TY - JOUR

T1 - Infrared properties of boundaries in one-dimensional quantum systems

AU - Friedan, Daniel

AU - Konechny, Anatoly

PY - 2006/3/20

Y1 - 2006/3/20

N2 - We present some partial results on the general infrared behaviour of bulk critical 1D quantum systems with a boundary. We investigate whether the boundary entropy, s(T), is always bounded below as the temperature T decreases towards 0, and whether the boundary always becomes critical in the infrared limit. We show that failure of these properties is equivalent to certain seemingly pathological behaviours far from the boundary. One of our approaches uses real time methods, in which locality at the boundary is expressed by analyticity in the frequency. As a preliminary, we use real time methods to prove again that the boundary beta function is the gradient of the boundary entropy, which implies that s(T) decreases with T. The metric on the space of boundary couplings is interpreted as the renormalized susceptibility matrix of the boundary, made finite by a natural subtraction.

AB - We present some partial results on the general infrared behaviour of bulk critical 1D quantum systems with a boundary. We investigate whether the boundary entropy, s(T), is always bounded below as the temperature T decreases towards 0, and whether the boundary always becomes critical in the infrared limit. We show that failure of these properties is equivalent to certain seemingly pathological behaviours far from the boundary. One of our approaches uses real time methods, in which locality at the boundary is expressed by analyticity in the frequency. As a preliminary, we use real time methods to prove again that the boundary beta function is the gradient of the boundary entropy, which implies that s(T) decreases with T. The metric on the space of boundary couplings is interpreted as the renormalized susceptibility matrix of the boundary, made finite by a natural subtraction.

U2 - 10.1088/1742-5468/2006/03/P03014

DO - 10.1088/1742-5468/2006/03/P03014

M3 - Article

SN - 1742-5468

VL - 2006

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 3

ER -