Quantum Melting of Spin `Solids’ in 2D

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 the emergent elementary excitations. By contrast, defining a quantum spin `solid’ as a state that spontaneously breaks the lattice translation symmetry (be it via Né order or by forming a valence bond crystal), I will pose the following question — how do quantum solids `melt’ and how does entanglement establish itself in a QSL? To answer this question, I will present our recent work on several 2D systems, from the familiar spin-1/2 on a frustrated square lattice, 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. In the last part of the talk, I will 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.