Ground states of a Bose–Hubbard ladder in an artificial magnetic field: field-theoretical approach

Tokuno, Akiyuki; Georges, Antoine

doi:10.1088/1367-2630/16/7/073005

Cited by 98 publications

(119 citation statements)

References 54 publications

(124 reference statements)

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“…At arbitrary boson filling and uniform flux there is a transition from the low field Meissner phase to a high field vortex phase [12], reminiscent of type-II superconductivity. The low field model with V ⊥ = 0 at n 0 = 2/a exhibits a superfluid with Meissner currents and a Mott insulator with Meissner currents for weak enough U [50]. The ground state for χ = π/a at integer filling is a chiral superfluid, a chiral Mott insulator or a Mott insulator [50,51].…”

Section: Model and Previous Resultsmentioning

confidence: 99%

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

et al. 2017

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We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge c = 1, which is a precursor of the two-dimensional Laughlin state at ν = 1/2. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.

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Section: Model and Previous Resultsmentioning

confidence: 99%

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

et al. 2017

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“…At small values of φ, we find a Meissner phase (M-MI) while at large The M-SF phase has one gapless mode (central charge c = 1), while the V-SF has c = 2. We expect M-SF and V-SF to be adiabatically connected to the corresponding phases established at weak interactions [34,37,44].…”

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confidence: 86%

“…Bosons on a ladder subjected to gauge fields have been the topic of previous theoretical work [37][38][39][40][41][42][43][44] (see also [45,46] for 2D lattices), yet complete quantitative phase diagrams are lacking. In our work, we use DMRG to systematically explore the full dependence on J ⊥ , φ, and filling and, as a main result, we observe both gapped and gapless Meissner and vortex phases for stronglyinteracting bosons.…”

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confidence: 99%

“…The emergence of a two-component Luttinger liquid (LL) at large values of φ becomes transparent in the low-density limit where it is connected with the development of a double-minimum structure in the singleparticle dispersion ǫ k for φ > φ cr (J ⊥ ) [42,44]. Note that the physics at low densities is very similar to that of frustrated chains in high magnetic fields below saturation (see [54][55][56] and references therein).…”

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confidence: 99%

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Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

et al. 2015

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We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.Introduction. The quantum states of interacting electrons in the presence of spin-orbit coupling and magnetic fields are attracting significant attention in condensed matter physics because of their connection to Quantum Hall physics [1], topological insulators [2-4] and the emergence of unusual excitations in low dimensions [5,6]. Recent progress with quantum gas experiments has led to the realization of artificial gauge fields [7], both in the continuum [8][9][10] and for bosons in optical lattices [11][12][13][14], paving the way for future experiments on the interplay of interactions, dimensionality, and gauge fields in a systematic manner. This has motivated theoretical research into the physics of strongly interacting particles in the presence of abelian and non-abelian gauge fields and various questions such as the Quantum Hall effect with bosons [15][16][17][18][19][20][21][22], unusual quantum magnetism [23][24][25][26], and the emergence of topologically protected phases [27][28][29] have been addressed.

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“…The artificial gauge fields, which allow one to generate spinorbit couplings and effective magnetic fields, opens a new path to explore quantum Hall effect and topological phases of matters. Our cluster Gutzwiller meanfield approach can also be extended to investigate the bosonic ladders in the presence of an artificial magnetic field [26,[57][58][59][60][61][62][63], such as the observation of chiral currents [57], the measurement of Chern number in Hofstadter bands [58,63], and the two-leg Bose-Hubbard ladder under a magnetic flux [26,61]. In addition, our cluster Gutzwiller mean-field approach may also use to explore the non-equilibrium dynamics of two coupled onedimensional Luttinger liquids [64] and the dynamical instability of interacting bosons in disordered lattices [65].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

et al. 2015

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We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For a unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the inter-chain tunneling is much stronger than the intra-chain one. The fractional insulator phases can not be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the inter-chain bias. In the many-body Landau-Zener process, in which the inter-chain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.

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Ground states of a Bose–Hubbard ladder in an artificial magnetic field: field-theoretical approach

Cited by 98 publications

References 54 publications

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

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