Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals. We introduce a tensor-product regularization 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 fractionalization and emergent gauge fluctuations.
Two-dimensional Rokhsar-Kivelson (RK) dimer models on bipartite lattices are generally limited to translation-symmetry-broken dimer crystals. We introduce a tensor-product regularization 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 fractionalization and emergent gauge fluctuations.
We construct a mapping between the two-dimensional toric code model in external magnetic fields, hz and hx, and the three-dimensional classical Ising system with plaquette interactions, which is equivalent to the three-dimensional Z2 gauge Higgs model with anisotropy between the imaginary time and spatial directions. The isotropic limit of the latter model was studied using Monte Carlo simulations on large (up to 603) lattices in order to determine the stability of the topological phase against generic magnetic field perturbations and to resolve fine details of the phase diagram. We find that the topological phase is bounded by second-order transition lines, which merge into a first-order line at what appears to be a multicritical point arising from the competition between the Higgs and confinement transitions in the Z2 gauge system. An effective field theory for this type of multicritical point (if one actually exists) is not known. Our results have potential applications to frustrated magnets, quantum computation, lattice gauge models in particle physics, and critical phenomena.
We investigate the quantum phase diagram of an “odd” variant of the two-dimensional Ising Fradkin-Shenker model, characterized by a uniform background of static e and m charges. Using large-scale tensor network and exact diagonalization methods, we determine the topology of the phase diagram, identifying an “odd” deconfined phase, confinement- and Higgs-induced valence bond solids (VBS), and a trivial paramagnet. Most notably, we uncover an exotic multicritical point along the self-dual line, where electric and magnetic excitations are related by an enriched Z 2 duality. This transition is marked by the simultaneous onset of confinement, Higgs condensation, translational symmetry breaking, and spontaneous duality symmetry breaking. Within our numerical accuracy, the transition appears continuous, involving the softening of excitation gaps for e and m anyons at finite momentum. At intermediate couplings, we further identify VBS phases with enlarged unit cells, potentially indicating frustration-induced crystalline order beyond commensurate limits.
Recently, quantum dimer models have attracted a great deal of interest as a paradigm for the study of exotic quantum phases. Much of this excitement has centered on the claim that a certain class of quantum dimer model can support a quantum U(1)-liquid phase with deconfined fractional excitations in three dimensions. These fractional monomer excitations are quantum analogs of the magnetic monopoles found in spin ice. In this paper, we use extensive quantum Monte Carlo simulations to establish the ground-state phase diagram of the quantum dimer model on the three-dimensional diamond lattice as a function of the ratio $\ensuremath{\mu}$ of the potential to kinetic-energy terms in the Hamiltonian. We find that, for ${\ensuremath{\mu}}_{c}=0.75\ifmmode\pm\else\textpm\fi{}0.02$, the model undergoes a first-order quantum phase transition from an ordered ``R state'' into an extended quantum U(1)-liquid phase, which terminates in a quantum critical Rokhsar-Kivelson (RK) point for $\ensuremath{\mu}=1$. This confirms the published field-theoretical scenario. We present detailed evidence for the existence of the U(1)-liquid phase and indirect evidence for the existence of its photon and monopole excitations. Simulations are benchmarked against a variety of exact and perturbative results, and a comparison is made of different variational wave functions. We also explore the ergodicity of the quantum dimer model on a diamond lattice within a given flux sector, identifying a new conserved quantity related to transition graphs of dimer configurations. These results complete and extend the previous analysis of O. Sikora et al. [Phys. Rev. Lett. 103, 247001 (2009)].
The deconfined phase of (2+1)-dimensional Zk gauge theory exhibits topological order, with e and m anyons that have a $2\ensuremath{\pi}/k$ braiding phase. Proliferating either e or m drives Higgs or confinement transitions, respectively. At the multicritical point where these transitions meet, the theory enjoys an additional duality symmetry that exchanges e and m anyons. This symmetry forces anyons with nontrivial braiding to close their gaps simultaneously, giving rise to a critical theory that mixes strong interactions with mutual statistics. We propose an effective $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge theory with a mutual Chern-Simons term at level k to describe the vicinity of the multicritical point for $k\ensuremath{\ge}4$. The emergence of a global $\mathrm{U}{(1)}^{\mathrm{top}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}^{\mathrm{top}}$ symmetry at the critical point imposes powerful constraints on universal properties of the phase transition. In particular, we show that (1) the lattice magnetic flux operator embeds as a conserved U(1) current with protected scaling dimension; (2) the first-order line emanating from the critical point for k=2 disappears generically for sufficiently large k; (3) the correlation length exponent approaches that of the three-dimensional XY model with corrections of order 1/k2 in the large-k limit. These predictions can be tested in near-term numerical simulations and pave the way for a more general exploration of topological quantum criticality enriched with anyon-permuting symmetries.
From QED3 to Self-Dual Multicriticality in the Fradkin-Shenker Model
We consider the Fradkin-Shenker Z2 gauge-Higgs lattice model in 2+1 dimensions, i.e. the toric code deformed by an in-plane magnetic field. Its phase diagram contains a multicritical CFT with gapless, mutually non-local electric and magnetic particles, exchanged by a Z2D self-duality symmetry. We introduce a staggered generalization of the model in which these particles carry global U(1)e and U(1)m charges, respectively, and we propose a continuum QFT description in terms of QED3 with Nf=2 Dirac fermion flavors and a charge-two Higgs field with Yukawa couplings. The conjectured phase diagram harbors a multicritical CFT with (O(2)e×O(2)m)⋊Z2D symmetry, some of which is emergent in the QFT description. We compute the scaling dimensions of some operators using a large-Nf expansion and find agreement with the emergent selection rules. The staggered model admits a deformation to the original Fradkin-Shenker model, which maps to unit-charge monopole operators in Higgs-Yukawa-QED3 that break the U(1)e×U(1)m symmetry. We show explicitly that this deformation reproduces all features of the Fradkin-Shenker phase diagram. Finally, we propose a multicritical duality between Higgs-Yukawa-QED3 and the easy-plane CP1 model (i.e. two-flavor scalar QED3 with a suitable potential), which describes spin-1/2 anti-ferromagnets on a square lattice. This duality implies a first-order line of Néel-VBS transitions ending in a deconfined quantum multicritical point, described by the same O(2)e×O(2)m symmetric CFT that arises in the staggered Fradkin-Shenker model, which separates it from a gapped Z2 spin liquid phase.
We consider a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We focus on a quantum dimer model on the triangular lattice, with doubly periodic edge weights. For simplicity we consider a 2×1 periodic model in which all weights are set to one except for a tunable horizontal edge weight labeled α. We analytically show that the model exhibits a continuous quantum phase transition at α=3, changing from a topological Z2 quantum spin liquid (α<3) to a columnar ordered state (α>3). The dimer-dimer correlator decays exponentially on both sides of the transition with the correlation length ξ∝1/∣α−3∣ and as a power-law at criticality. The vison correlator exhibits an exponential decay in the spin liquid phase, but becomes a constant in the ordered phase, which we explain in terms of loop statistics of the double-dimer model. Using finite-size scaling of the vison correlator, we extract critical exponents consistent with the 2D Ising universality class. Additionally, we analytically show that the topological Rényi entropy of order ∞ (topological min-entropy) changes from log2 for the quantum spin liquid phase α<3, to 0 for the ordered phase α>3, thereby analytically confirming the topological nature of the phase transition.