메뉴 건너뛰기




Volumn 80, Issue 16, 2009, Pages

Quantum Hall quasielectron operators in conformal field theory

Author keywords

[No Author keywords available]

Indexed keywords


EID: 72849150413     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.165330     Document Type: Article
Times cited : (55)

References (64)
  • 1
    • 22244440948 scopus 로고
    • 10.1103/PhysRevLett.50.1395
    • R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983). 10.1103/PhysRevLett.50. 1395
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 1395
    • Laughlin, R.B.1
  • 2
    • 1842460762 scopus 로고
    • 10.1016/0550-3213(91)90407-O
    • G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991). 10.1016/0550- 3213(91)90407-O
    • (1991) Nucl. Phys. B , vol.360 , pp. 362
    • Moore, G.1    Read, N.2
  • 3
    • 0000270607 scopus 로고
    • 10.1103/PhysRevLett.63.199
    • J. K. Jain, Phys. Rev. Lett. 63, 199 (1989). 10.1103/PhysRevLett.63.199
    • (1989) Phys. Rev. Lett. , vol.63 , pp. 199
    • Jain, J.K.1
  • 9
    • 0002260211 scopus 로고
    • 10.1142/S0217732391000336
    • S. Fubini, Mod. Phys. Lett. A 6, 347 (1991). 10.1142/S0217732391000336
    • (1991) Mod. Phys. Lett. A , vol.6 , pp. 347
    • Fubini, S.1
  • 10
    • 4243812765 scopus 로고
    • 10.1103/PhysRevB.42.8133
    • B. Blok and X. G. Wen, Phys. Rev. B 42, 8133 (1990). 10.1103/PhysRevB.42. 8133
    • (1990) Phys. Rev. B , vol.42 , pp. 8133
    • Blok, B.1    Wen, X.G.2
  • 11
    • 72849127635 scopus 로고    scopus 로고
    • We shall denote the quasielectron position with η̄ rather than η for reasons that will be clear later.
    • We shall denote the quasielectron position with η̄ rather than η for reasons that will be clear later.
  • 13
    • 84926087383 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, England
    • J. K. Jain, Composite Fermions (Cambridge University Press, Cambridge, England, 2007).
    • (2007) Composite Fermions
    • Jain, J.K.1
  • 15
    • 33744723980 scopus 로고
    • 10.1103/PhysRevLett.51.605
    • F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983). 10.1103/PhysRevLett. 51.605
    • (1983) Phys. Rev. Lett. , vol.51 , pp. 605
    • Haldane, F.D.M.1
  • 16
    • 42049094261 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.77.155308
    • E. J. Bergholtz and A. Karlhede, Phys. Rev. B 77, 155308 (2008). 10.1103/PhysRevB.77.155308
    • (2008) Phys. Rev. B , vol.77 , pp. 155308
    • Bergholtz, E.J.1    Karlhede, A.2
  • 18
    • 72849153213 scopus 로고    scopus 로고
    • There a systematic way of improving the wave functions involves increasing the Hilbert space by including excitons, i.e., states with one or more composite fermions excited to a higher (unfilled) effective Landau level while conserving the total angular momentum.
    • There a systematic way of improving the wave functions involves increasing the Hilbert space by including excitons, i.e., states with one or more composite fermions excited to a higher (unfilled) effective Landau level while conserving the total angular momentum.
  • 19
    • 72849152529 scopus 로고    scopus 로고
    • One is free to use representations with other linear combinations of the boson fields or additional auxiliary boson fields, as long as one does not change the correlations of the electron and hole operators, namely, □ Vα (z) Vβ (w) □ ∼ (z-w) Kαβ and □ Vα (z) Hβ (w) □ ∼ (z-w) δαβ where K is the K matrix of the state (Ref.).
