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arXiv:2304.11747 · Physical Review A

Quantum phases of constrained bosons on a two-leg Bose-Hubbard ladder

Ashirbad Padhan, Rajashri Parida, Sayan Lahiri, Mrinal Kanti Giri, Tapan Mishra

Published Jul 25, 2023• 5 citations
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Abstract

Bosons in periodic potentials with very strong local interactions, known as constrained bosons, often exhibit interesting physical behavior. We investigate the ground-state properties of a two-leg Bose-Hubbard ladder by imposing a three-body constraint in one leg and a hard-core constraint in the other. By using the cluster mean-field theory approximation and the density matrix renormalization group method, we show that at unit filling, for strong two-body attraction among the three-body constrained bosons, the system becomes a gapped pair-Mott insulator where all the bosons form strong bound pairs and occupy the leg with the three-body constraint. With increase in hopping strength, this pair-Mott insulator phase undergoes a phase transition to the gapless superfluid phase for equal leg and rung hopping strengths. However, when the rung hopping is stronger compared to the leg hopping, we obtain a crossover to another gapped phase which is called the rung-Mott insulator phase where the bosons prefer to delocalize on the rungs rather than the legs. By moving away from unit filling, the system remains in the superfluid phase except for a small region below the gapped phase where a pair superfluid phase is stabilized in the regime of strong attractive interaction. We further extend our studies by considering the three-body constraint in both the legs and find that the crossover from the gapped to gapped phase does not occur; rather, the system undergoes a transition from a pair-rung-Mott insulator phase to the superfluid phase at unit filling. Moreover, in this case, we find the signature of the pair superfluid phase on either side of this gapped phase.

DOI
10.1103/physreva.108.013316

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Bosons in periodic potentials with very strong local interactions, known as constrained bosons, often exhibit interesting physical behavior. We investigate the ground-state properties of a two-leg Bose-Hubbard ladder by imposing a three-body constraint in one leg and a hard-core constraint in the other. By using the cluster mean-field theory approximation and the density matrix renormalization group method, we show that at unit filling, for strong two-body attraction among the three-body constrained bosons, the system becomes a gapped pair-Mott insulator where all the bosons form strong bound pairs and occupy the leg with the three-body constraint. With increase in hopping strength, this pair-Mott insulator phase undergoes a phase transition to the gapless superfluid phase for equal leg and rung hopping strengths. However, when the rung hopping is stronger compared to the leg hopping, we obtain a crossover to another gapped phase which is called the rung-Mott insulator phase where the bosons prefer to delocalize on the rungs rather than the legs. By moving away from unit filling, the system remains in the superfluid phase except for a small region below the gapped phase where a pair superfluid phase is stabilized in the regime of strong attractive interaction. We further extend our studies by considering the three-body constraint in both the legs and find that the crossover from the gapped to gapped phase does not occur; rather, the system undergoes a transition from a pair-rung-Mott insulator phase to the superfluid phase at unit filling. Moreover, in this case, we find the signature of the pair superfluid phase on either side of this gapped phase.
We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest-neighbor interactions by imposing the onsite three-body constraint. We find three distinct phases; namely, the atomic superfluid (ASF), dimer superfluid (DSF), and the dimer rung insulator (DRI). In the absence of the interchain nearest-neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest-neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest-neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self-consistent cluster mean-field theory.
We consider the Bose-Hubbard model on a two-leg ladder under an artificial magnetic field and investigate the superfluid--to--Mott insulator transition in this setting. Recently, this system has been experimentally realized [M. Atala et al., Nature Phys. 10, 588 (2014)], albeit in a parameter regime that is far from the Mott transition boundary. Depending on the strength of the magnetic field, the single-particle spectrum has either a single ground state or two degenerate ground states. The transition between these two phases is reflected in the many-particle properties. We first investigate these phases through the Bogoliubov approximation in the superfluid regime and calculate the transition boundary for weak interactions. For stronger interactions the system is expected to form a Mott insulator. We calculate the Mott transition boundary as a function of the magnetic field and interleg coupling with mean-field theory, strong-coupling expansion, and density matrix renormalization group (DMRG). Finally, using the DMRG, we investigate the particle-hole excitation gaps of this system at different filling factors and find peaks at simple fractions, indicating the possibility of correlated phases.
One-dimensional free fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain, the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depend on the so-called Jordan-Wigner string, real-space observables are similar for free fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed and leads to a totally different physics between free fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but nontrivial model of hard-core bosons hopping in a two-leg ladder geometry. At half filling, while a band insulator appears for fermions at large interchain hopping ${t}_{\ensuremath{\perp}}>2t$ only, a Mott gap opens up for bosons as soon as ${t}_{\ensuremath{\perp}}\ensuremath{\ne}0$ through a Kosterlitz-Thouless transition. Away from half filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a nontrivial filling-dependent Luttinger parameter $1/2\ensuremath{\leqslant}{K}_{s}\ensuremath{\leqslant}1$. Consequences for experiments in cold atoms and spin ladders in a magnetic field, as well as disorder effects, are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a one-dimensional superfluid and an insulating Bose glass phase.
We analyze the ground-state properties of three-body constrained bosons in a one-dimensional optical lattice with staggered hoppings analogous to the double-well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint, several gapped phases such as the Mott insulators and dimer--bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair--bond-order phase at unit filling, which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities, we see the signatures of the gapless pair superfluid phase.
We investigate the ground-state properties of a nonlocally coupled bosonic system in a bilayer optical superlattice by considering bosons in one layer to be of soft core in nature and separately allowing two- and three-body hard-core constraints on the other layer. We find that the presence of different constraints on bosons in one layer influences the overall phase diagram exhibiting various Mott insulator phases at incommensurate densities due to the presence of the superlattice potential apart from the usual Mott insulators at commensurate densities. Moreover, the presence of two- or three-body constraints significantly modifies the Mott insulator to superfluid phase transition points as a function of the superlattice potential. Due to the various competing interactions, constraints, and superlattice potential, the phase diagrams exhibit significantly different features. We obtain the complete phase diagrams by using the cluster mean-field-theory approach. We further extend this work to a coupled two-leg ladder superlattice where we obtain similar physics using the density-matrix renormalization-group method.
By means of Monte Carlo techniques, we study the role of disorder on a system of hard-core bosons in a two-leg ladder with both intrachain (ttt) and interchain (${t}^{\ensuremath{'}}$) hoppings. We find that the phase diagram as a function of the boson density, disorder strength, and ${t}^{\ensuremath{'}}/t$ is far from being trivial. This contrasts with the case of spinless fermions where standard localization arguments apply and an Anderson-localized phase pervades the whole phase diagram. A compressible Bose-glass phase always intrudes between the Mott insulator with zero (or one) bosons per site and the superfluid that is stabilized for weak disorder. At half-filling, there is a direct transition between a (gapped) rung-Mott insulator and a Bose glass, which is driven by exponentially rare regions where disorder is suppressed. Finally, by doping the rung-Mott insulator, a direct transition to the superfluid is possible only in the clean system, whereas the Mott phase is always surrounded by the a Bose glass when disorder is present. The phase diagram based on our numerical evidence is finally reported.