Research Paper: Thermodynamic Response Functions in the Quantum Critical Region of Spin-1/2 XY Chain Model

Document Type : Research Paper

Authors

1 Instructor, Department of Physics, University of Guilan, Rasht, Iran

2 Instructor, Department of Physics, University of Guilan, Rasht, Iran.

3 Professor, Department of Physics, University of Guilan, Rasht, Iran

4 Assistant Professor, Department of Physics, University of advanced studied, Zanjan, Iran

Abstract

The spin-1/2 XY chain model in the presence of a transverse magnetic field is considered. The ground state phase diagram consists of two gapped ferromagnetic and the paramagnetic phases. These two phases are separated from each other by the quantum critical point, a neighborhood of which, is known as the quantum critical region. First, using the fermionization approach the Hamiltonian is diagonalized and the spectrum is obtained. Then, using energy spectrum of the system, free energy and thermodynamic quantities such as entropy, specific heat, magnetic expansion coefficient and Grüneisen ratio are calculated and the behavior of these quantities is studied in the quantum critical region. Results show that the different behavior of the specific heat in the critical region is related to the work in the isothermal process. Moreover, the Grüneisen ratio is always independent of the temperature in the critical quantum regions.

Keywords

Main Subjects


[1] Sachdev S., “Quantum Phase Transitions”, Cambridge University Press, Cambridge (1999).
[2] Gu B., Su G., Gao S., Magnetic properties of J–J–J' quantum Heisenberg chains with spin S= 1/2, 1, 3/2 and 2 in a magnetic field, Journal of Physics: Condensed Matter 17,6081 (2005).
[3] Zhu L., Garst M., Rosch A., Si Q., Universally diverging Grüneisen parameter and the magnetocaloric effect close to quantum critical point, Phys. Rev. Lett.91, 066404 (2003).
[4] Tishin A. M., Spichkin Y. I., The magnetocaloric effect and its applications, Institute of Physics Publishing, Bristol, Philadelphia, (2003).
[5] Zhitomirsky M. E., Honecker A., Magnetocaloric effect in one-dimensional antiferromagnets, Theory and Experiment 07, P07012 (2004).
[6] Garst M., Rosch A., Sign change of the Grüneisen parameter and magnetocaloric effect near quantum critical points, Physical Review B 72, 205129 (2005).
[7] Ribeiro G. A. P., The magnetocaloric effect in integrable spin-s chains, Journal of Statistical Mechanics: Theory and Experiment, P12016 (2010).
[8] Trippe C., Honecker A., Klümper A., Ohanyan V., Exact calculation of the magnetocaloric effect in the spin-1/2 XXZ chain, Physical Review B 81, 054402 (2010).
[9] Wolf B, Tsui Y., Jaiswal-Nagar D., Tutsch U., Honecker A., Removic-Langer K., Magnetocaloric effect and magnetic cooling near a field-induced quantum-critical point, Proceedings of the National Academy of Sciences108, 6862-6866 (2011).
[10] Jahangiri J., Amiri F., Mahdavifar S., Thermodynamic behavior near the quantum orders in dimerized spin S=1/2 two-leg ladders, Journal of Magnetism and Magnetic Materials 439, 22-29 (2017).
[11] Merchant P., Normand B., Kramer K., Boehm M., Morrow D., and Ruegg C., Quantum and classical criticality in a dimerized quantum antiferromagnet, Nat. Phys. 10, 373 (2014).
[12] Schuberth E., Tippmann M., Steinke L., Lausberg S., Steppke A., Brando M., Krellner C., Geibel C., Yu R., Si Q., Emergence of superconductivity in the canonical heavy-electron metal YbRh2Si2, Science 351, 485 (2016).
[13] Wu J., Zhou F., and Wu C., Quantum criticality of bosonic systems with the Lifshitz dispersion, Phys. Rev. B 96, 085140 (2017).
[14] Wu J.,  Zhu L.,  Si Q., Crossovers and critical scaling in the one-dimensional transverse-field Ising model, Phys. Rev. B 97, 245127 (2018).
[15] Mancini M., “Fermionization of Spin Systems”, Thesis, (2008).
[16] Bogoliubov N., “On the theory of superfluidity.” J. Phys 11.1, 23 (1947).
[17] Mofidnakhaei F., Khastehdel Fumani F., Mahdavifar S., and Vahedi J., “Quantum correlations in anisotropic XY-spin chains in a transverse magnetic field”, Phase Transitions 91, no. 12 1256-1267 (2018).
[18] Zhitomirsky M. E., Tsunetsugu H., Exact low-temperature behavior of a kagome antiferromagnet at high-fields, Phys. Rev. B.70, 100403 (2004).
[19] Hasanzadeh J., Feiznejad Z., Mahdavifar S., Specific heat of the 1D spin-1/2 Ising model with added Dzyaloshinskii- Moriya interaction, J. Supercond. Nov. Magn. 27, 595, (2014).
[20] Amiri F., Mahdavifar S., Hadipour H., Shahri Naseri M., Thermodynamics of the spin-1/2 Two-leg ladder compound (C5H12N2)2CuBr4, J. Low Temp. Phys. 177, 203 (2014).