Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGround State Properties of Anti-Ferromagnetic Spinor Bose gases in One Dimension
108
0
0.0
(
0
)
Authors
Yajiang Hao
Ask ChatGPT about the research
No Arabic abstract
We investigate the ground state properties of anti-ferromagnetic spin-1 Bose gases in one dimensional harmonic potential from the weak repulsion regime to the strong repulsion regime. By diagonalizing the Hamiltonian in the Hilbert space composed of the lowest eigenstates of single particle and spin components, the ground state wavefunction and therefore the density distributions, magnetization distribution, one body density matrix, and momentum distribution for each components are obtained. It is shown that the spinor Bose gases of different magnetization exhibit the same total density profiles in the full interaction regime, which evolve from the single peak structure embodying the properties of Bose gases to the fermionized shell structure of spin-polarized fermions. But each components display different density profiles, and magnetic domains emerge in the strong interaction limit for $M=0.25$. In the strong interaction limit, one body density matrix and the momentum distributions exhibit the same behaviours as those of spin-polarized fermions. The fermionization of momentum distribution takes place, in contrast to the $delta$-function-like distribution of single component Bose gases in the full interaction region.
rate research
Read More
The ground state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground state wave function which permits to solve the Fermi sign problem in the following respects (i) the nodal surface is known, permitting exact calculations (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system, thus allowing simulation of a large number of fermions. Due to the mapping the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground state energy has been calculated in homogeneous and trapped geometries by using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the large-density ideal Fermi gas/Tonks-Girardeau limit, where low lying excitations are phonons. Exact density profiles are confronted to the ones calculated within the local density approximation which predicts a change from a semicircular to inverted parabolic shape of the density profile as the value of the charge is increased.
Dynamical fermionization refers to the phenomenon in Tonks-Girardeau (TG) gases where, upon release from harmonic confinement, the gass momentum density profile evolves asymptotically to that of an ideal Fermi gas in the initial trap. This phenomenon has been demonstrated theoretically in hardcore and anyonic TG gases, and recently experimentally observed in a strongly interacting Bose gas. We extend this study to a one dimensional (1D) spinor gas of arbitrary spin in the strongly interacting regime, and analytically prove that the total momentum distribution after the harmonic trap is turned off approaches that of a spinless ideal Fermi gas, while the asymptotic momentum distribution of each spin component takes the same shape of the initial real space density profile of that spin component. Our work demonstrates the rich physics arising from the interplay between the spin and the charge degrees of freedom in a spinor system.
By using the numerically exact density-matrix renormalization group (DMRG) approach, we investigate the ground states of harmonically trapped one-dimensional (1D) fermions with population imbalance and find that the Larkin-Ovchinnikov (LO) state, which is a condensed state of fermion pairs with nonzero center-of-mass momentum, is realized for a wide range of parameters. The phase diagram comprising the two phases of i) an LO state at the trap center and a balanced condensate at the periphery and ii) an LO state at the trap center and a pure majority component at the periphery, is obtained. The reduced two-body density matrix indicates that most of the minority atoms contribute to the LO-type quasi-condensate. With the time-dependent DMRG, we also investigate the real-time dynamics of a system of 1D fermions in response to a spin-flip excitation.
Although there is a broad consensus on the fact that critical behavior in stacked triangular Heisenberg antiferromagnets --an example of frustrated magnets with competing interactions-- is described by a Landau-Ginzburg-Wilson Hamiltonian with O(3)$times$O(2) symmetry, the nature of the phase transition in three dimensions is still debated. We show that spin-one Bose gases provide us with a simulator of the O(3)$times$O(2) model. Using a renormalization-group approach, we argue that the transition is weakly first order and shows pseudoscaling behavior, and give estimates of the pseudocritical exponent $ u$ in $^{87}$Rb, $^{41}$K and $^7$Li atom gases which can be tested experimentally.
We theoretically study dilute superfluidity of spin-1 bosons with antiferromagnetic interactions and synthetic spin-orbit coupling (SOC) in a one-dimensional lattice. Employing a combination of density matrix renormalization group and quantum field theoretical techniques we demonstrate the appearance of a robust superfluid spin-liquid phase in which the spin-sector of this spinor Bose-Einstein condensate remains quantum disordered even after introducing quadratic Zeeman and helical magnetic fields. Despite remaining disordered, the presence of these symmetry breaking fields lifts the perfect spin-charge separation and thus the nematic correlators obey power-law behavior. We demonstrate that, at strong coupling, the SOC induces a charge density wave state that is not accessible in the presence of linear and quadratic Zeeman fields alone. In addition, the SOC induces oscillations in the spin and nematic expectation values as well as the bosonic Greens function. These non-trivial effects of a SOC are suppressed under the application of a large quadratic Zeeman field. We discuss how our results could be observed in experiments on ultracold gases of $^{23}$Na in an optical lattice.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
