Abstract
The transverse-field XY chain with the long-range interactions was investigated by means of the exact-diagonalization method. The algebraic decay rate \(\sigma \) of the long-range interaction is related to the effective dimensionality \(D(\sigma )\), which governs the criticality of the transverse-field-driven phase transition at \(H=H_c\). According to the large-N analysis, the phase boundary \(H_c(\eta )\) exhibits a reentrant behavior within \(2<D < 3.065\ldots \), as the XY-anisotropy \(\eta \) changes. On the one hand, as for the \(D=(2+1)\) and \((1+1)\) short-range XY magnets, the singularities have been determined as \(H_c(\eta ) -H_c(0) \sim |\eta |\) and 0, respectively, and the transient behavior around \(D \approx 2.5\) remains unclear. As a preliminary survey, setting \((\sigma ,\eta )=(1 ,0.5)\), we investigate the phase transition by the agency of the fidelity, which seems to detect the singularity at \(H=H_c\) rather sensitively. Thereby, under the setting \( \sigma =4/3\) (\(D=2.5\)), we cast the fidelity data into the crossover-scaling formula with the properly scaled \(\eta \), aiming to determine the multi-criticality around \(\eta =0\). Our result indicates that the multi-criticality is identical to that of the \(D=(2+1)\) magnet, and \(H_c(\eta )\)’s linearity might be retained down to \(D>2\).
Similar content being viewed by others
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study, and did not need any data.]
References
J. Maziero, H.C. Guzman, L.C. Céleri, M.S. Sarandy, R.M. Serra, Phys. Rev. A 82, 012106 (2010)
Z.-Y. Sun, Y.-Y. Wu, J. Xu, H.-L. Huang, B.-F. Zhan, B. Wang, C.-B. Duanpra, Phys. Rev. A 89, 022101 (2014)
G. Karpat, B. Çakmak, F.F. Fanchini, Phys. Rev. B 90, 104431 (2014)
Q. Luo, J. Zhao, X. Wang, Phys. Rev. E 98, 022106 (2018)
A. Steane, Rep. Prog. Phys. 61, 117 (1998)
C.H. Bennett, D.P. DiVincenzo, Nature 404, 247 (2000)
P. Adelhardt, J.A. Koziol, A. Schellenberger, K.P. Schmidt, Phys. Rev. B 102, 174424 (2020)
N. Defenu, A. Trombettoni, S. Ruffo, Phys. Rev. B 96, 104432 (2017)
A. Dutta, J.K. Bhattacharjee, Phys. Rev. B 64, 184106 (2001)
T. Koffel, M. Lewenstein, L. Tagliacozzo, Phys. Rev. Lett. 109, 267203 (2012)
L.S. Campana, L. De Cesare, U. Esposito, M.T. Mercaldo, I. Rabuffo, Phys. Rev. B 82, 024409 (2010)
Z.-X. Gong, M.F. Maghrebi, A. Hu, M. Foss-Feig, P. Richerme, C. Monroe, A.V. Gorshkov, Phys. Rev. B 93, 205115 (2016)
S. Fey, K.P. Schmidt, Phys. Rev. B 94, 075156 (2016)
M.F. Maghrebi, Z.-X. Gong, A.V. Gorshkov, Phys. Rev. Lett. 119, 023001 (2017)
I. Frérot, P. Naldest, T. Roscilde, Phys. Rev. B 95, 245111 (2017)
S.S. Roy, H.S. Dhar, Phys. Rev. A 99, 062318 (2019)
R. Puebla, O. Marty, M.B. Plenio, Phys. Rev. A 100, 032115 (2019)
M.E. Fisher, S.-K. Ma, B.G. Nickel, Phys. Rev. Lett. 29, 917 (1972)
J. Sak, Phys. Rev. B 8, 281 (1973)
