TY - JOUR

T1 - Infrared catastrophe and tunneling into strongly correlated electron systems

T2 - Exact x-ray edge limit for the one-dimensional electron gas and two-dimensional Hall fluid

AU - Patton, Kelly R.

AU - Geller, Michael R.

PY - 2006

Y1 - 2006

N2 - In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Green's function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results were obtained for the DOS of the one-dimensional electron gas and two-dimensional Hall fluid when the corrections to the x-ray edge limit were neglected and when the corresponding Nozières-De Dominicis integral equations were solved by resummation of a divergent perturbation series. Here we reexamine the x-ray edge limit for these two models by solving these integral equations exactly, finding the expected modifications of the DOS exponent in the one-dimensional case but finding no changes in the DOS of the two-dimensional Hall fluid with short-range interaction. Our analysis provides an exact solution of the Nozières-De Dominicis equation for the two-dimensional electron gas in the lowest Landau level.

AB - In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Green's function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results were obtained for the DOS of the one-dimensional electron gas and two-dimensional Hall fluid when the corrections to the x-ray edge limit were neglected and when the corresponding Nozières-De Dominicis integral equations were solved by resummation of a divergent perturbation series. Here we reexamine the x-ray edge limit for these two models by solving these integral equations exactly, finding the expected modifications of the DOS exponent in the one-dimensional case but finding no changes in the DOS of the two-dimensional Hall fluid with short-range interaction. Our analysis provides an exact solution of the Nozières-De Dominicis equation for the two-dimensional electron gas in the lowest Landau level.

UR - http://www.scopus.com/inward/record.url?scp=33744942105&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.73.245306

DO - 10.1103/PhysRevB.73.245306

M3 - Article

AN - SCOPUS:33744942105

SN - 1098-0121

VL - 73

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 24

M1 - 245306

ER -