The collapse of Hall gaps in the integer quantum Hall liquid in a quantumwire is investigated. Motivated by recent experiment [Pallecchi et al. PRB 65,125303 (2002)] previous approaches are extended to treat confinement effectsand the exchanged enhanced g-factor in quantum wires. Two scenarios for thecollapse of the $\nu =1$ state are discussed. In the first one the $\nu =1$state becomes unstable at $B_{cr}^{(1)}$, due to the exchange interaction andcorrelation effects, coming from the edge-states screening. In the secondscenario, a transition to the $\nu =2$ state occurs at $B_{cr}^{(2)}$, with asmaller effective channel width, caused by the redistribution of the chargedensity. This effect turns the Hartree interaction essential in calculating thetotal energy and changes $B_{cr}^{(2)}$ drastically. In both scenarios, theexchange enhanced g-factor is suppressed for magnetic fields lower than$B_{cr}$. Phase diagrams for the Hall gap collapse are determined. The criticalfields, activation energy, and optical $g$-factor obtained are compared withexperiments. Within the accuracy of the available data, the first scenario ismost probable to be realized.
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