The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a ${\mathbb{Z}}_{2}$ topological spin liquid, the exact nature of the topological phase is still unclear. In this paper, we introduce semionic resonating valence-bond (RVB) states, this is, resonating valence-bond states which are in the ${\mathbb{Z}}_{2}$ -ordered double-semion phase, and study them using projected entangled pair states. We investigate their physics and study their suitability as an ansatz for the HAFM, as compared to a conventional RVB state which is in the toric-code ${\mathbb{Z}}_{2}$ topological phase. In particular, we find that a suitably optimized ``semionic simplex RVB'' outperforms the equally optimized conventional ``simplex RVB'' state, and that the entanglement spectrum (ES) of the semionic RVB behaves very differently from the ES of the conventional RVB, which suggests using the ES to discriminate the two phases. Finally, we also discuss the possible relevance of space-group symmetry breaking in valence-bond wave functions with double-semion topological order.The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a ${\mathbb{Z}}_{2}$ topological spin liquid, the exact nature of the topological phase is still unclear. In this paper, we introduce semionic resonating valence-bond (RVB) states, this is, resonating valence-bond states which are in the ${\mathbb{Z}}_{2}$-ordered double-semion phase, and study them using projected entangled pair states. We investigate their physics and study their suitability as an ansatz for the HAFM, as compared to a conventional RVB state which is in the toric-code ${\mathbb{Z}}_{2}$ topological phase. In particular, we find that a suitably optimized ``semionic simplex RVB'' outperforms the equally optimized conventional ``simplex RVB'' state, and that the entanglement spectrum (ES) of the semionic RVB behaves very differently from the ES of the conventional RVB, which suggests using the ES to discriminate the two phases. Finally, we also discuss the possible relevance of space-group symmetry breaking in valence-bond wave functions with double-semion topological order.

arXiv:1407.7773Physical Review BSep 17, 201417 citations

Study of maximal bipartite entanglement and robustness in resonating-valence-bond states

Muzaffar Qadir Lone, Sudhakar Yarlagadda

We study maximal bipartite entanglement in valence-bond states and show that the average bipartite entanglement $E_v^2$ , between a sub-system of two spins and the rest of the system, can be maximized through a homogenized superposition of the valence-bond states. Our derived maximal $E_v^2$ rapidly increases with system size and saturates at its maximum allowed value. We also demonstrate that our maximal $E^2_v$ states are ground states of an infinite range Heisenberg model (IRHM) and represent a new class of resonating-valence-bond (RVB) states. The entangled RVB states produced from our IRHM are robust against interaction of spins with both local and global phonons and represent a new class of decoherence free states.We study maximal bipartite entanglement in valence-bond states and show that the average bipartite entanglement $E_v^2$, between a sub-system of two spins and the rest of the system, can be maximized through a homogenized superposition of the valence-bond states. Our derived maximal $E_v^2$ rapidly increases with system size and saturates at its maximum allowed value. We also demonstrate that our maximal $E^2_v$ states are ground states of an infinite range Heisenberg model (IRHM) and represent a new class of resonating-valence-bond (RVB) states. The entangled RVB states produced from our IRHM are robust against interaction of spins with both local and global phonons and represent a new class of decoherence free states.

arXiv:1012.3543Dec 16, 20100 citations

Entanglement spectrum and covalent bonding

David ChangMo Yang, Norm M. Tubman

Bulletin of the American Physical SocietyMar 5, 20150 citations

Kaszlikowskiet al.Reply:

Dagomir Kaszlikowski, Aditi Sen, Ujjwal Sen +1 more

In Phys. Rev. Lett. 99, 170502 (2007) (arXiv:quant-ph/0703227), we prove that resonating-valence-bond (RVB) states on arbitrary lattices possess genuine multiparty entanglement, and provide bounds on two-particle entanglement (and correlators). We also conjecture on the entanglement in large and small portions of the whole lattice. The proof, bound, and conjecture are not considered in the Comment in Phys. Rev. Lett. 101, 248901 (2008) (arXiv:0812.1932v1 [quant-ph]). Next we take two examples: "RVB gas" and "RVB liquid". RVB liquid for arbitrary lattice size is not considered in the Comment. Two-party entanglement of RVB gas for relatively large lattice size is derived by an independent method in the Comment, and it agrees with our result. Multi-party entanglement of RVB gas is not considered in the Comment. Lastly, we consider an RVB liquid on a 4x4 square lattice and there was an error in the calculation of two-party entanglement in the second decimal place, as noted in the Comment. Note that this calculation was nowhere used in our Letter to derive other results. Moreover, the conclusion of "no two-particle entanglement" is still true for the RVB liquid on a 4x4 square lattice.In Phys. Rev. Lett. 99, 170502 (2007) (arXiv:quant-ph/0703227), we prove that resonating-valence-bond (RVB) states on arbitrary lattices possess genuine multiparty entanglement, and provide bounds on two-particle entanglement (and correlators). We also conjecture on the entanglement in large and small portions of the whole lattice. The proof, bound, and conjecture are not considered in the Comment in Phys. Rev. Lett. 101, 248901 (2008) (arXiv:0812.1932v1 [quant-ph]). Next we take two examples: "RVB gas" and "RVB liquid". RVB liquid for arbitrary lattice size is not considered in the Comment. Two-party entanglement of RVB gas for relatively large lattice size is derived by an independent method in the Comment, and it agrees with our result. Multi-party entanglement of RVB gas is not considered in the Comment. Lastly, we consider an RVB liquid on a 4x4 square lattice and there was an error in the calculation of two-party entanglement in the second decimal place, as noted in the Comment. Note that this calculation was nowhere used in our Letter to derive other results. Moreover, the conclusion of "no two-particle entanglement" is still true for the RVB liquid on a 4x4 square lattice.

arXiv:0901.0100Physical Review LettersDec 10, 20082 citations

The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a

{\mathbb{Z}}_{2}

topological spin liquid, the exact nature of the topological phase is still unclear. In this paper, we introduce semionic resonating valence-bond (RVB) states, this is, resonating valence-bond states which are in the

{\mathbb{Z}}_{2}

-ordered double-semion phase, and study them using projected entangled pair states. We investigate their physics and study their suitability as an ansatz for the HAFM, as compared to a conventional RVB state which is in the toric-code

{\mathbb{Z}}_{2}

topological phase. In particular, we find that a suitably optimized ``semionic simplex RVB'' outperforms the equally optimized conventional ``simplex RVB'' state, and that the entanglement spectrum (ES) of the semionic RVB behaves very differently from the ES of the conventional RVB, which suggests using the ES to discriminate the two phases. Finally, we also discuss the possible relevance of space-group symmetry breaking in valence-bond wave functions with double-semion topological order.

We study maximal bipartite entanglement in valence-bond states and show that the average bipartite entanglement

E_v^2

, between a sub-system of two spins and the rest of the system, can be maximized through a homogenized superposition of the valence-bond states. Our derived maximal

E_v^2

rapidly increases with system size and saturates at its maximum allowed value. We also demonstrate that our maximal

E^2_v

states are ground states of an infinite range Heisenberg model (IRHM) and represent a new class of resonating-valence-bond (RVB) states. The entangled RVB states produced from our IRHM are robust against interaction of spins with both local and global phonons and represent a new class of decoherence free states.