arXiv:1012.2036 · Modern Physics Letters B

PHASE DIAGRAM OF ONE-DIMENSIONAL ALKALINE-EARTH COLD FERMIONIC ATOMS

Heloise Nonne, E. Boulat, Sylvain Capponi, P. Lecheminant

Published May 23, 2011• 15 citations

Abstract

The phase diagram of one-dimensional alkaline-earth fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.

DOI: 10.1142/s0217984911026668

Related papers

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

V. Bois, Sylvain Capponi, P. Lecheminant +2 more

arXiv:1410.2974Physical Review BFeb 23, 201539 citations

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

V. Bois, Pierre Fromholz, P. Lecheminant

arXiv:1602.00866Physical review. B./Physical review. BApr 13, 201614 citations

Confinement versus deconfinement of Cooper pairs in one-dimensional spin- 3∕2 fermionic cold atoms

Sylvain Capponi, Guillaume Roux, P. Azaria +2 more

arXiv:cond-mat/0612456Physical Review BMar 16, 200754 citations

Study of the ionic Peierls-Hubbard model using density matrix renormalization group methods

Yu‐Zhong Zhang, Chao Wu, Hua Lin

arXiv:cond-mat/0401535Physical Review BSep 28, 20056 citations

Competing orders in the generalized Hund chain model at half filling

Heloise Nonne, E. Boulat, Sylvain Capponi +1 more

arXiv:1006.3884Physical Review BOct 22, 201025 citations

Two-orbital physics of high-spin fermionic alkaline-earth atoms confined in a one-dimensional chain

E. Szirmai

arXiv:1307.7558Physical Review BNov 26, 20137 citations

arXiv:1012.2036 · Modern Physics Letters B

PHASE DIAGRAM OF ONE-DIMENSIONAL ALKALINE-EARTH COLD FERMIONIC ATOMS

Heloise Nonne, E. Boulat, Sylvain Capponi, P. Lecheminant

Published May 23, 2011• 15 citations

arXiv HTML PDF

Abstract

DOI: 10.1142/s0217984911026668

Related papers

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

V. Bois, Sylvain Capponi, P. Lecheminant +2 more

We investigate possible realizations of exotic $\mathrm{SU}(N)$ symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard $\mathrm{SU}(N)$ 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 $\mathrm{SU}(N)$ phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the $\mathrm{SU}(N)$ topological phases found here.We investigate possible realizations of exotic $\mathrm{SU}(N)$ symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard $\mathrm{SU}(N)$ 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 $\mathrm{SU}(N)$ phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the $\mathrm{SU}(N)$ topological phases found here.

arXiv:1410.2974Physical Review BFeb 23, 201539 citations

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

V. Bois, Pierre Fromholz, P. Lecheminant

We investigate the zero-temperature phase diagram of two-orbital $\mathrm{SU}(N$ ) 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 $\mathrm{SU}(N$ ) 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.We investigate the zero-temperature phase diagram of two-orbital $\mathrm{SU}(N$) 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 $\mathrm{SU}(N$) 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.

arXiv:1602.00866Physical review. B./Physical review. BApr 13, 201614 citations

Confinement versus deconfinement of Cooper pairs in one-dimensional spin- 3∕2 fermionic cold atoms

Sylvain Capponi, Guillaume Roux, P. Azaria +2 more

The phase diagram of spin- $3∕2$ fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.The phase diagram of spin-$3∕2$ fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.

arXiv:cond-mat/0612456Physical Review BMar 16, 200754 citations

Study of the ionic Peierls-Hubbard model using density matrix renormalization group methods

Yu‐Zhong Zhang, Chao Wu, Hua Lin

Density matrix renormalization group methods are used to investigate the quantum phase diagram of a one-dimensional half-filled ionic Peierls-Hubbard model at the antiadiabatic limit where quantum phonon fluctuations are taken into account partially. We found that two continuous phase transitions always exist from dimerized spin-gapped (bond-order-wave) state to band-insulator and undimerized spin-gapless (Mott-insulator) phase while undimerized spin-gapless phase vanishes at the adiabatic limit. Our results indicate that quantum phonon fluctuations, electron-electron interaction, and ionic potential combine in the formation of the bond-order wave phase.Density matrix renormalization group methods are used to investigate the quantum phase diagram of a one-dimensional half-filled ionic Peierls-Hubbard model at the antiadiabatic limit where quantum phonon fluctuations are taken into account partially. We found that two continuous phase transitions always exist from dimerized spin-gapped (bond-order-wave) state to band-insulator and undimerized spin-gapless (Mott-insulator) phase while undimerized spin-gapless phase vanishes at the adiabatic limit. Our results indicate that quantum phonon fluctuations, electron-electron interaction, and ionic potential combine in the formation of the bond-order wave phase.

