Abstract

For several decades, the attention of both theoretical and experimental physicists has focused on finding examples of quantum spin liquids (QSL) — exotic phases of matter characterized by the spin fractionalization, whereby the energy and momentum are carried not by spin waves, but by emergent elementary excitations. By contrast, defining a quantum spin ‘solid’ as a state that spontaneously breaks the lattice translation symmetry, I shall pose the following question — how do quantum solids ‘melt’ and how does entanglement establish itself in a QSL ? To answer this question, I shall present our recent work on several 2D systems, from the familiar spin-1/2 on frustrated lattices, to the perhaps less familiar models of spin-1 and SU(3) objects. We study these models using the density matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS) techniques, supplemented by the analytical mean-field and linear flavor wave theory calculations. I shall also discuss another mechanism of quantum ‘melting’, induced by a strong magnetic field — the conventional picture is that this process can be understood as a Bose-Einstein condensation of the auxiliary bosons. Here we show that a more exotic, non-BEC transition occurs when magnetic frustration drives the system across the Lifshitz point, and we find an exotic bosonic liquid that avoids the BEC altogether — so-called Bose metal with algebraic correlations.