Physics (Internal)
Condensation of Anyons in Quantum Magnets
This event is part of the Condensed Matter Theory Seminar Series.
Abstract: One-dimensional (1D) quantum magnets can realize exotic states of matter such as Luttinger liquids (1,2), valence bond solids (3,4), and spin supersolids (5). A unique characteristic of 1D systems is that transmutations of particle statistics preserve the range and local nature of interactions. This is the main reason behind the success of spin-fermion transformations, such as the Jordan-Wigner mapping (6), for solving one-dimensional quantum magnets (6-8). A simple generalization of such transformations allows for a mapping between spins and anyons, unusual particles that generalize the concept of fermions and bosons. By exploiting this generalization, we find exact ground states of S = 1/2 frustrated spin XXZ ladders, and introduce an efficient method for computing relevant correlation functions. These novel states are anyon condensates that spontaneously break the Hamiltonian symmetry associated with particle-number conservation. In contrast to the familiar Bose-Einstein condensates, the condensed particles satisfy anionic statistics. 1. Luttinger, J. M. An Exactly Soluble Model of a Many-Fermion System. J. Math. Phys. 4, 1154 (1963). 2. Mattis, D.C. & Lieb, E.H. Exact Solution of a Many-Fermion System and Its Associated Boson Field. J. Math. Phys. 6, 304 (1965). 3. Haldane, F.D.M. Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis N´eel State. Phys. Rev. Lett. 50, 1153 (1983). 4. Affleck, I. , Kennedy, T., Lieb, E. & Tasaki, H. Rigorous results on valence-bond ground states in antiferromagnets. Phys. Rev. Lett. 59, 799 (1987). 5. Sengupta, P. & Batista, C.D. Spin Supersolid in an Anisotropic Spin-One Heisenberg Chain. Phys. Rev. Lett. 99, 217205 (2007). 6. Jordan, P. & Wigner, E. P. On Pauli’s Equivalence Ban. Z. Physik 47, 631 (1928). 7. Lieb, E. , Schultz, T. & Mattis, D. Two Soluble Models of an Antiferromagnetic Chain. Ann. Phys. 16, 407 (1961). 8. Lieb , E. & Mattis, D. Mathematical Physics in One Dimension, Academic Press, New York and London, (1966).