Volovik 2006 poles and zeroes can emerge and

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Unformatted text preview: d=0, D=1 with interactions G. Volovik, 2006 Poles and zeroes can emerge and disappear in pairs Thursday, January 6, 2011 29 VG, 2010 Switching on interactions det G = ￿Dh −Df n=1 ￿ Dh n=1 (iω − rn ) (iω − ￿n ) The invariant at d=0, D=1 with interactions G. Volovik, 2006 Poles and zeroes can emerge and disappear in pairs energy pole parameter Thursday, January 6, 2011 29 VG, 2010 Switching on interactions det G = ￿Dh −Df n=1 ￿ Dh n=1 (iω − rn ) (iω − ￿n ) The invariant at d=0, D=1 with interactions Poles and zeroes can emerge and disappear in pairs det G = energy parameter Thursday, January 6, 2011 VG, 2010 Switching on interactions G. Volovik, 2006 pole 29 zero parameter ￿Dh −Df n=1 ￿ Dh n=1 (iω − rn ) (iω − ￿n ) The invariant at d=0, D=1 with interactions Poles and zeroes can emerge and disappear in pairs det G = energy parameter Thursday, January 6, 2011 VG, 2010 Switching on interactions G. Volovik, 2006 pole 29 ￿Dh −Df n=1 ￿ Dh n=1 zero parameter parameter (iω − rn ) (iω − ￿n ) The invariant at d=0, D=1 with interactions Poles and zeroes can emerge and disappear in pairs det G = energy parameter Thursday, January 6, 2011 VG, 2010 Switching on interactions G. Volovik, 2006 pole 29 ￿Dh −Df n=1 ￿ Dh n=1 (iω − rn ) (iω − ￿n ) zero parameter parameter parameter Fidkowski-Kitaev model (2010) t1 t∗ 1 t1 t2 t∗ 2 30 quartic interactions t∗ 1 g t1 t 1 = t2 Thursday, January 6, 2011 t2 Fidkowski-Kitaev model (2010) t1 t∗ 1 t1 t2 t∗ 2 30 quartic interactions t∗ 1 g t1 t 1 = t2 Thursday, January 6, 2011 t2 Phase transition Fidkowski-Kitaev model (2010) t1 t∗ 1 t1 t2 t∗ 2 30 quartic interactions t∗ 1 g No phase transition t1 t 1 = t2 Thursday, January 6, 2011 t2 Phase transition Fidkowski-Kitaev model (2010) t1 t∗ 1 t1 t2 t∗ 2 30 quartic interactions t∗ 1 g A. Essin, VG: Green’s function has a zero at zero energy No phase transition t1 t 1 = t2 Thursday, January 6, 2011 t2 Phase transition Conclusions and open questions 1. Single particle Green’s functions - a powerful tool to understand topological insulators without or even with interactions. 2. Zeroes of the Green’s functions. What are they, when do they appear, how can they be detected, why are they important for interacting topological insulators? Thursday, January 6, 2011 31 32 The end Thursday, January 6, 2011...
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