Devil's staircases, quantum dimer models, and stripe formation in strong coupling models of quantum frustration

TL;DR

This paper introduces a 2D quantum dimer model exhibiting an infinite sequence of striped phases forming an incomplete devil's staircase, illustrating how large-period stripe order can emerge in frustrated quantum systems with short-range interactions.

Contribution

It presents a generic, short-range interacting quantum dimer model that demonstrates an infinite devil's staircase of striped phases without symmetry breaking or fine-tuning.

Findings

Displays an infinite number of periodic striped phases at T=0

Phases form an incomplete devil's staircase with arbitrarily large periods

Provides a mechanism for large-period stripe formation in frustrated quantum magnets

Abstract

We construct a two-dimensional microscopic model of interacting quantum dimers that displays an infinite number of periodic striped phases in its T=0 phase diagram. The phases form an incomplete devil's staircase and the period becomes arbitrarily large as the staircase is traversed. The Hamiltonian has purely short-range interactions, does not break any symmetries of the underlying square lattice, and is generic in that it does not involve the fine-tuning of a large number of parameters. Our model, a quantum mechanical analog of the Pokrovsky-Talapov model of fluctuating domain walls in two dimensional classical statistical mechanics, provides a mechanism by which striped phases with periods large compared to the lattice spacing can, in principle, form in frustrated quantum magnetic systems with only short-ranged interactions and no explicitly broken symmetries.