Four-coloring model and frustrated superfluidity in the diamond lattice

TL;DR

This paper introduces a four-coloring model for frustrated superfluidity in a diamond lattice, revealing a critical phase with algebraic order and quantum fluctuation-induced orbital ordering.

Contribution

It presents a novel four-coloring model for superfluidity on the diamond lattice, demonstrating emergent magnetostatic behavior and quantum order-by-disorder effects.

Findings

Extensive degeneracy in superfluid ground states due to coloring constraints

Power-law decay of phase and orbital correlations indicating algebraic order

Quantum fluctuations induce Néel orbital order breaking sublattice symmetry

Abstract

We propose a novel four-coloring model which describes "frustrated superfluidity" of $p$-band bosons in the diamond optical lattice. The superfluid phases of the condensate wavefunctions on the diamond-lattice bonds are mapped to four distinct colors at low temperatures. The fact that a macroscopic number of states satisfy the constraints that four differently colored bonds meet at the same site leads to an extensive degeneracy in the superfluid ground state at the classical level. We demonstrate that the phase of the superfluid wavefunction as well as the orbital angular momentum correlations exhibit a power-law decay in the degenerate manifold that is described by an emergent magnetostatic theory with three independent flux fields. Our results thus provide a novel example of critical superfluid phase with algebraic order in three dimensions. We further show that quantum fluctuations favor a N\'eel ordering of orbital angular moments with broken sublattice symmetry through the order-by-disorder mechanism.