Supernematic

TL;DR

This paper introduces a new quantum phase called supernematic, where a global conserved quantity is enforced by geometric constraints, leading to a phase that breaks rotational symmetry without superfluidity or topological order.

Contribution

It demonstrates a mechanism linking microscopic geometry to a macroscopically phase-coherent state via a non-perturbative tiling invariant in a frustrated bosonic system.

Findings

Identification of a supernematic phase with broken rotational symmetry

Protection of a global quantum number through geometric constraints

Spontaneous symmetry breaking driven by quantum fluctuations

Abstract

Quantum theory of geometrically frustrated systems is usually approached as a gauge theory where the local conservation law becomes the Gauss law. Here we show that it can do something fundamentally different: enforce a global conserved quantity via a non-perturbative tiling invariant, rigorously linking microscopic geometry to a new macroscopically phase-coherent state. In a frustrated bosonic model on the honeycomb lattice in the cluster-charging regime at fractional filling, this mechanism protects a conserved global quantum number, the sublattice polarization $\tilde{N} = N_A - N_B$. Quantum fluctuation drives the spontaneous symmetry breaking of this global U(1) symmetry to result in a supernematic (SN) phase -- an incompressible yet phase-coherent quantum state that breaks rotational symmetry without forming a superfluid or realizing topological order. This establishes a route to a novel quantum many-body state driven by combinatorial constraints.