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arXiv:1703.07742 · Physical review. B./Physical review. B

Vortex lattice melting in a boson ladder in an artificial gauge field

E. Orignac, R. Citro, M. Di Dio, S. De Palo

Published Jul 25, 2017• 37 citations
arXivHTMLPDF

Abstract

We consider a two-leg boson ladder in an artificial U(1) gauge field and show that, in the presence of interleg attractive interaction, the flux induced vortex state can be melted by dislocations. For increasing flux, instead of the Meissner to vortex transition in the commensurate-incommensurate universality class, first, an Ising transition from the Meissner state to a charge density wave takes place, then, at higher flux, the melted vortex phase is established via a disorder point where incommensuration develops in the rung current correlation function and in momentum distribution. Finally, the quasi-long-range ordered vortex phase is recovered for sufficiently small interaction. Our predictions for the observables, such as the spin current and the static structure factor, could be tested in current experiments with cold atoms in bosonic ladders.

DOI
10.1103/physrevb.96.014518

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We consider a two-leg boson ladder in an artificial U(1) gauge field and show that, in the presence of interleg attractive interaction, the flux induced vortex state can be melted by dislocations. For increasing flux, instead of the Meissner to vortex transition in the commensurate-incommensurate universality class, first, an Ising transition from the Meissner state to a charge density wave takes place, then, at higher flux, the melted vortex phase is established via a disorder point where incommensuration develops in the rung current correlation function and in momentum distribution. Finally, the quasi-long-range ordered vortex phase is recovered for sufficiently small interaction. Our predictions for the observables, such as the spin current and the static structure factor, could be tested in current experiments with cold atoms in bosonic ladders.
We consider a two leg bosonic ladder in a U(1)U(1)U(1) gauge field with both interleg hopping and interleg repulsion. As a function of the flux, the interleg interaction converts the commensurate-incommensurate transition from the Meissner to a Vortex phase, into an Ising-type of transition towards a density wave phase. A disorder point is also found after which the correlation functions develop a damped sinusoid behavior signaling a melting of the vortex phase. We discuss the differences on the phase diagram for attractive and repulsive interleg interaction. In particular, we show how repulsion favors the Meissner phase at low flux and a phase with a second incommensuration in the correlation functions for intermediate flux, leading to a richer phase diagram than in the case of interleg attraction. The effect of the temperature on the chiral current is also discussed.
A boson two-leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and density matrix renormalization group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is ρπ and close to it, where ρ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung–rung correlation function and the spin–spin and charge–charge static structure factors.
The phase diagram of a half-filled hard-core boson two-leg ladder in a flux is investigated by means of numerical simulations based on the density matrix renormalization group (DMRG) algorithm and bosonization. We calculate experimentally accessible observables such as the momentum distribution, as well as rung current, density wave, and bond-order wave correlation functions, allowing us to identify the Mott Meissner and Mott vortex states. We follow the transition from commensurate Meissner to incommensurate vortex state at increasing interchain hopping until the critical value [Piraud et al. Phys. Rev. B 91, 140406 (2015)] above which the Meissner state is stable at any flux. For flux close to $\ensuremath{\pi}$, and below the critical hopping, we observe the formation of a second incommensuration in the Mott vortex state that could be detectable in current experiments.
We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.
We investigate hard-core bosons at half filling on a three-leg ladder under the uniform artificial gauge field. By analyzing current patterns and correlation functions, we uncover a rich quantum phase diagram containing multiple superfluid and insulating phases. In bosonic ladder systems, increasing the gauge flux typically destabilizes the Meissner phase and leads to vortex phases characterized by circulating currents. In the present system, however, we find that charge-density-wave (CDW) phases emerge precisely in such a flux regime despite the presence of only an on-site interaction, where vortex states are naturally expected and are indeed realized in nearby parameter regions. While part of this behavior can be qualitatively understood from a strong-coupling perspective, we also identify an isolated CDW region that cannot be connected to such limits. Furthermore, upon increasing the artificial gauge flux, we observe a reentrant sequence of quantum phase transitions, CDW →\to→ vortex-superfluid →\to→ CDW, revealing a strong competition between the vortex phase and the density-wave order.
Quasi-one-dimensional lattice systems such as flux ladders with artificial gauge fields host rich quantum-phase diagrams that have attracted great interest. However, so far, most of the work on these systems has concentrated on zero-temperature phases while the corresponding finite-temperature regime remains largely unexplored. The question if and up to which temperature characteristic features of the zero-temperature phases persist is relevant in experimental realizations. We investigate a two-leg ladder lattice in a uniform magnetic field and concentrate our study on chiral edge currents and momentum-distribution functions, which are key observables in ultracold quantum-gas experiments. These quantities are computed for hard-core bosons as well as noninteracting bosons and spinless fermions at zero and finite temperatures. We employ a matrix-product-state based purification approach for the simulation of strongly interacting bosons at finite temperatures and analyze finite-size effects. Our main results concern the vortex-fluid-to-Meissner crossover of strongly interacting bosons. We demonstrate that signatures of the vortex-fluid phase can still be detected at elevated temperatures from characteristic finite-momentum maxima in the momentum-distribution functions, while the vortex-fluid phase leaves weaker fingerprints in the local rung currents and the chiral edge current. In order to determine the range of temperatures over which these signatures can be observed, we introduce a suitable measure for the contrast of these maxima. The results are condensed into a finite-temperature crossover diagram for hard-core bosons.