Heisenberg spin chain with random-sign couplings
Abstract: We study the 1D quantum Heisenberg chain with randomly ferromagnetic or antiferromagnetic couplings (a model previously studied by approximate strong-disorder RG). We find that, at least for sufficiently large spin $S$, the ground state has ``spin glass'' order. The spin waves on top of this state have the dynamical exponent ${z=3/2}$, intermediate between the values $z=1$ of the antiferromagnet and ${z=2}$ of the ferromagnet. DMRG simulations are in good agreement with the analytical results for spins ${S=1}$ and ${S=3/2}$. The case ${S=1/2}$ shows large finite size effects: we suggest that this case is also ordered, but with a small ordered moment.
- F. Iglói and C. Monthus, Physics reports 412, 277 (2005).
- B. Ammon and M. Sigrist, Journal of the Physical Society of Japan 68, 1018 (1999).
- D. S. Fisher, Phys. Rev. B 50, 3799 (1994).
- D. Mattis, Physics Letters A 56, 421 (1976).
- R. B. Stinchcombe and I. R. Pimentel, Phys. Rev. B 38, 4980 (1988).
- I. R. Pimentel and R. B. Stinchcombe, Phys. Rev. B 40, 4947 (1989).
- A. Boukahil and D. L. Huber, Phys. Rev. B 40, 4638 (1989).
- I. Avgin and D. L. Huber, Phys. Rev. B 56, 2320 (1997).
- I. Avgin and D. L. Huber, Phys. Rev. B 57, 8269 (1998).
- V. Gurarie and J. T. Chalker, Physical Review B 68, 134207 (2003).
- A. Altland and B. D. Simons, Condensed matter field theory (Cambridge university press, 2010).
- E. Lieb and D. Mattis, Journal of Mathematical Physics 3, 749 (1962).
- P. Sheng, Scattering and localization of classical waves in random media, Vol. 8 (World Scientific, 1990).
- S. Sachdev, Quantum Phases of Matter (Cambridge University Press, 2023).
- A. Auerbach, Interacting electrons and quantum magnetism (Springer Science & Business Media, 1998).
- J. Colpa, Physica A: Statistical Mechanics and its Applications 93, 327 (1978).
- S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
- S. R. White, Phys. Rev. B 48, 10345 (1993).
- U. Schollwöck, Annals of Physics 326, 96 (2011), january 2011 Special Issue.
- S. R. White, Phys. Rev. B 72, 180403 (2005).
- F. Iglói and C. Monthus, Physics Reports 412, 277 (2005).
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