Quantum phases and transitions with a macroscopic magnetic moment

Exploring the vicinity of a quantum critical point requires availability of a tuning parameter (other than the temperature) which can modify parameters in the Hamiltonian. One of the most convenient is an applied magnetic field. It couples via the Zeeman term to the total spin, and can thus drive quantum phase transitions between phases with and without a macroscopic magnetic moment. Often, the total spin operator commutes with the Hamiltonian, and in these cases the conservation law has strong consequences for the theory of the quantum critical point. The papers below explore a number of experimentally relevant quantum critical points of this type, and show how the conservation of total spin leads has clear experimental signatures in the quantum critical fluctuations.

Experimental examples of such transitions are in B. C. Watson et al., Physical Review Letters 86, 5168 (2001), S. A. Vitkalov et al., Physical Review Letters 87, 086401 (2001), and G. Chaboussant et al., Physical Review Letters 80, 2713 (1998).


  1. Quantum phase transitions and conserved charges, S. Sachdev, Zeitschrift fur Physik B 94, 469 (1994); cond-mat/9312018.
  2. Finite temperature properties of quantum antiferromagnets in a uniform magnetic field in one and two dimensions, S. Sachdev, T. Senthil, and R. Shankar, Physical Review B 50, 258 (1994); cond-mat/9401040.
  3. Continuum quantum ferromagnets at finite temperature and the quantum Hall effect, N. Read and S. Sachdev, Physical Review Letters 75, 3509 (1995); cond-mat/9507103.
  4. Zero temperature phase transitions in quantum Heisenberg ferromagnets, S. Sachdev and T. Senthil, Annals of Physics 251, 76 (1996); cond-mat/9602028.
  5. Universal low temperature properties of quantum and classical ferromagnetic chains, M. Takahashi, H. Nakamura, and S. Sachdev, Physical Review B 54, R744 (1996); cond-mat/9602114.
  6. Multicritical crossovers near the dilute Bose gas quantum critical point, K. Damle and S. Sachdev, Physical Review Letters 76, 4412 (1996); cond-mat/9602073.
  7. Universal critical temperature for Kosterlitz-Thouless transitions in bilayer quantum magnets, M. Troyer and S. Sachdev, Physical Review Letters 81, 5418 (1998); cond-mat/9807393.
  8. Quantum spin glass transition in the two dimensional electron gas, S. Sachdev, Pramana 58, 285 (2002); cond-mat/0109309.
  9. Quantum phases and phase transitions of Mott insulators , S. Sachdev in Quantum magnetism, U. Schollwock, J. Richter, D. J. J. Farnell and R. A. Bishop eds, Lecture Notes in Physics, Springer, Berlin (2004), cond-mat/0401041.
  10. Quantum critical dynamics of the two-dimensional Bose gas , S. Sachdev and E. R. Dunkel, Physical Review B 73, 085116 (2006); cond-mat/0510365.
  11. Magnetization of the Shastry-Sutherland antiferromagnet near the Ising limit, F. Liu and S. Sachdev, arXiv:0904.3018.