Density wave states in superfluid

Jinwu Ye

Keita Shimizu, Takahiro Hirano, Jonghoon Park +2 more

In this paper, we study the nonequilibrium dynamics of the Bose–Hubbard model with the nearest-neighbor repulsion by using time-dependent Gutzwiller (GW) methods. In particular, we vary the hopping parameters in the Hamiltonian as a function of time, and investigate the dynamics of the system from the density wave (DW) to the superfluid (SF) crossing a first-order phase transition and vice versa. From the DW to SF, we find scaling laws for the correlation length and vortex density with respect to the quench time. This is a reminiscence of the Kibble–Zurek scaling for continuous phase transitions and contradicts the common expectation. We give a possible explanation for this observation. On the other hand from SF to DW, the system evolution depends on the initial SF state. When the initial state is the ground state obtained by the static GW methods, a coexisting state of the SF and DW domains forms after passing through the critical point. Coherence of the SF order parameter is lost as the system evolves. This is a phenomenon similar to the glass transition in classical systems. When the state starts from the SF with small local phase fluctuations, the system obtains a large size DW domain structure with thin domain walls.

H. Haug, K. Weiss

P. Schlottmann, Andrei A. Zvyagin

In the context of ultracold fermionic atoms with effective spin S confined to an elongated trap we study the one-dimensional gas interacting via an attractive δ-function potential using the Bethe ansatz solution. There are N = 2 S + 1 fundamental states: The particles can either be unpaired or clustered in bound states of 2, 3, ..., 2 S and 2S + 1 atoms. In a magnetic field, the rich ground state phase diagram consists of these N states and various mixed phases in which combinations of the fundamental states coexist. The phase diagram simplifies considerably in zero-field, where only bound states of N atoms can exist. Due to the harmonic confinement and within the local density approximation, the density profile of bound states decreases along the tube from the center of the trap to its boundaries. In an array of tubes with weak Josephson tunneling superfluid order may arise. In zero-field the response functions determining the superfluid and density wave order are calculated using conformal field theory and the exact Bethe ansatz solution. The response function for superfluidity consists of a power law with distance, while the correlation function for density waves is a power law of distance times a sinusoidal factor oscillating with distance with a period given by two times the Fermi momentum. For S = 1/2 superfluidity is a possibility for all densities and density waves can be excluded. For S ≥ 3/2 superfluidity may occur at low densities but at high densities it gives way to density waves. We discuss the scenario of phase separation where for S ≥ 3/2 the system has superfluid long-range order toward the trap boundaries and density waves at its center.

Wanzhou Zhang, Laixi Li, Wenan Guo

We study the zero-temperature phase diagram of hardcore bosons on the dual of the bowtie lattice. Two types of striped diagonal long-range order (striped order I and striped order II) are discussed. A state with type-II striped order and superfluidity is found, even without nearest-neighbor repulsion. The emergence of such a state is due to the inhomogeneity and the anisotropy of the lattice structure. However, neither the translational symmetry nor the symmetry between sublattices of the original lattice is broken in this state. In this paper, we restrict a ``solid state'' of lattice bosons as a diagonal long-range-ordered state breaking either the translational symmetry of the original lattice or the symmetry of different sublattices. We thus name such a phase a striped superfluid phase. In the presence of a nearest-neighbor repulsion, we find two striped charge-density-wave phases with boson density $\ensuremath{\rho}=1/2$ (with striped order I) and $\ensuremath{\rho}=2/3$ (with striped order II), respectively, when the hopping amplitude is small compared with the repulsion. The striped charge-density wave I state is a solid, in which the translational symmetry of the original lattice is broken. We observe a rather special first-order phase transition showing an interesting multiloop hysteresis phenomenon between the two striped charge-density-wave phases when the hopping term is small enough. This can be accounted for by the special degeneracy of the ground states near the classical limit. The striped superfluid phase reappears outside the two striped charge-density-wave phases. The transition between the striped charge-density wave I and striped superfluid phases is first order while the transition between striped charge-density wave II and the striped superfluid phases is continuous. We find that the superfluid stiffness is anisotropic in the striped superfluid states with and without repulsion. In the striped superfluid state with repulsion, the superfluid stiffness is subject to different types of anisotropy in the region near half filling and above 2/3 filling.

José Tito Mendonça