From Quantum Dimers to the $π$-flux Toric Code via Deconfined Multicriticality
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908909712703488 |
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| author | Chaubey, Ankush Moroz, Sergej Bhattacharjee, Subhro |
| author_facet | Chaubey, Ankush Moroz, Sergej Bhattacharjee, Subhro |
| contents | 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 $\mathbb{Z}_2$ topological liquid. In this framework, the $\mathbb{Z}_2$ 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 $3\mathrm{D}$ XY$^{\ast}$ transition between the $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23154 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Quantum Dimers to the $π$-flux Toric Code via Deconfined Multicriticality Chaubey, Ankush Moroz, Sergej Bhattacharjee, Subhro Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory 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 $\mathbb{Z}_2$ topological liquid. In this framework, the $\mathbb{Z}_2$ 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 $3\mathrm{D}$ XY$^{\ast}$ transition between the $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ 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. |
| title | From Quantum Dimers to the $π$-flux Toric Code via Deconfined Multicriticality |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.23154 |