raedt methods.

## Contribution

It provides a detailed analysis of the ground state, low-energy excitations, and thermodynamic properties of the 2D random-singlet state, highlighting the role of frustration and comparing with 1D systems.

## Key findings

- Ground state consists of isolated singlet-dimers and orphan spins.
- Low-energy excitations include singlet-to-triplet and orphan spin diffusion.
- Enhanced dynamical liquid-like features observed in 2D random-singlet state.

## Abstract

The nature of the randomness-induced quantum spin liquid state, the random-singlet state, is investigated in two dimensions (2D) by means of the exact-diagonalization and the Hams-de Raedt methods for several frustrated lattices, e.g., the triangular, the kagome and the J_1-J_2 square lattices. Properties of the ground state, the low-energy excitations and the finite-temperature thermodynamic quantities are investigated. The ground state and the low-lying excited states consist of nearly isolated singlet-dimers, clusters of resonating singlet-dimers, and orphan spins. Low-energy excitations are either singlet-to-triplet excitations, diffusion of orphan spins accompanied by the recombination of nearby singlet-dimers, creation or destruction of resonating singlet-dimers clusters. The latter two excitations give enhanced dynamical `liquid-like' features to the 2D random-singlet state. Comparison is made with the random-singlet state in a 1D chain without frustration, the similarity and the difference between in 1D and in 2D being highlighted. Frustration in a wide sense, not only the geometrical one but also including the one arising from the competition between distinct types of interactions, play an essential role in stabilizing this frustrated random singlet state. Recent experimental situations on both organic and inorganic materials are reviewed and discussed.