Characterization of exotic orders in quantum spin systems

S. M. Girvin

Shunsuke Furukawa, Grégoire Misguich, Masaki Oshikawa

We propose a new method based on reduced density matrices for determining order parameters of quantum spin systems. Our method can extract the order parameter directly from ground-state wave functions without prior knowledge, and thus has a potential for detecting unknown exotic orders. We numerically apply our method to the multiple-spin exchange model on the ladder and detect the staggered dimer and the scalar chiral orders which have been found in previous studies. We also consider the resonating valence bond liquid in a solvable quantum dimer model and demonstrate through reduced density matrices that its ground states cannot be characterized by any local order parameter.

Seiji Miyashita, Seiji Miyashita

K. S. Raman, Eduardo Fradkin, Roderich Moessner +2 more

Abstract We discuss how quantum dimer models may be used to provide “proofs of principle ” for the existence of exotic magnetic phases in quantum spin systems. The material presented here is an overview of some of the results of Refs. [8] and [9]. 1

Changfeng Chen

Alexander Rasmussen

Exotic quantum systems -- those with macroscopic quantum behavior with no classical analogue -- have been a mainstay of condensed matter theory since the discovery of the quantum Hall effect. Since then, several families of related systems have been uncovered. Some, such as topological insulators, were predicted first and found experimentally later. Others are more elusive, like strongly correlated bosonic symmetry protected topological phases in high dimension, of which concrete evidence is still lacking. In this dissertation, we study several examples of exotic quantum systems. For SPT phases, we present a physically motivated classification scheme for interacting bosons and a bulk signature independent of boundary. We then construct a new, beyond Landau-Ginzburg second-order phase transition between two ordered phases of the Heisenberg magnet on the triangular lattice. Finally, we investigate an infinite family of spin liquid states, and conjecture on their connection to black holes.