From exotic phases to microscopic Hamiltonians

TL;DR

This paper demonstrates how to construct microscopic SU(2) invariant spin-1/2 Hamiltonians that realize exotic quantum phases, using perturbative techniques and decoration procedures to guide experimental and numerical exploration.

Contribution

It introduces a method to reverse-engineer local Hamiltonians that exhibit predicted exotic phases, bridging effective models and microscopic realizations.

Findings

Realization of deconfined resonating valence bond liquids

Demonstration of a devil's staircase of phases with Cantor deconfinement

Identification of a 3D U(1) liquid phase with photonic excitations

Abstract

We report recent analytical progress in the quest for spin models realising exotic phases. We focus on the question of `reverse-engineering' a local, SU(2) invariant S=1/2 Hamiltonian to exhibit phases predicted on the basis of effective models, such as large-N or quantum dimer models. This aim is to provide a point-of-principle demonstration of the possibility of constructing such microscopic lattice Hamiltonians, as well as to complement and guide numerical (and experimental) approaches to the same question. In particular, we demonstrate how to utilise peturbed Klein Hamiltonians to generate effective quantum dimer models. These models use local multi-spin interactions and, to obtain a controlled theory, a decoration procedure involving the insertion of Majumdar-Ghosh chainlets on the bonds of the lattice. The phases we thus realise include deconfined resonating valence bond liquids, a devil's staircase of interleaved phases which exhibits Cantor deconfinement, as well as a three-dimensional U(1) liquid phase exhibiting photonic excitations.