arXiv:cond-mat/0401535Physical Review BSep 28, 20056 citations

Competing orders in the generalized Hund chain model at half filling

Heloise Nonne, E. Boulat, Sylvain Capponi +1 more

By using a combination of several nonperturbative techniques---a one-dimensional field theoretical approach together with numerical simulations using density-matrix renormalization group---we present an extensive study of the phase diagram of the generalized Hund model at half filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin $\frac{3}{2}$ , other cold gases such as ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott-insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg electronic ladders with interchain hopping. Our results obtained from a weak-coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.By using a combination of several nonperturbative techniques---a one-dimensional field theoretical approach together with numerical simulations using density-matrix renormalization group---we present an extensive study of the phase diagram of the generalized Hund model at half filling. This model encloses the physics of various strongly correlated one-dimensional systems, such as two-leg electronic ladders, ultracold degenerate fermionic gases carrying a large hyperfine spin $\frac{3}{2}$, other cold gases such as ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott-insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg electronic ladders with interchain hopping. Our results obtained from a weak-coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.

arXiv:1006.3884Physical Review BOct 22, 201025 citations

Two-orbital physics of high-spin fermionic alkaline-earth atoms confined in a one-dimensional chain

E. Szirmai

We study the effect of the coupling between the electronic ground state of high-spin alkaline-earth fermionic atoms and their metastable optically excited state, when the system is confined in a one-dimensional chain, and show that the system provides a possible realization of a finite momentum pairing (Fulde-Ferrell-Larkin-Ovchinnikov-like) state without spin- or bare mass imbalance. We determine the $\ensuremath{\beta}$-functions of the renormalization group trajectories for general spin and analyze the structure of the possible gapped and gapless states in the hydrodynamic limit. Due to the SU( $N$ ) symmetry in the spin space, complete mode separation can not be observed even in the fully gapless 2 $N$ -component Luttinger liquid state. Contrary, four velocities characterize the system. We solve the renormalization group equations for spin-9/2 strontium-87 isotope and analyze in detail its phase diagram. The fully gapless Luttinger liquid state does not stabilize in the two-orbital system of the ${}^{87}$ Sr atoms, instead, different gapped non-Gaussian fixed points are identified either with dominant density or superconducting fluctuations. The superconducting states are stable in a nontrivial shaped region in the parameter space as a consequence of the coupling between the two electronic states.We study the effect of the coupling between the electronic ground state of high-spin alkaline-earth fermionic atoms and their metastable optically excited state, when the system is confined in a one-dimensional chain, and show that the system provides a possible realization of a finite momentum pairing (Fulde-Ferrell-Larkin-Ovchinnikov-like) state without spin- or bare mass imbalance. We determine the $\ensuremath{\beta}$-functions of the renormalization group trajectories for general spin and analyze the structure of the possible gapped and gapless states in the hydrodynamic limit. Due to the SU($N$) symmetry in the spin space, complete mode separation can not be observed even in the fully gapless 2$N$-component Luttinger liquid state. Contrary, four velocities characterize the system. We solve the renormalization group equations for spin-9/2 strontium-87 isotope and analyze in detail its phase diagram. The fully gapless Luttinger liquid state does not stabilize in the two-orbital system of the ${}^{87}$Sr atoms, instead, different gapped non-Gaussian fixed points are identified either with dominant density or superconducting fluctuations. The superconducting states are stable in a nontrivial shaped region in the parameter space as a consequence of the coupling between the two electronic states.

arXiv:1307.7558Physical Review BNov 26, 20137 citations

We investigate possible realizations of exotic

\mathrm{SU}(N)

symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard

\mathrm{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

\mathrm{SU}(N)

phase, which we fully characterize by its entanglement properties. We also propose sets of nonlocal order parameters that characterize the

\mathrm{SU}(N)

topological phases found here.

We investigate the zero-temperature phase diagram of two-orbital

\mathrm{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

\mathrm{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.

The phase diagram of spin-

3∕2

fermionic cold atoms trapped in a one-dimensional optical lattice is investigated at quarter filling (one atom per site) by means of large-scale numerical simulations. In full agreement with a recent low-energy approach, we find two phases with confined and deconfined Cooper pairs separated by an Ising quantum phase transition. The leading instability in the confined phase is an atomic-density wave with subdominant quartet superfluid instability made of four fermions. Finally, we reveal the existence of a bond-ordered Mott insulating phase in some part of the repulsive regime.

\frac{3}{2}

, other cold gases such as ytterbium 171 or alkaline-earth condensates. A particular emphasis is laid on the possibility to enumerate and exhaust the eight possible Mott-insulating phases by means of a duality approach. We exhibit a one-to-one correspondence between these phases and those of the two-leg electronic ladders with interchain hopping. Our results obtained from a weak-coupling analysis are in remarkable quantitative agreement with our numerical results carried out at moderate coupling.

N

) symmetry in the spin space, complete mode separation can not be observed even in the fully gapless 2

N

-component Luttinger liquid state. Contrary, four velocities characterize the system. We solve the renormalization group equations for spin-9/2 strontium-87 isotope and analyze in detail its phase diagram. The fully gapless Luttinger liquid state does not stabilize in the two-orbital system of the

{}^{87}

Sr atoms, instead, different gapped non-Gaussian fixed points are identified either with dominant density or superconducting fluctuations. The superconducting states are stable in a nontrivial shaped region in the parameter space as a consequence of the coupling between the two electronic states.