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We study the low-energy asymptotics of the half-filled Hubbard model with acircular Fermi surface in $d=1+\epsilon$ continuous dimensions, based on theone-loop renormalization-group (RG) method. Peculiarity of the $d=1+\epsilon$dimensions is incorporated through the mathematica structure of the elementaryparticle-partcile (PP) and particle-hole (PH) loops: infrared logarithmicsingularity of the PH loop is smeared for $\epsilon>0$. The RG flows indicatethat a quantum phase transition (QPT) from a metallic phase to the Mottinsulator phase occurs at a finite on-site Coulomb repulsion $U$ for$\epsilon>0$. We also discuss effects of randomness.Comment: 12 pages, 10 eps figure

physical review. b, condensed matter

Quantum phase transitions and collapse of the Mott gap in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>ε</mml:mi></mml:math>dimensional Hubbard model with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>umklapp …

Quantum phase transitions and collapse of the Mott gap in thed=1+εdimensional Hubbard model with2kFumklapp …