Critical Properties of Quantum Many-Body Systems with 1/r^2 Interaction

Abstract

We review recent results obtained for a class of one-dimensional quantum models with $1/r^2$ long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum boson model, the SU($\nu$) spin chain, the OSp($\nu$,1) supersymmetric {\it t-J} model, and a new hierarchy of models related to the fractional quantum Hall effect. We further investigate the class of $1/r^2$ models with harmonic confinement by means of a newly proposed method of the renormalized-harmonic oscillator solution.

46pages, Revtex

Cited by in corpus (9)

• Integrable $1/r^2$ Spin Chain with Reflecting End
• Universal description of dissipative Tomonaga-Luttinger liquids with SU($N$) spin symmetry: Exact spectrum and critical exponents
• Exact ground states of quantum many-body systems under confinement
• Critical Properties of the Calogero-Sutherland Model with Boundaries
• Exact Solutions of Generalized Calogero-Sutherland Models -- BC_N and C_N cases
• On the spectrum of S=1/2 XXX Heisenberg chain with elliptic exchange
• All the Exact Solutions of Generalized Calogero-Sutherland Models
• Calogero Model(s) and Deformed Oscillators
• Parent Hamiltonians of Jastrow Wavefunctions