Abstract
The random quantum Ashkin-Teller chain is studied numerically by means of time-dependent Density-Matrix Renormalization Group. The critical lines are estimated as the location of the peaks of the integrated autocorrelation times, computed from spin-spin and polarization-polarization autocorrelation functions. Disorder fluctuations of magnetization and polarization are observed to be maximum on these critical lines. Entanglement entropy leads to the same phase diagram, though with larger finite-size effects. The decay of spin-spin and polarization-polarization autocorrelation functions provides numerical evidence of the existence of a double Griffiths phase when taking into account finite-size effects. The two associated dynamical exponents z increase rapidly as the critical lines are approached, in agreement with the recent conjecture of a divergence at the two transitions in the thermodynamic limit.
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References
A.B. Harris, J. Phys. C 7, 1671 (1974)
S. Wiseman, E. Domany, Phys. Rev. E 51, 3074 (1995)
J. Cardy, J.L. Jacobsen, Phys. Rev. Lett. 79, 4063 (1997)
J. L. Jacobsen, J. L. Cardy, Nucl. Phys. B 515, 701 (1998)
B.M. McCoy, T.T. Wu, Phys. Rev. 176, 631 (1968)
B.M. McCoy, T.T. Wu, Phys. Rev. 188, 982 (1969)
R.B. Griffiths, Phys. Rev. Lett. 23, 17 (1969)
T. Vojta, J. Phys. A 39, R143 (2006)
H. Rieger, A.P. Young, Quantum Spin Glasses, in: Complex Behaviour of Glassy Systems, Lecture Notes in Physics, edited by Miguel Rub, Conrado Prez-Vicente (Springer, Berlin, Heidelberg, 1997), Vol. 492
C. Chatelain, Europhys. Lett. 102, 66007 (2013)
C. Chatelain, Phys. Rev. E 89, 032105 (2014)
T.D. Schultz, D.C. Mattis, E.H. Lieb, Rev. Mod. Phys. 36, 856 (1964)
R. Shankar, G. Murthy, Phys. Rev. B 36, 536 (1987)
A.P. Young, H. Rieger, Phys. Rev. B 53, 8486 (1996)
C. Dasgupta, S.-K. Ma, Phys. Rev. B 22, 1305 (1980)
D.S. Fisher, Phys. Rev. Lett. 69, 534 (1992)
D.S. Fisher, Phys. Rev. B 51, 6411 (1995)
F. Iglói, C. Monthus, Phys. Rep. 412, 277 (2005)
F. Iglói, H. Rieger, Phys. Rev. B 57, 11404 (1998)
I. Kovács, F. Iglói, Phys. Rev. B 82, 054437 (2010)
I. Kovács, F. Iglói, Phys. Rev. B 83, 174207 (2011)
I. Kovács, F. Iglói, Eur. Phys. Lett. 97, 67009 (2012)
T. Senthil, S.N. Majumdar, Phys. Rev. Lett. 76, 3001 (1996)
E. Carlon, C. Chatelain, B. Berche, Phys. Rev. B 60, 12974 (1999)
M. Kohmoto, M. den Nijs, L.P. Kadanoff, Phys. Rev. B 24, 5229 (1981)
J. Ashkin, E. Teller, Phys. Rev. 64, 178 (1943)
C. Fan, Phys. Lett. A 39, 136 (1972)
C. Fan, Phys. Rev. B 6, 902 (1972)
G. Kamieniarz, P. Kozłowski, R. Dekeyser, Phys. Rev. E 55, 3724 (1997)
E. Carlon, P. Lajkó, F. Iglói, Phys. Rev. Lett. 87, 277201 (2001)
F. Hrahsheh, R. Narayanan, J.A. Hoyos, T. Vojta, Phys. Rev. B 89, 014401 (2014)
F. Hrahsheh, J.A. Hoyos, T. Vojta, Phys. Rev. B 86, 214204 (2012)
B. Derrida, H. Hilhorst, J. Phys. C 14, L539 (1981)
S.R. White, Phys. Rev. Lett. 69, 2863 (1992)
S.R. White, Phys. Rev. B 48, 10345 (1993)
U. Schollwoeck, Rev. Mod. Phys. 77, 259 (2005)
L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517 (2008)
G. Vidal, J.I. Latorre, E. Rico, A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003)
P. Calabrese, J. Cardy, J. Stat. Mech.: Theor. Exp. 2004, P06002 (2004)
G. Refael, J.E. Moore, Phys. Rev. Lett. 93, 260602 (2004)
F. Iglói, R. Juhász, P. Lajkó, Phys. Rev. Lett. 86, 1343 (2001)
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Chatelain, C., Voliotis, D. Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain. Eur. Phys. J. B 89, 18 (2016). https://doi.org/10.1140/epjb/e2015-60593-3
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DOI: https://doi.org/10.1140/epjb/e2015-60593-3