    • One is free to use representations with other linear combinations of the boson fields or additional auxiliary boson fields, as long as one does not change the correlations of the electron and hole operators, namely, □ Vα (z) Vβ (w) □ ∼ (z-w) Kαβ and □ Vα (z) Hβ (w) □ ∼ (z-w) δαβ where K is the K matrix of the state (Ref.).
  • 21
    • 72849136320 scopus 로고    scopus 로고
    • Ph.D. thesis, University of Amsterdam
    • E. Ardonne, Ph.D. thesis, University of Amsterdam, 2002.
    • (2002)
    • Ardonne, E.1
  • 22
    • 72849138733 scopus 로고    scopus 로고
    • It is not obvious that this method will result in wave functions describing N electrons forming a quantum Hall droplet-i.e., a state that is homogenous up to distances on the order of the magnetic length away from the edge. That this is in fact the case can be understood by mapping the compactified plane to the sphere, where a homogeneous background charge can be introduced without breaking the conformal symmetry, by coupling it to the Gaussian curvature (Ref.). One can then show that the resulting correlators, which by construction describe a homogenous system, reproduce the result from the plane with the ad hoc prescription of taking a single compensating background point charge to infinity.
    • It is not obvious that this method will result in wave functions describing N electrons forming a quantum Hall droplet-i.e., a state that is homogenous up to distances on the order of the magnetic length away from the edge. That this is in fact the case can be understood by mapping the compactified plane to the sphere, where a homogeneous background charge can be introduced without breaking the conformal symmetry, by coupling it to the Gaussian curvature (Ref.). One can then show that the resulting correlators, which by construction describe a homogenous system, reproduce the result from the plane with the ad hoc prescription of taking a single compensating background point charge to infinity.
  • 24
    • 72849150964 scopus 로고    scopus 로고
    • We are, in fact, indebted to
    • We are, in fact, indebted to A. A. Zamolodchikov, for pointing out to us that the transformations could be of use in our formalism.
    • Zamolodchikov, A.A.1
  • 25
    • 0000329826 scopus 로고
    • 10.1103/PhysRevLett.69.953
    • X. G. Wen and A. Zee, Phys. Rev. Lett. 69, 953 (1992). 10.1103/PhysRevLett.69.953
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 953
    • Wen, X.G.1    Zee, A.2
  • 27
    • 26344477250 scopus 로고
    • 10.1103/PhysRevLett.52.1583
    • B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984). 10.1103/PhysRevLett.52. 1583
    • (1984) Phys. Rev. Lett. , vol.52 , pp. 1583
    • Halperin, B.I.1
  • 28
    • 0002985514 scopus 로고
    • See, e.g., 10.1142/S0217979292000037
    • See, e.g., S. C. Zhang, Int. J. Mod. Phys. B 6, 25 (1992). 10.1142/S0217979292000037
    • (1992) Int. J. Mod. Phys. B , vol.6 , pp. 25
    • Zhang, S.C.1
  • 29
    • 0003414482 scopus 로고
    • 2nd ed., edited by R. Prange and S. Girvin (Springer, New York
    • R. B. Laughlin, in The Quantum Hall Effect, 2nd ed., edited by, R. Prange, and, S. Girvin, (Springer, New York, 1990).
    • (1990) The Quantum Hall Effect
    • Laughlin, R.B.1
  • 31
  • 32
    • 0009085178 scopus 로고
    • 10.1016/0370-2693(85)91359-0
    • S. A. Kivelson and M. Roček, Phys. Lett. B 156, 85 (1985). 10.1016/0370-2693(85)91359-0
    • (1985) Phys. Lett. B , vol.156 , pp. 85
    • Kivelson, S.A.1    Roček, M.2
  • 33
  • 36
    • 0002782929 scopus 로고
    • 10.1103/PhysRevLett.65.1502
    • N. Read, Phys. Rev. Lett. 65, 1502 (1990). 10.1103/PhysRevLett.65.1502
    • (1990) Phys. Rev. Lett. , vol.65 , pp. 1502
    • Read, N.1
  • 37
    • 0010954187 scopus 로고
