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arXiv:2201.09497

Phase diagram of the two-component bosonic system with pair hopping in synthetic dimension

Chenrong Liu, Zhi Lin

Published Jan 24, 2022• 0 citations
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Abstract

We systematically study the ground-state phase diagrams and the demixing effect of a two-dimensional two-component bosonic system with pair hopping in synthetic dimension by using the cluster Gutzwiller mean-field method. Our results show that when the interexchange symmetry between the two species is broken, the regions of the super-counter-fluidity state in the phase diagram are dramatically shrunk whenever the on-site pair hopping term is turned on or off. Unexpectedly, the non-integer Mott phase and the molecular superfluid phase predicted in our previous work \citetext{Z. Lin et al., \textcolor{blue}{Phys. Rev. Lett. \textbf{125}, 245301 (2020)}}, can only exist in such a system that the pair hopping term is opened, and more importantly, its interexchange symmetry must be broken. Moreover, the demixing effect of the two-component bosonic system with synthetic pair hopping interaction has also been studied, and we find that an incompletely demixed state is formed in the system when the strength of the interspecies on-site repulsive interaction is sufficiently large.

DOI
10.48550/arxiv.2201.09497

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We systematically study the ground-state phase diagrams and the demixing effect of a two-dimensional two-component bosonic system with pair hopping in synthetic dimension by using the cluster Gutzwiller mean-field method. Our results show that when the interexchange symmetry between the two species is broken, the regions of the super-counter-fluidity state in the phase diagram are dramatically shrunk whenever the on-site pair hopping term is turned on or off. Unexpectedly, the non-integer Mott phase and the molecular superfluid phase predicted in our previous work \citetext{Z. Lin et al., \textcolor{blue}{Phys. Rev. Lett. \textbf{125}, 245301 (2020)}}, can only exist in such a system that the pair hopping term is opened, and more importantly, its interexchange symmetry must be broken. Moreover, the demixing effect of the two-component bosonic system with synthetic pair hopping interaction has also been studied, and we find that an incompletely demixed state is formed in the system when the strength of the interspecies on-site repulsive interaction is sufficiently large.
We study two-component (or pseudospin-1/2) bosons with pair hopping interactions in synthetic dimension, for which a feasible experimental scheme on a square optical lattice is also presented. Previous studies have shown that two-component bosons with on-site interspecies interaction can only generate nontrivial interspecies paired superfluid (super-counter-fluidity or pair-superfluid) states. In contrast, apart from interspecies paired superfluid, we reveal two new phases by considering this additional pair hopping interaction. These novel phases are intraspecies paired superfluid (molecular superfluid) and an exotic noninteger Mott insulator which shows a noninteger atom number at each site for each species, but an integer for total atom number.
Motivated by recent experiments on two-component systems, we investigate the ground-state phase diagram of a mixture of two bosonic species by means of path-integral quantum Monte Carlo simulations by a two-worm algorithm. The mixture is trapped in a square lattice at different filling conditions. Various quantum phases are stabilized depending on the interplay between intra- and interspecies interactions and on the filling factors. We show that the ground-state phase diagram at half-filling features a demixed superfluid phase and a demixed Mott-insulator phase when the interspecies interaction becomes greater than the intraspecies repulsion, and a double-superfluid phase or a supercounterflow otherwise. We show that demixing, characterized by spatial separation of the two species, can be detected experimentally through the effects of anisotropy revealed by time-of-flight images. We also study how demixing effects depend on the filling factor of the two components. Finally, we find that the supercounterflow phase is preserved in the presence of unbalanced populations.
Using the single-site Gutzwiller method, we theoretically study the ground state and the interspecies entanglement properties of interexchange symmetric multicomponent (two- and three-component) bosonic mixtures in an optical lattice, and the results are generalized to an nnn-component (n=2,3,4,...)(n=2,3,4,...)(n=2,3,4,...) system. We compute the mean-field phase diagram, the interspecies entanglement entropy, and the ground-state spectral decomposition. Three phases---namely, the nnn-component superfluid state (nSF), the nnn-component Mott insulator state (nMI), and the supercounterfluid state (SCF)---are observed. Interestingly, we find that there are $n\ensuremath{-}1$ SCF lobes to separate every two neighboring nMI lobes in the phase diagram. More importantly, we derive the exact general expression of the interspecies entanglement entropy for the SCF phase. In addition, we also investigate the demixing effect of an nnn-component mixture and demonstrate that the mixing-demixing critical point is independent of nnn.
Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is obtained by the Gutzwiller-type variational technique in the plane of filling and interaction parameters. Various ground-state properties are also studied by the quantum Monte Carlo method. Our model exhibits two types of diagonal long-range orders; the density order around the density n=1/2n=1/2n=1/2 and the Ising-type component order near n=1n=1n=1. The quantum Monte Carlo results for the transitions from the superfluid state to these two ordered states show marked contrast with the Gutzwiller results. Namely, although they are both accompanied by phase separation into commensurate (n=1/2n=1/2n=1/2 or n=1n=1n=1) and incommensurate density phases, these transitions are both continuous. The continuous growth of the component correlation severely suppresses the superfluidity as well as the inverse of the effective mass in the critical region of the component order transition in contrast to the persistence of the superfluidity in the density-ordered state. We propose a mechanism of the mass enhancement observed even far from the Mott insulating filling n=1n=1n=1, when the Ising-type component order persists into n≠1n \neq 1n=1. Possible relevance of this type of mass enhancement in other systems is also discussed.
Various types of superfluid-insulator transitions are investigated for two-component lattice boson systems in two dimensions with on-site hard-core repulsion and the component-dependent intersite interaction. The mean-field phase diagram is obtained by the Gutzwiller-type variational technique. Various ground-state properties are also studied by the quantum Monte Carlo method. Our model exhibits two types of diagonal long-range orders; the density order around the density n =1/2 and the Ising-type component order near n =1. In contrast to the Gutzwiller results, the Monte Carlo results show that the continuous growth of the component correlation severely suppresses the superfluidity as well as the inverse of the effective mass in the critical region of the component order transition. We propose a mechanism of this mass enhancement observed even far from the Mott insulating filling n =1, when the Ising-type component order persists into n ≠1. Possible relevance of this type of mass enhancement in other systems is also discussed.
Following a proposed scheme for realizing the time-periodically modulated Rabi frequency in experiments, we suggest density-dependent hoppings of two-species hardcore bosons in a one-dimensional optical lattice. Distinct from the previous work [Phys. Rev. Res. 2, 013275 (2020)], we study effects in the first resonance region. In the effective Hamiltonian, the intraspecies hopping occurs only if the density discrepancy of the other species on these sites is zero, while the interspecies one is allowed once the relevant density discrepancy becomes nonzero. At integer-1 filling, the quantum phase diagram of the effective Hamiltonian is determined by the perturbation analysis together with numerical calculations. We find that in the limit of dominant J1{J}_{1}J1​, the system becomes a double-degenerate dimerized state spontaneously breaking the translation symmetry. The interplay of J0,J1{J}_{0}, {J}_{1}J0​,J1​, and the fixed U‾=1\overline{U}=1U=1 leads to three BKT transition lines and a tricritical BKT point. Exact transition lines are obtained by the level spectroscopic technique. Besides, general physical properties, including the charge gap, neutral gap, superfluid density, and dimerization strength, are investigated as well.