Discretized versus continuous models of p-wave interacting fermions in one dimension

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.013602· OSTI ID:21442951

Muth, Dominik; Fleischhauer, Michael; Schmidt, Bernd ^[1]

---

1. Fachbereich Physik und Forschungszentrum OPTIMAS, Technische Universitaet Kaiserslautern, D-67663 Kaiserslautern (Germany)

We present a general mapping between continuous and lattice models of Bose and Fermi gases in one dimension, interacting via local two-body interactions. For s-wave interacting bosons we arrive at the Bose-Hubbard model in the weakly interacting, low-density regime. The dual problem of p-wave interacting fermions is mapped to the spin-1/2 XXZ model close to the critical point in the highly polarized regime. The mappings are shown to be optimal in the sense that they produce the least error possible for a given discretization length. As an application we examine the ground state of an interacting Fermi gas in a harmonic trap, calculating numerically real-space and momentum-space distributions as well as two-particle correlations. In the analytically known limits the convergence of the results of the lattice model with the continuous one is shown.

• OSTI ID: 21442951
• Journal Information: Physical Review. A, Vol. 82, Issue 1; Other Information: DOI: 10.1103/PhysRevA.82.013602; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOSE-EINSTEIN GAS
CONVERGENCE
CORRELATIONS
FERMI GAS
FERMIONS
GROUND STATES
HUBBARD MODEL
INTERACTING BOSON MODEL
P WAVES
S WAVES
SPACE
SPIN
TRAPS
TWO-BODY PROBLEM
ANGULAR MOMENTUM
CRYSTAL MODELS
ENERGY LEVELS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
NUCLEAR MODELS
PARTIAL WAVES
PARTICLE PROPERTIES
SHELL MODELS