We construct a lattice model of topological order (kagome quantum spin liquids) and solve it with unbiased quantum Monte Carlo simulations. A three-stage anyon condensation with two transitions from a ${\mathbb{Z}}_{2}\ensuremath{\boxtimes}{\mathbb{Z}}_{2}$ topological order to a ${\mathbb{Z}}_{2}$ topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.We construct a lattice model of topological order (kagome quantum spin liquids) and solve it with unbiased quantum Monte Carlo simulations. A three-stage anyon condensation with two transitions from a ${\mathbb{Z}}_{2}\ensuremath{\boxtimes}{\mathbb{Z}}_{2}$ topological order to a ${\mathbb{Z}}_{2}$ topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.

arXiv:2009.00070Physical review. B./Physical review. BJan 6, 202121 citations

Experimenting with Topological States of Bose-Einstein Condensates

Chandra Raman

Dec 1, 20060 citations

Topological order in interacting one-dimensional Bose Systems

Fabian Grusdt, Michael H oning, Michael Fleischhauer

Bulletin of the American Physical SocietyJun 9, 20150 citations

Loop Condensation in Quantum Dimer Models

C.M. Herdman, K. Birgitta Whaley

Topologically ordered phases of matter are quantum liquids with a non-local quantum order. Because of their unique properties due to the non-local quantum entanglement present in these phases, topological phases have been proposed as the basis of a physically fault-tolerant quantum computer. The formation of such topological order is well understood in terms of the mechanism of loop condensation in systems with loop-like degrees of freedom. Certain quantum dimer models posses topologically ordered dimer liquid ground states and can be mapped to loop models. In this dissertation we present a study of the geometric properties of the loop condensates of quantum dimer models and related models using classical Monte Carlo as well as ground state quantum Monte Carlo calculations. Additionally, we present an approach for the robust experimental generation of a topologically ordered phase in a system of neutral atoms trapped in an optical lattice.Topologically ordered phases of matter are quantum liquids with a non-local quantum order. Because of their unique properties due to the non-local quantum entanglement present in these phases, topological phases have been proposed as the basis of a physically fault-tolerant quantum computer. The formation of such topological order is well understood in terms of the mechanism of loop condensation in systems with loop-like degrees of freedom. Certain quantum dimer models posses topologically ordered dimer liquid ground states and can be mapped to loop models. In this dissertation we present a study of the geometric properties of the loop condensates of quantum dimer models and related models using classical Monte Carlo as well as ground state quantum Monte Carlo calculations. Additionally, we present an approach for the robust experimental generation of a topologically ordered phase in a system of neutral atoms trapped in an optical lattice.

Bulletin of the American Physical SocietyJan 1, 20111 citation

Categories of quantum liquids I

Liang Kong, Hao Zheng

Abstract We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd’s work on condensation completion. Based on this theory, we prove some fundamental results on Em-multi-fusion higher categories and their higher centers. We also outline a theory of unitary higher categories based on a ∗-version of condensation completion. After these mathematical preparations, based on the idea of topological Wick rotation, we develop a unified mathematical theory of all quantum liquids, which include topological orders, SPT/SET orders, symmetry-breaking orders and CFT-like gapless phases. We explain that a quantum liquid consists of two parts, the topological skeleton and the local quantum symmetry, and show that all nD quantum liquids form a ∗-condensation complete higher category whose equivalence type can be computed explicitly from a simple coslice 1-category.Abstract We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd’s work on condensation completion. Based on this theory, we prove some fundamental results on Em-multi-fusion higher categories and their higher centers. We also outline a theory of unitary higher categories based on a ∗-version of condensation completion. After these mathematical preparations, based on the idea of topological Wick rotation, we develop a unified mathematical theory of all quantum liquids, which include topological orders, SPT/SET orders, symmetry-breaking orders and CFT-like gapless phases. We explain that a quantum liquid consists of two parts, the topological skeleton and the local quantum symmetry, and show that all nD quantum liquids form a ∗-condensation complete higher category whose equivalence type can be computed explicitly from a simple coslice 1-category.

arXiv:2011.02859Journal of High Energy PhysicsAug 4, 202234 citations

Topological stirring of two-dimensional atomic Bose-Einstein condensates

Nick P. Proukakis

Dec 31, 20130 citations

{\mathbb{Z}}_{2}

topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.