Bipartite Rokhsar Kivelson points and Cantor deconfinement
Abstract
Quantum dimer models on bipartite lattices exhibit Rokhsar Kivelson points with exactly known critical ground states and deconfined spinons. We examine generic, weak perturbations around these points. In d= 2+1 we find a first-order transition between a “plaquette” valence bond crystal and a region with a devil’s staircase of commensurate and incommensurate valence bond crystals. In the part of the phase diagram where the staircase is incomplete, the incommensurate states exhibit a gapless photon and deconfined spinons on a set of finite measure, almost but not quite a deconfined phase in a compact U (1) gauge theory in d= 2+1 ! In d= 3+1 , we find a continuous transition between the U (1) resonating valence bond phase and a deconfined staggered valence bond crystal. In an appendix, we comment on analogous phenomena in quantum vertex models, most notably the existence of a continuous transition on the triangular lattice in d= 2+1 .
- Publication:
-
Physical Review B
- Pub Date:
- June 2004
- DOI:
- 10.1103/PhysRevB.69.224415
- arXiv:
- arXiv:cond-mat/0311353
- Bibcode:
- 2004PhRvB..69v4415F
- Keywords:
-
- 75.10.Jm;
- 05.70.Fh;
- 05.50.+q;
- 74.20.Mn;
- Quantized spin models;
- Phase transitions: general studies;
- Lattice theory and statistics;
- Nonconventional mechanisms;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Superconductivity
- E-Print:
- 9 pages