    • 10.1103/PhysRevB.31.1191
    • D. J. Thouless and Y.-S. Wu, Phys. Rev. B 31, 1191 (1985). 10.1103/PhysRevB.31.1191
    • (1985) Phys. Rev. B , vol.31 , pp. 1191
    • Thouless, D.J.1    Wu, Y.-S.2
  • 38
    • 72849120068 scopus 로고    scopus 로고
    • But, and this is very important, this conclusion is only valid provided there are no degeneracies in the multihole states, i.e., the state is completely determined by the position of the quasiparticles. This is not true for the Pfaffian state and this is precisely what opens the possibility for non-Abelian statistics. In CFT language, the fusion rules are now more complicated since there is an underlying SU(2) current algebra, which allows for two different splitting channels of the Laughlin hole.
    • But, and this is very important, this conclusion is only valid provided there are no degeneracies in the multihole states, i.e., the state is completely determined by the position of the quasiparticles. This is not true for the Pfaffian state and this is precisely what opens the possibility for non-Abelian statistics. In CFT language, the fusion rules are now more complicated since there is an underlying SU(2) current algebra, which allows for two different splitting channels of the Laughlin hole.
  • 39
    • 0005839937 scopus 로고
    • 10.1103/PhysRevB.34.1031
    • W. P. Su, Phys. Rev. B 34, 1031 (1986). 10.1103/PhysRevB.34.1031
    • (1986) Phys. Rev. B , vol.34 , pp. 1031
    • Su, W.P.1
  • 42
    • 1542763507 scopus 로고
    • 10.1080/00018739500101566
    • X.-G. Wen, Adv. Phys. 44, 405 (1995). 10.1080/00018739500101566
    • (1995) Adv. Phys. , vol.44 , pp. 405
    • Wen, X.-G.1
  • 43
    • 0030592675 scopus 로고    scopus 로고
    • n-1-dimensional spinor braiding statistics in paired quantum hall states
    • DOI 10.1016/0550-3213(96)00430-0, PII S0550321396004300
    • C. Nayak and F. Wilczek, Nucl. Phys. B 479, 529 (1996). 10.1016/0550-3213(96)00430-0 (Pubitemid 126161210)
    • (1996) Nuclear Physics B , vol.479 , Issue.3 , pp. 529-553
    • Nayak, C.1    Wilczek, F.2
  • 44
    • 0031498067 scopus 로고    scopus 로고
    • 10.1016/S0550-3213(97)00612-3
    • V. Gurarie and C. Nayak, Nucl. Phys. B 506, 685 (1997). 10.1016/S0550-3213(97)00612-3
    • (1997) Nucl. Phys. B , vol.506 , pp. 685
    • Gurarie, V.1    Nayak, C.2
  • 45
    • 59249089187 scopus 로고    scopus 로고
    • 10.1103/PhysRevB.79.045308
    • N. Read, Phys. Rev. B 79, 045308 (2009). 10.1103/PhysRevB.79.045308
    • (2009) Phys. Rev. B , vol.79 , pp. 045308
    • Read, N.1
  • 46
    • 72849146947 scopus 로고    scopus 로고
    • We want to stress that this technical difficulty does not affect the construction of the hierarchy ground states where there is a finite density of quasielectrons and where the charge is naturally neutralized by a new constant U(1) charge distribution that contributes to the physical background electric charge.
    • We want to stress that this technical difficulty does not affect the construction of the hierarchy ground states where there is a finite density of quasielectrons and where the charge is naturally neutralized by a new constant U(1) charge distribution that contributes to the physical background electric charge.
  • 47
    • 72849139139 scopus 로고    scopus 로고
    • As explained in Ref., the operator Vα+1 is not unique. Technically speaking, there is a freedom in picking the coefficient of φα+1 when bosonizing the hole operator Hα since any even-integer braiding statistics of Hb is permitted, cf. Eq. -this leads to different Vα+1 ∼ ∂H bα -1 Vα. Physically, these different choices correspond to how closely one can "pack" the quasiparticles in the condensate. For instance, starting from 1/3, the "minimal" choice 5/3 in Eq. takes us to 2/5. Choosing the coefficient 5/3+2 = 11/3 instead, gives the less dense state 4/11 etc. The relation is independent of this choice.
