Crossovers near quantum critical points: general issues

A number of papers discussing theoretical issues related to finite temperature crossovers near a quantum critical point have been collected together in this category. Papers 1-10 deal mainly with low-dimensional systems which only have a critical point at zero temperatures, but do not have any finite temperature phase transitions. There can nevertheless be intricate crossovers between distinct finite temperature regimes, and also between different zero temperature quantum critical points (paper 5). Papers 10, 12, 13, 14 consider higher dimensional cases in which there is a line of finite temperature phase transitions connecting with a zero temperature critical point. The case where both the finite temperature and zero temperature phase transitions are below their respective upper-critical dimensions is one of considerable subtlety and requires a fairly sophisticated analysis to extract the universal behaviors: these issues are discussed in paper 10 for static properties, and in paper 13 for dynamic properties.


  1. Theory of two-dimensional quantum antiferromagnets with a nearly-critical ground state, A.V. Chubukov, S. Sachdev, and J. Ye, Physical Review B 49, 11919 (1994); cond-mat/9304046.
  2. Polylogarithm identities in a conformal field theory in three dimensions, S. Sachdev, Physics Letters B 309, 285 (1993); hep-th/9305131.
  3. Quantum phase transitions and conserved charges, S. Sachdev, Zeitschrift fur Physik B 94, 469 (1994); cond-mat/9312018.
  4. 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.
  5. Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions, S. Sachdev, A.V. Chubukov, and A. Sokol, Physical Review B 51, 14874 (1995); cond-mat/9411066.
  6. Universal, finite temperature, crossover functions of the quantum transition in the Ising chain in a transverse field, S. Sachdev, Nuclear Physics B 464, 576 (1996); cond-mat/9509147.
  7. Low temperature relaxational dynamics of the Ising chain in a transverse field, S. Sachdev and A.P. Young, Physical Review Letters 78, 2220 (1997); cond-mat/9609185.
  8. Quantum phase transitions in spin systems and the high temperature limit of continuum quantum field theories, S. Sachdev, 19th IUPAP International Conference on Statistical Physics, Hao Bailin ed., World Scientific, Singapore (1996); cond-mat/9508080.
  9. Multicritical crossovers near the dilute Bose gas quantum critical point, K. Damle and S. Sachdev, Physical Review Letters 76, 4412 (1996); cond-mat/9602073.
  10. Theory of finite temperature crossovers near quantum critical points close to, or above, their upper-critical dimension, S. Sachdev, Physical Review B 55, 142 (1997); cond-mat/9606083.
  11. A quantum-critical trio: solvable models of finite temperature crossovers near quantum phase transitions, S. Sachdev, Strongly Correlated Magnetic and Superconducting Systems, G. Sierra and M.A. Martin-Delgado eds., Springer Verlag, Berlin (1997).
  12. 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.
  13. Universal relaxational dynamics near two-dimensional quantum critical points, S. Sachdev, Physical Review B 59, 14054 (1999); cond-mat/9810399.
  14. High temperature relaxational dynamics in low-dimensional quantum field theories, S. Sachdev, Highlights in Condensed Matter Physics, B.K. Chung and M.A. Virasoro eds., World Scientific, Singapore (2000); cond-mat/9811110.
  15. Comment on "Critical spin dynamics of the 2D quantum Heisenberg antiferromagnets: Sr2CuO2Cl2 and Sr2Cu3O4Cl2", S. Sachdev and O.A. Starykh, cond-mat/0101394.
  16. Finite temperature dynamics near quantum phase transitions, S. Sachdev, keynote talk at the 11th International Conference on Recent Progress in Many-Body Theories, UMIST, Manchester UK, 9-13 July, 2001, edited by Raymond F. Bishop, Tobias Brandes, Klaus A. Gernoth, Niels R. Walet and Yang Xian, World Scientific, Singapore (2002); cond-mat/0110161.
  17. Conductivity of thermally fluctuating superconductors in two dimensions, S. Sachdev, Proceedings of 7th International Conference on Materials and Mechanisms of Superconductivity and High Temperature Superconductors, Rio de Janeiro, May 25-30 (2003), Physica 408-410C, 218 (2004); cond-mat/0308063.
  18. Quantum critical dynamics of the two-dimensional Bose gas , S. Sachdev and E. R. Dunkel, Physical Review B 73, 085116 (2006); cond-mat/0510365.
  19. Entanglement entropy in the O(N) model, M. A. Metlitski, C. A. Fuertes, and S. Sachdev, Physical Review B 80, 115122 (2009); arXiv:0904.4477.
  20. Where is the quantum critical point in the cuprate superconductors ?, S. Sachdev, Talk at the Conference on Quantum Criticality and Novel Phases, Dresden, August 2-5, 2009, Physica Status Solidi B 247, 537 (2010); arXiv:0907.0008.
  21. Quantum criticality and the phase diagram of the cuprates, S. Sachdev, Physica C 470, S4 (2010); Keynote talk, 9th International Conference on Materials and Mechanisms of Superconductivity, Tokyo, Sep 7-12, 2009, arXiv:0910.0846.
  22. Finite temperature dissipation and transport near quantum critical points , S. Sachdev, contributed chapter to the book Understanding Quantum Phase Transitions, edited by Lincoln D. Carr (Taylor & Francis, Boca Raton, 2010) arXiv:0910.1139.
  23. Scaling of the thermal spectral function for quantum critical bosons in one dimension, T. Barthel, U. Schollwöck, and S. Sachdev, arXiv:1212.3570