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Register a new userPhase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
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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 two-orbital 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 (non-degenerate, 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 non-local order parameters that characterize the SU(N) topological phases found here.
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We investigate the phase diagram of the half-filled SU(N) Hubbard-Heisenberg model with hopping t, exchange J and Hubbard U, on a square lattice. In the large-N limit, and as a function of decreasing values of t/J, the model shows a transition from a d-density wave state to a spin dimerized insulator. A similar behavior is observed at N=6 whereas at N=2 a spin density wave insulating ground state is stabilized. The N=4 model, has a d-density wave ground state at large values of t/J which as a function of decreasing values of t/J becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power-law,resulting in gapless spin excitations at q = (pi,pi). Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors q = (0,pi) and q = (pi,0). This gapless spin liquid state is equally found in the SU(4) Heisenberg model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a pi-flux phase is offered. Our results stem from projective (T=0) quantum Monte-Carlo simulations on lattice sizes ranging up to 24 X 24.
We demonstrate that supervised machine learning (ML) with entanglement spectrum can give useful information for constructing phase diagram in the half-filled one-dimensional extended Hubbard model. Combining ML with infinite-size density-matrix renormalization group, we confirm that bond-order-wave phase remains stable in the thermodynamic limit.
A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and gapped phases depending on the parity of $N$ for attractive interactions at half-filling. The analogue of the Haldane phase of the spin-1 Heisenberg chain is stabilized for N=2 with non-local string charge correlation, and pseudo-spin 1/2 edge states. At the heart of this even-odd behavior is the existence of a spin-singlet pseudo-spin $N/2$ operator which governs the low-energy properties of the model for attractive interactions and gives rise to the Haldane physics.
We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical $Z_2$ gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the Density Matrix Renormalization Group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling $2/3$.
The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $delta$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the $SU(2|2)$ supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.
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