Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological phases support both pointlike and stringlike excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the following question: How do different types of topological excitations contribute to the entanglement entropy or, alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological order? We are mainly interested in (3+1)D topological order that can be realized in Dijkgraaf-Witten (DW) gauge theories, which are labeled by a finite group $G$ and its group 4-cocycle $\ensuremath{\omega}\ensuremath{\in}{\mathcal{H}}^{4}[G;\text{U}(1)]$ up to group automorphisms. We find that each topological excitation contributes a universal constant $ln{d}_{i}$ to the entanglement entropy, where ${d}_{i}$ is the quantum dimension that depends on both the structure of the excitation and the data $(G,\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega})$. The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory $(G,\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega})$. In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles $\ensuremath{\omega}$ from the others.Excitations in (3+1)-dimensional [(3+1)D] topologically ordered phases have very rich structures. (3+1)D topological phases support both pointlike and stringlike excitations, and in particular the loop (closed string) excitations may admit knotted and linked structures. In this work, we ask the following question: How do different types of topological excitations contribute to the entanglement entropy or, alternatively, can we use the entanglement entropy to detect the structure of excitations, and further obtain the information of the underlying topological order? We are mainly interested in (3+1)D topological order that can be realized in Dijkgraaf-Witten (DW) gauge theories, which are labeled by a finite group $G$ and its group 4-cocycle $\ensuremath{\omega}\ensuremath{\in}{\mathcal{H}}^{4}[G;\text{U}(1)]$ up to group automorphisms. We find that each topological excitation contributes a universal constant $ln{d}_{i}$ to the entanglement entropy, where ${d}_{i}$ is the quantum dimension that depends on both the structure of the excitation and the data $(G,\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega})$. The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory $(G,\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega})$. In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles $\ensuremath{\omega}$ from the others.

arXiv:1710.11168Physical review. B./Physical review. BFeb 26, 201835 citations

Quantum Quenches in Topological Systems

Graham Kells, Diptiman Sen, Johannes K. Slingerland +1 more

Bulletin of the American Physical SocietyMar 6, 20140 citations

Anyonic braiding in optical lattices

Chuanwei Zhang, V. W. Scarola, Sumanta Tewari +1 more

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates.Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates.

arXiv:quant-ph/0609101Proceedings of the National Academy of SciencesNov 13, 200767 citations

Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

Steven A. Blundell, M. D. Núñez-Regueiro

arXiv:cond-mat/0204405The European Physical Journal BFeb 1, 200366 citations

Topological Quantum Matter

Thomas Klein Kvorning

Springer thesesJan 1, 20182 citations

Topological quantum paramagnet in a quantum spin ladder

Darshan G. Joshi, Andreas P. Schnyder

It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they can easily be manipulated by an applied field. Here, we study triplon excitations in an $S=1/2$ quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By bulk-boundary correspondence, we find that the nonzero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they can easily be manipulated by an applied field. Here, we study triplon excitations in an $S=1/2$ quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By bulk-boundary correspondence, we find that the nonzero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.

arXiv:1705.06764Physical review. B./Physical review. BDec 20, 201722 citations

G

and its group 4-cocycle $\ensuremath{\omega}\ensuremath{\in}{\mathcal{H}}^{4}[G;\text{U}(1)]$ up to group automorphisms. We find that each topological excitation contributes a universal constant

ln{d}_{i}

to the entanglement entropy, where

{d}_{i}

is the quantum dimension that depends on both the structure of the excitation and the data $(G,\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega})$. The entanglement entropy of the excitations of the linked/unlinked topology can capture different information of the DW theory $(G,\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega})$. In particular, the entanglement entropy introduced by Hopf-link loop excitations can distinguish certain group 4-cocycles $\ensuremath{\omega}$ from the others.

S=1/2

quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By bulk-boundary correspondence, we find that the nonzero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.