Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnyons from Three-Body Hard-Core Interactions in One Dimension
89
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Traditional anyons in two dimensions have generalized exchange statistics governed by the braid group. By analyzing the topology of configuration space, we discover that an alternate generalization of the symmetric group governs particle exchanges when there are hard-core three-body interactions in one-dimension. We call this new exchange symmetry the traid group and demonstrate that it has abelian and non-abelian representations that are neither bosonic nor fermionic, and which also transform differently under particle exchanges than braid group anyons. We show that generalized exchange statistics occur because, like hard-core two-body interactions in two dimensions, hard-core three-body interactions in one dimension create defects with co-dimension two that make configuration space no longer simply-connected. Ultracold atoms in effectively one-dimensional optical traps provide a possible implementation for this alternate manifestation of anyonic physics.
rate research
Read More
We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the interval.
We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbour two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $Uleq-2t$ and positive $V>0$ a large trimer is stabilized, which persists as $Vrightarrow infty$, while both attractive $Uleq0$ and $Vleq0$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $Vrightarrow -infty$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V>>t$, $U<-2t$ the bound-state behavior qualitatively evolves with larger $|U|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.
We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.
Motivated by previous suggestions that three-body hard-core interactions in lower-dimensional ultracold Bose gases might provide a way for creation of non-Abelian anyons, the exact ground state of a harmonically trapped 1D Bose gas with three-body hard-core interactions is constructed by duality mapping, starting from an $N$-particle ideal gas of mixed symmetry with three-body nodes, which has double occupation of the lowest harmonic oscillator orbital and single occupation of the next $N-2$ orbitals. It has some similarity to the ground state of a Tonks-Girardeau gas, but is more complicated. It is proved that in 1D any system of $Nge 3$ bosons with three-body hard-core interactions also has two-body soft-core interactions of generalized Lieb-Liniger delta function form, as a consequence of the topology of the configuration space of $N$ particles in 1D, i.e., wave functions with emph{only} three-body hard core zeroes are topologically impossible. This is in contrast with the case of 2D, where pure three-body hard-core interactions do exist, and are closely related to the fractional quantized Hall effect. The exact ground state is compared with a previously-proposed Pfaffian-like approximate ground state, which satisfies the three-body hard-core constraint but is not an exact energy eigenstate. Both the exact ground state and the Pfaffian-like approximation imply two-body soft-core interactions as well as three-body hard-core interactions, in accord with the general topological proof.
We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and time scales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder $W_c(L, d)$ as a function of length $L$ and width $d$. In the quasi-1D case $W_c$ has a finite large-$L$ limit at fixed $d$, which increases strongly with $d$. In the 2D case $W_c(L,L)$ grows with $L$. The results are consistent with the avalanche picture of the many-body localization transition.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
