We study the universal long-distance behaviour of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one dimensional 1/r^2 interaction model). In particular, it is shown that these two wave functions coincide exactly when Laughlin state is confined in a narrow cylinder geometry. The seeming difference of dimensionality is merely a difference of representation of wave functions. We also give a recipe to interpret operators acting on states in the lowest Landau level in terms of the usual one dimensional Fermion operators, which is important for extracting the Tomonaga-Luttinger liquid behaviour of the edge states.We study the universal long-distance behaviour of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one dimensional 1/r^2 interaction model). In particular, it is shown that these two wave functions coincide exactly when Laughlin state is confined in a narrow cylinder geometry. The seeming difference of dimensionality is merely a difference of representation of wave functions. We also give a recipe to interpret operators acting on states in the lowest Landau level in terms of the usual one dimensional Fermion operators, which is important for extracting the Tomonaga-Luttinger liquid behaviour of the edge states.

Jan 1, 19941 citation

The Conductivity of the Tomonaga‐Luttinger Model

Victor Bârsan

physica status solidi (b)Jun 1, 19890 citations

LONG DISTANCE UNIVERSALITY OF LAUGHLIN STATE AND CALOGERO-SUTHERLAND MODEL

SATOSHI ISO

We study the universal long distance behavior of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one-dimensional 1/r2 interaction model). In particular, it is shown that these two wave functions coincide exactly when Laughlin state is confined in a narrow cylinder geometry. The seeming difference of dimensionality is merely a difference of representation of wave functions. We also give a recipe to interpret operators acting on states in the lowest Landau level in terms of the usual one-dimensional fermion operators, which is important for extracting the Tomonaga-Luttinger liquid behavior of the edge states.We study the universal long distance behavior of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one-dimensional 1/r2 interaction model). In particular, it is shown that these two wave functions coincide exactly when Laughlin state is confined in a narrow cylinder geometry. The seeming difference of dimensionality is merely a difference of representation of wave functions. We also give a recipe to interpret operators acting on states in the lowest Landau level in terms of the usual one-dimensional fermion operators, which is important for extracting the Tomonaga-Luttinger liquid behavior of the edge states.

arXiv:cond-mat/9404075Modern Physics Letters AJul 30, 19946 citations

A Two-Dimensional Analogue of the Luttinger Model

Edwin Langmann A

arXiv:math-ph/0606041Letters in Mathematical PhysicsApr 14, 20109 citations

Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge

Alexey Mikhajlovich Boyarsky, Vadim Cheianov, Oleg Ruchayskiy C

We give a microscopic derivation of the chiral Luttinger liquid theory $(\ensuremath{\chi}LL)$ for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state (IDLS) we quantize these deformations. In this way we obtain the low-energy projections of local microscopic operators and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. This shows that to describe experimental and numeric deviations from $\ensuremath{\chi}LL$ one needs to go beyond Laughlin's approximation. We show that in the large $N$ limit the IDLS is described by the dispersionless Toda hierarchy.We give a microscopic derivation of the chiral Luttinger liquid theory $(\ensuremath{\chi}LL)$ for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state (IDLS) we quantize these deformations. In this way we obtain the low-energy projections of local microscopic operators and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. This shows that to describe experimental and numeric deviations from $\ensuremath{\chi}LL$ one needs to go beyond Laughlin's approximation. We show that in the large $N$ limit the IDLS is described by the dispersionless Toda hierarchy.

arXiv:cond-mat/0402562Physical Review BDec 8, 200420 citations

N

limit the IDLS is described by the dispersionless Toda hierarchy.