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arXiv:2608.20173

Anyon condensates of dipoles in triangular ladders

Arjo Dasgupta, Luis Santos

Published Aug 20, 2026• 0 citations
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Abstract

Hard-core dipoles in triangular ladders are an excellent platform for the study of the interplay between frustration and long-range interactions, well described by a modified version of the celebrated $J_1$--$J_2$ model. Interestingly, as shown in [Phys. Rev. Lett. 109, 227203 (2012)], such a model presents, for particular exactly-solvable conditions, a peculiar phase known as an anyon condensate. We show that balanced anyon condensates are robust against deviations from the exactly-solvable conditions, and discuss the requirements for dipolar orientation and ladder geometry, to realize anyon condensates of dipoles in triangular ladders, whose anyonic nature may be easily revealed by time-of-flight measurements. Moreover, the ground-state physics in the vicinity of the exactly-solvable point is very rich, including a phase transition from anyon condensates into chiral superfluids, and self-bound Mott insulators, bond-order insulators, and chiral liquids.

DOI
10.48550/arxiv.2608.20173

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Hard-core dipoles in triangular ladders are an excellent platform for the study of the interplay between frustration and long-range interactions, well described by a modified version of the celebrated J1J_1J1​--J2J_2J2​ model. Interestingly, as shown in [Phys. Rev. Lett. 109, 227203 (2012)], such a model presents, for particular exactly-solvable conditions, a peculiar phase known as an anyon condensate. We show that balanced anyon condensates are robust against deviations from the exactly-solvable conditions, and discuss the requirements for dipolar orientation and ladder geometry, to realize anyon condensates of dipoles in triangular ladders, whose anyonic nature may be easily revealed by time-of-flight measurements. Moreover, the ground-state physics in the vicinity of the exactly-solvable point is very rich, including a phase transition from anyon condensates into chiral superfluids, and self-bound Mott insulators, bond-order insulators, and chiral liquids.
Dipoles in triangular optical ladders constitute a flexible platform for the study of the interplay between geometric frustration and long-range anisotropic interactions, and in particular for the observation of the spontaneous onset of chirality. Frustration magnifies the effect of the dipolar interactions in itinerant polarized dipolar bosons. As a result, the dipole-induced transition between a chiral superfluid and a nonchiral two-component superfluid may be observed for current state-of-the-art temperatures even for the weak intersite interaction characterizing magnetic atoms in standard optical lattices. On the other hand, pinned spin- 1 / 2 dipoles, which we discuss in the context of polar molecules in two rotational states, realize frustrated dipolar XXZ spin models. By controlling the external electric field strength and orientation, these systems can explore a rich ground-state landscape including chiral and nematic phases, as well as intriguing chiral dynamics.
Many-body systems with strong interactions often exhibit macroscopic behavior markedly absent in single-particle or noninteracting limits. Such emergent phenomena are well exemplified in lattice Hubbard models, where the interplay between interactions, geometric frustration, and magnetic flux gives rise to rich physics. Superconducting qubits naturally enable analog quantum simulation of Bose-Hubbard models, while offering tunable parameters, site-resolved control, and rapid experimental repetition rates. Here, we study a superconducting-qubit device that realizes the Bose-Hubbard model on a triangular-ladder lattice. By tuning the magnitude and sign of couplings, we engineer a synthetic magnetic flux to characterize the resulting half-filling ground state for various parameter regimes. We measure observables analogous to current-current correlators and bond kinetic energies, finding signatures consistent with chiral superfluids, Meissner superfluids, and bond-ordered insulators. Our results establish superconducting circuits as a platform for robustly probing quantum phases of matter in frustrated Bose-Hubbard systems, even in strongly correlated and gapless regimes.
Polar molecules in geometrically frustrated lattices may result in a very rich landscape of quantum phases, due to the nontrivial interplay between frustration, and two- and possibly three-body intersite interactions. In this paper we illustrate this intriguing physics for the case of hard-core polar molecules in frustrated triangular ladders. Whereas commensurate lattice fillings result in gapped phases with bond order and/or density-wave order, at incommensurate fillings we find chiral, two-component, and pair superfluids. We show as well that, remarkably, polar molecules in frustrated lattices allow for the observation of bond-ordered supersolids.
Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.
Raman-assisted hopping may be used to realize the anyon Hubbard model in one-dimensional optical lattices. We propose a feasible scenario that significantly improves the proposal of T. Keilmann et al. [Nat. Commun. 2, 361 (2011)], allowing as well for an exact realization of the two-body hard-core constraint, and for controllable effective interactions without the need of Feshbach resonances. We show that the combination of anyonic statistics and two-body hard-core constraint leads to a rich ground-state physics, including Mott insulators with attractive interactions, pair superfluids, dimer phases, and multicritical points. Moreover, the anyonic statistics results in a novel two-component superfluid of holon and doublon dimers, characterized by a large but finite compressibility and a multipeaked momentum distribution, which may be easily revealed experimentally.
We study the superfluid and insulating phases of interacting bosons on the triangular lattice with an inverted dispersion, corresponding to frustrated hopping between sites. The resulting single-particle dispersion has multiple minima at nonzero wave vectors in momentum space, in contrast to the unique zero-wave-vector minimum of the unfrustrated problem. As a consequence, the superfluid phase is unstable against developing additional chiral order that breaks time-reversal (T\mathcal{T}T) and parity (P\mathcal{P}P) symmetries by forming a condensate at nonzero wave vector. We demonstrate that the loss of superfluidity can lead to an even more exotic phase, the chiral Mott insulator, with nontrivial current order that breaks T,P\mathcal{T},\mathcal{P}T,P. These results are obtained via variational estimates, as well as a combination of bosonization and density-matrix renormalization group of triangular ladders, which, taken together, permit a fairly complete characterization of the phase diagram. We discuss the relevance of these phases to optical lattice experiments, as well as signatures of chiral symmetry breaking in time-of-flight images.