Supernematic

• URL: http://arxiv.org/abs/2511.10642v1
• Date: Fri, 14 Nov 2025 02:01:01 GMT
• Title: Supernematic
• Authors: Dan Mao, Eun-Ah Kim,
• Abstract summary: Quantum theory of geometrically frustrated systems is usually approached as a gauge theory where the local conservation law becomes the Gauss law.<n>We show that it can do something fundamentally different: enforce a global conserved quantity via a non-perturbative tiling invariant.<n>This establishes a route to a novel quantum many-body state driven by constraints.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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