Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

Nonne, H.; Moliner, M.; Capponi, Sylvain; Lecheminant, P.; Totsuka, Keisuke

doi:10.1209/0295-5075/102/37008

Cited by 69 publications

(118 citation statements)

References 53 publications

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“…which is directly relevant to ytterbium and strontium atoms) crosses over to the topological Haldane phase. A brief summary of these results has already been given in a recent paper [40] where we have found these SU(N ) topological phases for a particular 1D two-orbital SU(N ) model.…”

Section: Introductionsupporting

confidence: 54%

“…This SU(N ) spin chain has the self-conjugate representation (with N/2 rows and 2 columns) at each site and is not solvable. Nevertheless, we can obtain [40] a fairly good understanding of the properties of the ground state by constructing a series of model ground states, the VBS states [68,69], whose parent Hamiltonian is close to the original ones (41) and (43).…”

Section: A Su(n) Valence-bond-solid (Vbs) Statementioning

confidence: 99%

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Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

et al. 2015

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We investigate possible realizations of exotic SU(N ) symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of twoorbital generalizations of the standard SU(N ) Fermi-Hubbard model, directly relevant to recent experiments, is performed. Using state-of-the-art analytical and numerical techniques, we map out the zero-temperature phase diagrams at half-filling and identify several Mott-insulating phases. While some of them are rather conventional (nondegenerate, charge-density wave, or spin-Peierls-like), we also identify, for even N , two distinct types of SPT phases: an orbital Haldane phase, analogous to a spin-N/2 Haldane phase, and a topological SU(N ) phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the SU(N ) topological phases found here.

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Section: Introductionsupporting

confidence: 54%

Section: A Su(n) Valence-bond-solid (Vbs) Statementioning

confidence: 99%

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

et al. 2015

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“…(12). The main difference stems from the fact that we have now the constraints g 2 = g 4 and g 5 = g 7 in Eq.…”

Section: B G − E Model Casementioning

confidence: 99%

“…The one-loop RG calculation enables one to deduce the infrared (IR) properties of model (12) and thus to map out the zero-temperature phase diagram of the g − e model (1) and p-band model (4).…”

Section: One-loop Renormalization Group Analysismentioning

confidence: 99%

One-dimensional two-orbital SU(N) ultracold fermionic quantum gases at incommensurate filling: A low-energy approach

2016

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We investigate the zero-temperature phase diagram of two-orbital SU(N ) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the SU(N ) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the N = 2 case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of 2N fermions.

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“…By increasing the number of components above two, an interesting possibility of hosting exotic ground states like 2D spin liquids [7,8] or 1D topological states [9,10] emerges. A novel ingredient in multicomponent alkali-metal gases, different from the two-component case, is the presence of spin-changing collisions: two interacting atoms cannot only exchange their initial internal hyperfine states, but they can also change them to new values.…”

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confidence: 99%

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

2013

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Under the influence of an external magnetic field and spin-changing collisions, the band insulator state of one-dimensional s-wave repulsively interacting four-component fermions at half-filling transforms into Mott insulator states with a spontaneously doubled unit cell: a dimerized state for shallow lattices and a Néel state for deep lattices via an intermediate topological state. These Mott insulator phases could be of special interest for experiments as they can be reached starting from band insulator state and changing magnetic field adiabatically. [3,4]. At sufficiently low temperatures the MI phase should acquire a magnetic Néel (antiferromagnetic) ordering. Still it has not been resolved [5]; the main obstacle is the absence of efficient cooling methods in the presence of an optical lattice [6].By increasing the number of components above two, an interesting possibility of hosting exotic ground states like 2D spin liquids [7,8] or 1D topological states [9,10] emerges. A novel ingredient in multicomponent alkali-metal gases, different from the two-component case, is the presence of spin-changing collisions: two interacting atoms cannot only exchange their initial internal hyperfine states, but they can also change them to new values. The spin-changing collisions open a fascinating prospect to arrive at unconventional MI ground states of multicomponent Fermi gases starting from the band insulator (BI) state made of only two components having vanishing entropy per particle. For fermions due to the Pauli principle the minimal number of components required for BI to MI transformation is four.In this work we present the ground-state phases of fourcomponent alkali-metal fermions at half-filling obtained by nonperturbative analytical and numerical tools, particularly tailored for studying 1D systems. We identify various MI phases: Dimer and Néel states spontaneously break discrete lattice translational symmetry and are characterized by doubly degenerate ground state in thermodynamic limit and local order parameters; whereas singlet and a topological Haldane phase do not break any microscopic symmetry and are characterized by unique ground state and nonlocal parity and string orders, respectively. Even though these different MI phases are manifested below the ultralow temperatures, typical to the superexchange scale, the fact that one can start from the BI state and by adiabatically changing the magnetic field enter into these nontrivial states, makes the system of half-filled four-component alkali-metal fermions a particularly attractive candidate to resolve ground-state spin order in experiments on ultracold lattice gases. Note that the spin-changing collision processes, crucial for BI to MI transformations, are maximally pronounced at half-filling.Our main result, the ground-state phase diagram of four components of 40 K atoms, is presented in Fig. 1. Most importantly all states can be explored just by changing the lattice depth and strength of the external magnetic field without the need to modify the natura...

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Symmetry-protected topological phases of alkaline-earth cold fermionic atoms in one dimension

Cited by 69 publications

References 53 publications

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

One-dimensional two-orbital SU(N) ultracold fermionic quantum gases at incommensurate filling: A low-energy approach

Band-to-Mott-insulator transformations in four-component alkali-metal fermions at half-filling

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