G. Gori, M. Michelangeli, N. Defenu, A. Trombettoni, Phys. Rev. E 96, 012108 (2017)
M.C. Angelini, G. Parisi, F. Ricchi-Tersenghi, Phys. Rev. E 89, 062120 (2014)
J.S. Joyce, Phys. Rev. 146, 349 (1966)
S. Wald, M. Henkel, J. Stat. Mech. Theory Exp. P07006 (2015)
M. Henkel, J. Phys. A Math. Theor. 17, L795 (1984)
S. Jalal, R. Khare, S. Lal, arXiv:1610.09845
Y. Nishiyama, Eur. Phys. J. B 92, 167 (2019)
V. Mukherjee, A. Polkovnikov, A. Dutta, Phys. Rev. B 83, 075118 (2011)
I. Homrighausen, N.O. Abeling, V. Zauner-Stauber, J.C. Halimeh, Phys. Rev. B 96, 104436 (2017)
L. Vanderstraeten, M. Van Damme, H.P. Büchler, F. Verstraete, Phys. Rev. Lett. 121, 090603 (2018)
R. Goll, P. Kopietz, Phys. Rev. E 98, 022135 (2018)
E. Luijten, H.W.J. Blöte, Phys. Rev. Lett. 89, 025703 (2002)
E. Brezin, G. Parisi, F. Ricci-Tersenghi, J. Stat. Phys. 157, 855 (2014)
N. Defenu, A. Trombettoni, A. Codello, Phys. Rev. E 92, 052113 (2015)
Z. Zhu, G. Sun, W.-L. You, D.-N. Shi, Phys. Rev. A 98, 023607 (2018)
E.K. Riedel, F. Wegner, Z. Phys. 225, 195 (1969)
P. Pfeuty, D. Jasnow, M.E. Fisher, Phys. Rev. B 10, 2088 (1974)
H.T. Quan, Z. Song, X.F. Liu, P. Zanardi, C.P. Sun, Phys. Rev. Lett. 96, 140604 (2006)
P. Zanardi, N. Paunković, Phys. Rev. E 74, 031123 (2006)
H.-Q. Zhou, J.P. Barjaktarevi\(\tilde{{\rm c}}\), J. Phys. A Math. Theor. 41, 412001 (2008)
W.-C. Yu, H.-M. Kwok, J. Cao, S.-J. Gu, Phys. Rev. E 80, 021108 (2009)
W.-L. You, Y.-L. Dong, Phys. Rev. B 84, 174426 (2011)
A. Uhlmann, Rep. Math. Phys. 9, 273 (1976)
R. Jozsa, J. Mod. Opt. 41, 2315 (1994)
A. Peres, Phys. Rev. A 30, 1610 (1984)
T. Gorin, T. Prosen, T.H. Seligman, M. Žnidarič, Phys. Rep. 435, 33 (2006)
L. Wang, Y.-H. Liu, J. Imriška, P.N. Ma, M. Troyer, Phys. Rev. X 5, 031007 (2015)
A.F. Albuquerque, F. Alet, C. Sire, S. Capponi, Phys. Rev. B 81, 064418 (2010)
D.J. Amit, V. Martín-Mayor, Field Theory, the Renormalization Group, and Critical Phenomena (World Scientific, Singapore, 2005)
Y. Deng, H.W.J. Blöte, Phys. Rev. E 68, 036125 (2003)
V. Zapf, M. Jaime, C.D. Batista, Rev. Mod. Phys. 86, 563 (2014)
C. Itoi, S. Qin, I. Affleck, Phys. Rev. B 61, 6747 (2000)
Acknowledgements
This work was supported by a Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science (Grant No. 20K03767).
Author information
Authors and Affiliations
Contributions
The presented idea was conceived by YN. He also performed the computer simulations, analyzed the data, and wrote the manuscript.
Corresponding author
Rights and permissions
About this article
Cite this article
Nishiyama, Y. Fidelity-mediated analysis of the transverse-field XY chain with the long-range interactions: anisotropy-driven multi-criticality. Eur. Phys. J. B 94, 226 (2021). https://doi.org/10.1140/epjb/s10051-021-00245-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/s10051-021-00245-1