aqora

Strongly interacting mesoscopic systems of anyons in one dimension

Nikolaj Thomas Zinner

Using the fractional statistical properties of so-called anyonic particles, we present solutions of the Schr\"odinger equation for up to six strongly interacting particles in one-dimensional confinement that interpolate the usual bosonic and fermionic limits. These solutions are exact to linear order in the inverse coupling strength of the zero-range interaction of our model. Specifically, we consider two-component mixtures of anyons and use these to eludicate the mixing-demixing properties of both balanced and imbalanced systems. Importantly, we demonstrate that the degree of demixing depends sensitively on the external trap in which the particles are confined. We also show how one may in principle probe the statistical parameter of an anyonic system by injection a strongly interacting impurity and doing spectral or tunneling measurements.Using the fractional statistical properties of so-called anyonic particles, we present solutions of the Schr\"odinger equation for up to six strongly interacting particles in one-dimensional confinement that interpolate the usual bosonic and fermionic limits. These solutions are exact to linear order in the inverse coupling strength of the zero-range interaction of our model. Specifically, we consider two-component mixtures of anyons and use these to eludicate the mixing-demixing properties of both balanced and imbalanced systems. Importantly, we demonstrate that the degree of demixing depends sensitively on the external trap in which the particles are confined. We also show how one may in principle probe the statistical parameter of an anyonic system by injection a strongly interacting impurity and doing spectral or tunneling measurements.

arXiv:1406.3592Physical Review ADec 29, 201534 citations

Interacting electrons in one-dimensional confinements

T. Shirai, Hideaki Kasai, Wilson Agerico Diño +2 more

Surface ScienceAug 1, 20021 citation

Exact solution of strongly interacting confined quantum systems in one dimension

Artem G. Volosniev, D. V. Fedorov, A. S. Jensen +2 more

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and anti-ferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and anti-ferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.

Jun 19, 20133 citations

An Analysis of Solutions of the One-Dimensional Hubbard Model

Dorota Jakubczyk

Reports on Mathematical PhysicsDec 1, 20132 citations

Interacting electrons in the random potential in one dimension

Y.B. Xie

Exact solutions are obtained for electrons with an infinitely large on-site repulsion moving on a disordered lattice in one dimension. The system is found to be still localized, but the relevant charge Fermi surface is shifted because of the on-site interaction. Therefore, the frequency-dependent electric conductivity is quantitatively changed. An ideal experiment is also suggested to detect this effect.

Physical review. B, Condensed matterJan 15, 19923 citations

Ground states in one-dimensional electron systems

W. Hansen, D. Schmerek, Chr. Steinebach

Physics-UspekhiFeb 28, 19987 citations

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