From Quantum Dimers to the pi-flux Toric Code via Deconfined Multicriticality
cond-mat.str-el, cond-mat.stat-mech, hep-th
Submitted: 2026-03-24
Updated: 2026-03-24
Journal ref: Phys. Rev. B 114, 165131 (2026)
DOI: 10.1103/1bht-9h21
License: http://creativecommons.org/licenses/by/4.0/
The gist: Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals.
Terminology
Abstract
Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals. We introduce a tensor-product regularisation of the dimer Hilbert space that yields a qubit Hamiltonian interpolating from the RK model to the π-flux toric code, thereby accessing a deconfined Z 2 topological liquid. In this framework, the Z 2 liquid descends from a multicritical U(1) spin liquid through condensation of a charge-2 Higgs field, thus avoiding confinement. Using iDMRG together with low-energy field theory, we determine a phase diagram containing two continuous quantum phase transitions -- a 3 D XY transition between the Z 2 liquid and the columnar/plaquette-VBS, and a quantum Lifshitz transition between two dimer crystals -- alongside a first-order transition between the staggered crystal and the Z 2 liquid. Our field theory suggests a deconfined multicritical point described by an Abelian Higgs model with dynamical critical exponent, z=2, where the three transitions meet, highlighting the interplay of fractionalisation and emergent gauge fluctuations.
Sources
- Translational symmetry breaking in two-dimensional antiferromagnets and superconductors
- Odd Toric Code in a tilted field: Higgs-confinement multicriticality, spontaneous self-duality symmetry breaking, and valence bond solids
- Infinite size density matrix renormalization group, revisited
- Entanglement in topological systems
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