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arXiv:1712.08300 · Physical review. B./Physical review. B

From the SU(2) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

Debasish Banerjee, Fu-Jiun Jiang, T. Z. Olesen, Peter Orland A. B. C, U.‐J. Wiese

Published May 9, 2018• 29 citations
arXivHTMLPDF

Abstract

We consider the $(2+1)$-dimensional $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group] are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.

DOI
10.1103/physrevb.97.205108

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We consider the (2+1)(2+1)(2+1)-dimensional SU(2)SU(2)SU(2) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z(2)\mathbb{Z}(2)Z(2) center of the SU(2)SU(2)SU(2) gauge group] are confined to each other by fractionalized strings with a delocalized Z(2)\mathbb{Z}(2)Z(2) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
Recent work [Kundu, Damle, Phys. Rev. X 15, 011018 (2025)] has demonstrated that a class of S=1S=1S=1 kagome lattice antiferromagnets with competing anisotropies can exhibit unusual low-temperature behavior that is best described in terms of the statistical mechanics of an interesting interpolation between the fully-packed dimer model and the fully-packed loop model on the bipartite honeycomb lattice. On this and other bipartite lattices in two and three dimension, such fully-packed dimer-loop models generically have two distinct power-law correlated Coulomb phases, both of which admit a low-energy description in terms of a fluctuating divergence-free polarization vector field [Phys. Rev. X 15, 011018 (2025); arXiv:2510.11607]. The transition between these phases corresponds to a confinement transition for the Z2Z_2Z2​ part of the corresponding U(1)U(1)U(1) flux [Phys. Rev. X 15, 011018 (2025); arXiv:2510.11607]. Here we demonstrate that a variant of such a topological confinement transition can also exist in dimer-loop models on non-bipartite lattices such as the kagome and triangular lattices although the low-energy description does not feature any conserved U(1)U(1)U(1) flux. In these non-bipartite dimer-loop models, both phases are short-range correlated liquids, and the topological distinction between them is in terms of a Z2Z_2Z2​-valued winding number instead of the flux of a divergence-free polarization field. In spite of this key difference, this transition appears to be in the same Ising universality class as the analogous transition of the bipartite dimer-loop models. These kagome and triangular lattice dimer-loop models correspond respectively to the low-energy limit of a class of S=1S=1S=1 antiferromagnets with competing anisotropies on the ruby lattice comprising a corner-sharing arrangement of fully-frustrated squares and a lattice of corner-sharing fully-frustrated hexagons.
The U(1)\text{U}(1)U(1) quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric flux. The two phases are separated by a weak first-order phase transition with an emergent, almost exact SO(2)\text{SO}(2)SO(2) symmetry. We construct a quantum circuit on a chip to facilitate near-term quantum computations of the nontrivial string dynamics.
We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.
Nematic Confined Phases in the U(1)U(1)U(1) Quantum Link Model on a Triangular Lattice: An Opportunity for Near-Term Quantum Computations of String Dynamics on a Chip
The U(1)U(1)U(1) quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric flux. The two phases are separated by a weak first order phase transition with an emergent almost exact SO(2)SO(2)SO(2) symmetry. We construct a quantum circuit on a chip to facilitate near-term quantum computations of the non-trivial string dynamics.
We explore the ground-state physics of two-dimensional spin-1/2 U(1) quantum link models, one of the simplest nontrivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the large mass limit we observe Neél-like vortex-antivortex and striped crystalline phases, for small masses there is a transition from the striped phases into a disordered phase whose properties resemble those at the Rokhsar-Kivelson point of the quantum dimer model. This phase is characterized on ladders by boundary Haldane-like properties, such as vanishing parity and finite string ordering. Moreover, from studies of the string tension between gauge charges, we find that, whereas the striped phases are confined, the novel disordered phase present clear indications of being deconfined. Our results open exciting perspectives of studying highly nontrivial physics in quantum simulators, such as spin-liquid behavior and confinement-deconfinement transitions, without the need of explicitly engineering plaquette terms.
We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators. While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact. An efficient cluster algorithm is used to study these exotic phases. The (2+1)(2+1)(2+1)-d system is confining at zero temperature with a spontaneously broken translation symmetry. A crystalline phase exhibits confinement via multi-stranded strings between charge-anti-charge pairs. A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate SO(2)SO(2)SO(2) global symmetry. The low-energy physics is described by a (2+1)(2+1)(2+1)-d RP(1)\mathbb{R}P(1)RP(1) effective field theory, perturbed by a dangerously irrelevant SO(2)SO(2)SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.