Scaling with two divergent lengths in deconfined quantum criticality


Sandvik, A. (2017). Scaling with two divergent lengths in deconfined quantum criticality. Perimeter Institute. https://pirsa.org/17050007


Sandvik, Anders. Scaling with two divergent lengths in deconfined quantum criticality. Perimeter Institute, May. 24, 2017, https://pirsa.org/17050007


          @misc{ pirsa_PIRSA:17050007,
            doi = {10.48660/17050007},
            url = {https://pirsa.org/17050007},
            author = {Sandvik, Anders},
            keywords = {Other},
            language = {en},
            title = {Scaling with two divergent lengths in deconfined quantum criticality},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {may},
            note = {PIRSA:17050007 see, \url{https://pirsa.org}}

Anders Sandvik Boston University

Talk Type Scientific Series


The existence of a deconfined quantum-critical point [1] between the standard antiferromagnet
and a valence-bond solid in 2D S=1/2 quantum magnets has been controversial, in part due to
anomalous finite-size scaling behaviors observed in quantum Monte Carlo simulations interpreted by some as signs of a first-order transition. I will discuss a new finite-size scaling hypothesis in which a scaling function of two divergent length scales [the standard correlation length and a length-scale related to an emergent U(1) symmetry of the valence-bond solid] has a limiting form implying unconventional finite-size scaling behaviors, while maintaining conventional scaling in the thermodynamic limit [2]. This proposal goes beyond the standard scenario of a dangerously irrelevant perturbation as a source of the second length scale in, e.g., classical 3D clock models. Quantum Monte Carlo simulations of the J-Q model (a spin-1=2 Heisenberg model extended with certain multi-spin interactions) are in full agreement with the proposed scaling form, suggesting that deconfined quantum-criticality is an even richer phenomenon than initially imagined. Since finite temperature T plays the role of a finite imaginary-time dimension in quantum systems, the anomalous scaling behavior impacts also the scaling in the quantum-critical \fan" at T > 0. This is also observed in the J-Q model.

[1] H. Shao, W. Guo, and A. W. Sandvik, Science 352, 213 (2016).
[2] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, M. P. A. Fisher, Science 303, 1490 (2004).