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Classification of potential flows under renormalization group transformation
1. | Department of Mathematics, National Tsing Hua University, National Center of Theoretical Science, Hsinchu 300 |
2. | Institute of Mathematics, Free University Berlin, Arnimallee 3, D-14195 Berlin, Germany |
3. | Department of Physics and The National Center for Theoretical Science, National Tsing Hua University, Hsinchu 30013, Taiwan |
References:
[1] |
R. Shankar, Renormalization-group approach to interacting fermions, Rev. Mod. Phys., 66 (1994), 129-192.
doi: 10.1103/RevModPhys.66.129. |
[2] |
M. Salmhofer and C. Honerkamp, Fermionic renormalization group flows - technique and theory, Progress of Theoretical Physics, 105 (2001), 1-35.
doi: 10.1143/PTP.105.1. |
[3] |
W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden and K. Schönhammer, Functional renormalization group approach to correlated fermion systems, Rev. Mod. Phys., 84 (2012), 299-352.
doi: 10.1103/RevModPhys.84.299. |
[4] |
M. Fabrizio, Role of transverse hopping in a two-coupled-chains model, Phys. Rev. B, 48 (1993), 15838-15860.
doi: 10.1103/PhysRevB.48.15838. |
[5] |
L. Balents and M. P. A. Fisher, Weak-coupling phase diagram of the two-chain Hubbard model, Phys. Rev. B, 53 (1996), p12133.
doi: 10.1103/PhysRevB.53.12133. |
[6] |
H. J. Schulz, Phases of two coupled Luttinger liquids, Phys. Rev. B, 53 (1996), R2959-R2962.
doi: 10.1103/PhysRevB.53.R2959. |
[7] |
H.-H. Lin, L. Balents and M. P. A. Fisher, N-chain Hubbard model in weak coupling, Phys. Rev. B, 56 (1997), 6569-6593.
doi: 10.1103/PhysRevB.56.6569. |
[8] |
H.-H. Lin, L. Balents and M. P. A. Fisher, Exact SO(8) symmetry in the weakly-interacting two-leg ladder, Phys. Rev. B, 58 (1998), 1794-1825.
doi: 10.1103/PhysRevB.58.1794. |
[9] |
M.-H. Chang, W. Chen and H.-H. Lin, Renormalization group potential for quasi-one-dimensional correlated systems, Prog. Theor. Phys. Suppl., 160 (2005), 79-113.
doi: 10.1143/PTPS.160.79. |
[10] |
E. Szirmai and J. Solyom, Possible phases of two coupled n-component fermionic chains determined using an analytic renormalization group method, Phys. Rev. B, 74 (2006), p155110. |
[11] |
H.-Y. Shih, W.-M. Huang, S.-B. Hsu and H.-H. Lin, Hierarchy of relevant couplings in perturbative renormalization group transformations, Phys. Rev. B, 81 (2010), 121107(R).
doi: 10.1103/PhysRevB.81.121107. |
[12] |
A. Goriely and C. Hyde, Finite time blow-up in dynamical systems, Phys. Lett. A, 250 (1998), 311-318.
doi: 10.1016/S0375-9601(98)00822-6. |
[13] |
A. Goriely and C. Hyde, Necessary and sufficient conditions for finite time singularity in ordinary differential equations, J. of diff. eq., 161 (2000), 422-448.
doi: 10.1006/jdeq.1999.3688. |
[14] |
S. B. Hsu, Ordinary Differential Equations (second edition), World Scientific Press, 2013.
doi: 10.1142/8744. |
[15] |
J. K. Hale, Ordinary Differential Equations, Wiley-Interscience, 1969. |
[16] |
A. V. Chubukov, D. V. Efremov and I. Eremin, Magnetism, superconductivity, and pairing symmetry in iron-based superconductors, Phys. Rev. B, 78 (2008), 134512.
doi: 10.1103/PhysRevB.78.134512. |
[17] |
F. Wang, H. Zhai, Y. Ran, A. Vishwanath and D.-H. Lee, Functional renormalization-group study of the pairing symmetry and pairing mechanism of the FeAs-based high-temperature superconductor, Phys. Rev. Lett., 102 (2009), 047005.
