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arXiv:1411.3905 · Physical Review A

Two-leg fermionic Hubbard ladder system in the presence of state-dependent hopping

Shun Uchino, Thierry Giamarchi

Published Jan 6, 2015• 4 citations
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Abstract

We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin-density wave, and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.

DOI
10.1103/physreva.91.013604

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We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin-density wave, and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.
Motivated by recent experimental progress in the field of dipolar-Fermi gases, we investigate the quantum phases of dipolar fermions on a triangular ladder at half filling. Using density matrix renormalization group method, in the presence of onsite repulsion and intersite attractive interaction, we find an exotic spin-triplet superfluid phase in addition to the usual spin-density and charge-density waves. We examine the stability of the spin-triplet superfluid phase by varying hopping along the rungs of the triangle. The possibility of fermionic supersolidity has also been discussed, by considering three-body interaction in the Hamiltonian. We also study the effect of spin-dependent hopping on the stability of the spin-triplet superfluid phase.
Fermions in two dimensions, when subject to anisotropic spin-dependent hopping, can potentially give rise to unusual paired states in unpolarized mixtures that can behave as non-Fermi liquids. One possibility is a fully paired state with a gap for fermion excitations in which the Cooper pairs remain uncondensed. Such a ``Cooper-pair Bose-metal'' phase would be expected to have a singular Bose surface in momentum space. As demonstrated in the context of two-dimensional bosons hopping with a frustrating ring-exchange interaction, an analogous Bose-metal phase has a set of quasi-one-dimensional descendant states when put on a ladder geometry. Here we present a density matrix renormalization group study of the attractive Hubbard model with spin-dependent hopping on a two-leg ladder geometry. In our setup, one spin species moves preferentially along the leg direction, while the other does so along the rung direction. We find compelling evidence for the existence of a novel Cooper-pair Bose-metal phase in a region of the phase diagram at intermediate coupling. We further explore the phase diagram of this model as a function of hopping anisotropy, density, and interaction strength, finding a conventional superfluid phase as well as a phase of paired Cooper pairs with ddd-wave symmetry, similar to the one found in models of hard-core bosons with ring exchange. We argue that simulating this model with cold Fermi gases on spin-dependent optical lattices is a promising direction for realizing exotic quantum states.
The ground-state phase diagram of a two-leg fermionic dipolar ladder with inter-site interactions is studied using density matrix renormalization group (DMRG) techniques. We use a state-of-the-art implementation of the DMRG algorithm and finite size scaling to simulate large system sizes with high accuracy. We also consider two different model systems and explore stable phases in half and quarter filling factors. We find that in the half filling, the charge and spin gaps emerge in a finite value of the dipole-dipole and on-site interactions. In the quarter filling case, s-wave superconducting state, charge density wave, homogenous insulating and phase separation phases occur depend on the interaction values. Moreover, in the dipole-dipole interaction, the D-Mott phase emerges when the hopping terms along the chain and rung are the same, whereas, this phase has been only proposed for the anisotropic Hubbard model. In the half filling case, on the other hand, there is either charge-density wave or charged Mott order phase depends on the orientation of the dipole moments of the particles with respect to the ladder geometry.
We show that pronounced modulations in spin and charge densities can be induced by the insertion of a single hole in an otherwise half-filled two-leg Hubbard ladder. Accompanied with these modulations is a loosely bound structure of the doped charge with a spin-1/2, in contrast to the tightly bound case where such modulations are absent. These behaviors are caused by the interference of the Berry phases associated with a string of flipped spins (or ``phase strings'') left behind as a hole travels through a spin bath with a short-range antiferromagnetic order. The key role of the phase strings is also reflected in how the system responds to increasing spin polarization and the on-site repulsion, addition of a second hole, and increasing asymmetry between intra- and interchain hopping. Remarkably, all these properties persist down to ladders as short as $\ensuremath{\sim}10$ sites, as the smoking gun of the phase-string effect. They can therefore be studied in cold-atom experiments using the recently developed fermion microscope.
We investigate the ground state properties of spinless fermions on a two leg ladder, by allowing the nearest-neighbour hopping dimerization in one leg and uniform hopping in the other. In the non-interacting limit, we find that, at half-filling, the system exhibits robust topological behavior if the inter-leg hopping is allowed. Though depending on the dimerization pattern, the dimerized leg can be either topological or trivial in nature, here we show that by connecting such a leg to a uniform leg through inter-chain coupling, the overall system becomes topological irrespective of the dimerization pattern in the dimerized leg. As a result, a topological phase transition occurs as a function of the inter-leg hopping. When the inter-leg interaction is turned on, the topological phase survives, and we obtain an interaction induced topological phase transition. Finally, we reveal that when uniform interactions are included on all the bonds of the ladder, the topological phase transitions to a symmetry-broken charge-density wave (CDW) phase.
Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a nontrivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner-superfluid to vortex-superfluid transition, and a nontrivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a nonchiral and a chiral superfluid, both characterized by nontrivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.