    • As explained in Ref., the operator Vα+1 is not unique. Technically speaking, there is a freedom in picking the coefficient of φα+1 when bosonizing the hole operator Hα since any even-integer braiding statistics of Hb is permitted, cf. Eq. -this leads to different Vα+1 ∼ ∂H bα -1 Vα. Physically, these different choices correspond to how closely one can "pack" the quasiparticles in the condensate. For instance, starting from 1/3, the "minimal" choice 5/3 in Eq. takes us to 2/5. Choosing the coefficient 5/3+2 = 11/3 instead, gives the less dense state 4/11 etc. The relation is independent of this choice.
  • 48
    • 72849125390 scopus 로고    scopus 로고
    • This was the reason for including the gaussian factor in the definition of P (η̄ k).
    • This was the reason for including the gaussian factor in the definition of P (η̄ k).
  • 49
    • 0001525628 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.80.1505;
    • R. H. Morf, Phys. Rev. Lett. 80, 1505 (1998) 10.1103/PhysRevLett.80.1505
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 1505
    • Morf, R.H.1
  • 52
    • 46449093181 scopus 로고    scopus 로고
    • Quasi-particle properties from tunneling in the ν = 5/2 fractional quantum hall state
    • DOI 10.1126/science.1157560
    • I. P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, and K. W. West, Science 320, 899 (2008). 10.1126/science.1157560 (Pubitemid 351929581)
    • (2008) Science , vol.320 , Issue.5878 , pp. 899-902
    • Radu, I.P.1    Miller, J.B.2    Marcus, C.M.3    Kastner, M.A.4    Pfeiffer, L.N.5    West, K.W.6
  • 54
    • 0035129985 scopus 로고    scopus 로고
    • Non-Abelian statistics of half-quantum vortices in p-wave superconductors
    • DOI 10.1103/PhysRevLett.86.268
    • D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001). 10.1103/PhysRevLett.86.268 (Pubitemid 32131693)
    • (2001) Physical Review Letters , vol.86 , Issue.2 , pp. 268-271
    • Ivanov, D.A.1
  • 56
  • 59
    • 0001687379 scopus 로고
    • 10.1103/PhysRevLett.75.1186
    • T.-L. Ho, Phys. Rev. Lett. 75, 1186 (1995). 10.1103/PhysRevLett.75.1186
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 1186
    • Ho, T.-L.1
  • 60
    • 0035832125 scopus 로고    scopus 로고
    • Parafermion Hall states from coset projections of abelian conformal theories
    • DOI 10.1016/S0550-3213(00)00774-4, PII S0550321300007744
    • A. Cappelli, L. S. Georgiev, and I. Todorov, Nucl. Phys. B 599, 499 (2001). 10.1016/S0550-3213(00)00774-4 (Pubitemid 33376515)
    • (2001) Nuclear Physics B , vol.599 , Issue.3 , pp. 499-530
    • Cappelli, A.1    Georgiev, L.S.2    Todorov, I.T.3
  • 61
    • 0001402466 scopus 로고
    • 10.1103/PhysRevD.15.2875
    • J. B. Zuber and C. Itzykson, Phys. Rev. D 15, 2875 (1977). 10.1103/PhysRevD.15.2875
    • (1977) Phys. Rev. D , vol.15 , pp. 2875
    • Zuber, J.B.1    Itzykson, C.2
  • 62
    • 72849118033 scopus 로고    scopus 로고
    • In fact, they do not correspond to a specific fusion channel but rather a linear combination of the two.
    • In fact, they do not correspond to a specific fusion channel but rather a linear combination of the two.
  • 64
    • 72849144075 scopus 로고    scopus 로고
    • See, e.g., chapter 9 in Ref..
    • See, e.g., chapter 9 in Ref..


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.