doi: 10.1103/PhysRevLett.102.047005. |
[18] |
F. Wang and D.-H. Lee, The electron-pairing mechanism of iron-based superconductors, Science, 332 (2011), 200-204.
doi: 10.1126/science.1200182. |
show all references
References:
[1] |
R. Shankar, Renormalization-group approach to interacting fermions, Rev. Mod. Phys., 66 (1994), 129-192.
doi: 10.1103/RevModPhys.66.129. |
[2] |
M. Salmhofer and C. Honerkamp, Fermionic renormalization group flows - technique and theory, Progress of Theoretical Physics, 105 (2001), 1-35.
doi: 10.1143/PTP.105.1. |
[3] |
W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden and K. Schönhammer, Functional renormalization group approach to correlated fermion systems, Rev. Mod. Phys., 84 (2012), 299-352.
doi: 10.1103/RevModPhys.84.299. |
[4] |
M. Fabrizio, Role of transverse hopping in a two-coupled-chains model, Phys. Rev. B, 48 (1993), 15838-15860.
doi: 10.1103/PhysRevB.48.15838. |
[5] |
L. Balents and M. P. A. Fisher, Weak-coupling phase diagram of the two-chain Hubbard model, Phys. Rev. B, 53 (1996), p12133.
doi: 10.1103/PhysRevB.53.12133. |
[6] |
H. J. Schulz, Phases of two coupled Luttinger liquids, Phys. Rev. B, 53 (1996), R2959-R2962.
doi: 10.1103/PhysRevB.53.R2959. |
[7] |
H.-H. Lin, L. Balents and M. P. A. Fisher, N-chain Hubbard model in weak coupling, Phys. Rev. B, 56 (1997), 6569-6593.
doi: 10.1103/PhysRevB.56.6569. |
[8] |
H.-H. Lin, L. Balents and M. P. A. Fisher, Exact SO(8) symmetry in the weakly-interacting two-leg ladder, Phys. Rev. B, 58 (1998), 1794-1825.
doi: 10.1103/PhysRevB.58.1794. |
[9] |
M.-H. Chang, W. Chen and H.-H. Lin, Renormalization group potential for quasi-one-dimensional correlated systems, Prog. Theor. Phys. Suppl., 160 (2005), 79-113.
doi: 10.1143/PTPS.160.79. |
[10] |
E. Szirmai and J. Solyom, Possible phases of two coupled n-component fermionic chains determined using an analytic renormalization group method, Phys. Rev. B, 74 (2006), p155110. |
[11] |
H.-Y. Shih, W.-M. Huang, S.-B. Hsu and H.-H. Lin, Hierarchy of relevant couplings in perturbative renormalization group transformations, Phys. Rev. B, 81 (2010), 121107(R).
doi: 10.1103/PhysRevB.81.121107. |
[12] |
A. Goriely and C. Hyde, Finite time blow-up in dynamical systems, Phys. Lett. A, 250 (1998), 311-318.
doi: 10.1016/S0375-9601(98)00822-6. |
[13] |
A. Goriely and C. Hyde, Necessary and sufficient conditions for finite time singularity in ordinary differential equations, J. of diff. eq., 161 (2000), 422-448.
doi: 10.1006/jdeq.1999.3688. |
[14] |
S. B. Hsu, Ordinary Differential Equations (second edition), World Scientific Press, 2013.
doi: 10.1142/8744. |
[15] |
J. K. Hale, Ordinary Differential Equations, Wiley-Interscience, 1969. |
[16] |
A. V. Chubukov, D. V. Efremov and I. Eremin, Magnetism, superconductivity, and pairing symmetry in iron-based superconductors, Phys. Rev. B, 78 (2008), 134512.
doi: 10.1103/PhysRevB.78.134512. |
[17] |
F. Wang, H. Zhai, Y. Ran, A. Vishwanath and D.-H. Lee, Functional renormalization-group study of the pairing symmetry and pairing mechanism of the FeAs-based high-temperature superconductor, Phys. Rev. Lett., 102 (2009), 047005.
doi: 10.1103/PhysRevLett.102.047005. |
[18] |
F. Wang and D.-H. Lee, The electron-pairing mechanism of iron-based superconductors, Science, 332 (2011), 200-204.
doi: 10.1126/science.1200182. |
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