Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions

Cocks, Daniel; Orth, Peter P.; Rachel, Stephan; Buchhold, Michael; Hur, Karyn Le; Hofstetter, Walter

doi:10.1103/physrevlett.109.205303

Cited by 87 publications

(132 citation statements)

References 76 publications

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“…The effects of the spinanisotropy interaction λ = 1 in Eq. (24) and the behaviors of the RFH in the presence of external Zeeman fields will be discussed in separate publications [66,67]. Preliminary results show that indeed the C-C 0 , C-C π and C-IC magnons are the seeds to drive various quantum phase transitions under the effects of spin-anisotropy λ and the external magnetic fields Ω (Fig.10).…”

Section: Conclusion and Perspectives On Moving Away From The Solmentioning

confidence: 99%

“…Ref. [24] studied time-reversal invariant Hofstadter-Hubbard model of spin 1/2 fermions hopping on a square lattice subject to an Abelian flux α = p/q. This is the quantum spin Hall effects model in Fig.7b.…”

Section: Synthetic Rotated Spin-s Heisenberg Model In the Strong mentioning

confidence: 99%

“…In Sec.II, starting from the spinor boson Hubbard model in the presence of non-Abelian gauge fields (Fig.1a), in the strong coupling limit, we derive the Rotated Ferromagnetic Heisenberg model (RFHM), also stress its crucial differences than the previously well known modes such as Heisenberg model [1,2], Kitaev model [19,20], DzyaloshinskiiMoriya (DM) interaction [21,22] and some other strong coupling models [23,24]. In Sec.III, we introduce the Wilson loops (Fig.1b) to characterize gauge equivalent classes and frustrations of the RFHM.…”

Section: Introductionmentioning

confidence: 99%

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Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

2015

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We study quantum magnetism of interacting spinor bosons at integer fillings hopping in a square lattice in the presence of of non-Abelian gauge fields. In the strong coupling limit, it leads to the Rotated ferromagnetic Heisenberg model (RFHM) which is a new class of quantum spin model. We introduce Wilson loops to characterize frustrations and gauge equivalent classes. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground state. It supports not only commensurate magnons, but also a new gapped elementary excitation: in-commensurate magnons with two gap minima continuously tuned by the SOC strength. At low temperatures, these magnons lead to dramatic effects in many physical quantities such as density of states, specific heat, magnetization, uniform susceptibility, staggered susceptibility and various spin correlation functions. The commensurate magnons lead to a pinned central peak in the angle resolved light or atom Bragg spectroscopy. However, the in-commensurate magnons split it into two located at their two gap minima. At high temperatures, the transverse spin structure factors depend on the SOC strength explicitly. The whole set of Wilson loops can be mapped out by measuring the specific heat at the corresponding orders in the high temperature expansion. We argue that one gauge may be realized in current experiments and other gauges may also be realized in near future experiments. The results achieved along the exact solvable line sets up the stage to investigate dramatic effects when tuning away from it by various means. We sketch the crucial roles to be played by these magnons at other equivalent classes, with spin anisotropic interactions and in the presence of finite magnetic fields. Various experimental detections of these new phenomena are discussed. Rotated Anti-ferromagnetic Heisenberg model are also briefly mentioned.

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Section: Conclusion and Perspectives On Moving Away From The Solmentioning

confidence: 99%

Section: Synthetic Rotated Spin-s Heisenberg Model In the Strong mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

2015

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“…[24,25] should be easier to implement experimentally, it does not offer the versatility of the non-Abelian optical lattices discussed in this work. As a result, the system described in this paper has the potential to realize other kinds of topological insulating phases, such as, for instance, the Z 2 topological insulators characterized by a topological invariant ν Z2 = ±1 and exhibiting the quantum spin Hall effect [7,[34][35][36][37][60][61][62][63]. .…”

Section: Discussionmentioning

confidence: 99%

Realizing non-Abelian gauge potentials in optical square lattices: an application to atomic Chern insulators

Goldman¹,

Gerbier²,

Lewenstein³

2013

J. Phys. B: At. Mol. Opt. Phys.

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We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depict a checkerboard structure, allowing for laser-assisted tunneling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a "flavor" quantum number undergoing non-Abelian tunneling along nearest-neighbor links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighboring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunneling techniques. We demonstrate that a simple mapping allows to express this model in terms of matrix hopping operators, that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunneling methods applied to the checkerboard optical lattice.

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“…However, regardless of all efforts since the prediction of this Hofstadter spectrum, there has been very recent but still limited success in observing some of its signatures in graphenebased solid-state materials with artificially-engineered superlattices under real magnetic fields [3,4]. In addition, thanks to the recent realisation of artificial gauge fields in atomic systems [5][6][7][8][9][10][11][12], there is also an increasing interest on this subject from the cold-atom community [13][14][15][16][17][18][19][20]. In particular, by engineering spatially-dependent complex tunneling amplitudes with laser-assisted tunneling and a potential energy gradient, two groups have recently reported realisation of the Hofstadter-Harper Hamiltonian using neutral rubidium atoms that are loaded into laser-induced periodic potentials [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Attractive Hofstadter-Hubbard model with imbalanced chemical and vector potentials

Iskin

2015

Phys. Rev. A

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We study the interplay between the Hofstadter butterfly, strong interactions and Zeeman field within the mean-field Bogoliubov-de Gennes theory in real space, and explore the ground states of the attractive singleband Hofstadter-Hubbard Hamiltonian on a square lattice, including the exotic possibility of imbalanced vector potentials. We find that the cooperation between the vector potential and superfluid order breaks the spatial symmetry of the system, and flourish stripe-ordered Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like superfluid and supersolid phases that can be distinguished and characterized according to their coexisting pair-density (PDW), charge-density (CDW) and spin-density (SDW) wave orders. We also discuss confined systems and comment on the likelihood of observing such stripe-ordered phases by loading neutral atomic Fermi gases on laser-induced optical lattices under laser-generated artificial gauge fields.

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Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions

Cited by 87 publications

References 76 publications

Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

Realizing non-Abelian gauge potentials in optical square lattices: an application to atomic Chern insulators

Attractive Hofstadter-Hubbard model with imbalanced chemical and vector potentials

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