© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:0901.0100 · Physical Review Letters

Kaszlikowskiet al.Reply:

Dagomir Kaszlikowski, Aditi Sen, Ujjwal Sen, Vlatko Vedral

Published Dec 10, 2008• 2 citations

Abstract

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.

DOI: 10.1103/physrevlett.101.248902

Related papers

Comment on “Regional Versus Global Entanglement in Resonating-Valence-Bond States”

Fabien Alet, Daniel Braun, Grégoire Misguich

In a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant amount of) two-site entanglement, whereas they possess multi-body entanglement. Two examples ("RVB gas and liquid") are given to illustrate this claim, which essentially comes from a lower bound derived for spin correlators in VB states. We show in this Comment that (i) for the "RVB liquid" on the square lattice, the calculations and conclusions of Chandran et al. are incorrect. (ii) A simple analytical calculation gives the exact value of the correlator for the "RVB gas", showing that the bound found by Chandran et al. is tight. (iii) The lower bound for spin correlators in VB states is equivalent to a celebrated result of Anderson dating from more than 50 years ago.

arXiv:0812.1932•Physical Review Letters•Dec 10, 2008•4 citations

SU(4) topological resonating valence bond spin liquid on the square lattice

Olivier Gauthé, Sylvain Capponi, Didier Poilblanc

We generalize the construction of the spin-1/2 SU(2) resonating valence bond (RVB) state to the case of the self-conjugate $\mathbf{6}$ representation of SU(4). As for the case of SU(2) [J.-Y. Chen and D. Poilblanc, Phys. Rev. B 97, 161107(R) (2018)], we use the projected entangled pair state (PEPS) formalism to derive a simple (two-dimensional) family of generalized SU(4) RVB states on the square lattice. We show that, when longer-range SU(4)-singlet bonds are included, a local gauge symmetry is broken down from U(1) to ${\mathbb{Z}}_{2}$, leading to the emergence of a short-range spin liquid. Evidence for the topological nature of this spin liquid is provided by the investigation of the Renyi entanglement entropy of infinitely long cylinders and of the modular matrices. Relevance to microscopic models and experiments of ultracold atoms is discussed.

arXiv:1901.05905•Physical review. B./Physical review. B•Jun 26, 2019•8 citations

Reply to “Comment on ‘Single-particle entanglement’ ”

S. J. van Enk

I try to rebut Drezet's arguments [Phys. Rev. A. 74, 026301 (2006)]) against the state $\ensuremath{\mid}0⟩\ensuremath{\mid}1⟩+\ensuremath{\mid}1⟩\ensuremath{\mid}0⟩$ being entangled by agreeing with them. I also address some old arguments repeated by Drezet.

Physical Review A•Aug 21, 2006•33 citations

Effect of the intersite Coulomb interaction in the extended Hubbard model

Mei-Rong Li, Yong-Jun Wang, Chang-De Gong

Starting from the large-U Hubbard model combining the intersite Coulomb interaction V, we investigate the competition, on a square lattice, between the d-wave resonating-valence-bond (RVB) state and the staggered-flux-phases (SFP) state on the basis of F. C. Zhang's earlier work [Phys. Rev. Lett. 64, 974 (1990)]. We find that a very small V (0.1U) may help stabilize the SFP state by effectively suppressing the d-wave pairing amplitude and enhance the particle-hole correlation. We show in the phase diagram of V-\ensuremath{\delta} (the doping concentration) the critical curve of ${\mathit{V}}_{\mathit{c}}$(\ensuremath{\delta}) below which the RVB state is energetically favored while beyond this point a mixed state of SFP and RVB occurs, which has the lowest energy. We also find that the pure SFP state is not the most stable state in the whole V region.

Physical review. B, Condensed matter•Aug 1, 1992•1 citation

Entanglement Studies of Resonating Valence Bonds on the Frustrated Square Lattice

Alexander Seidel, Julia Wildeboer

Bulletin of the American Physical Society•Mar 5, 2018•0 citations

Entanglement studies of resonating valence bonds on the frustrated square lattice

Julia Wildeboer, Alexander Seidel

We study a short-range resonating valence bond (RVB) wave function with diagonal links on the square lattice that permits sign-problem free wave function Monte Carlo studies. Special attention is given to entanglement properties, in particular, the study of minimum entropy states (MES) according to the method of Zhang et al. [Phys. Rev. B 85, 235151 (2012)]. We provide evidence that the MES associated with the RVB wave functions can be lifted from an associated quantum dimer picture of these wave functions, where MES states are certain linear combinations of eigenstates of a 't Hooft ``magnetic loop''-type operator. From this identification, we calculate a value consistent with $ln(2)$ for the topological entanglement entropy directly for the RVB states via wave function Monte Carlo. This corroborates the ${\mathbb{Z}}_{2}$ nature of the RVB states. We furthermore define and elaborate on the concept of a ``pre-Kasteleyn'' orientation that may be useful for the study of lattices with nonplanar topology in general.

arXiv:1711.10717•Physical review. B./Physical review. B•Jun 3, 2020•1 citation

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 a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant amount of) two-site entanglement, whereas they possess multi-body entanglement. Two examples ("RVB gas and liquid") are given to illustrate this claim, which essentially comes from a lower bound derived for spin correlators in VB states. We show in this Comment that (i) for the "RVB liquid" on the square lattice, the calculations and conclusions of Chandran et al. are incorrect. (ii) A simple analytical calculation gives the exact value of the correlator for the "RVB gas", showing that the bound found by Chandran et al. is tight. (iii) The lower bound for spin correlators in VB states is equivalent to a celebrated result of Anderson dating from more than 50 years ago.

We generalize the construction of the spin-1/2 SU(2) resonating valence bond (RVB) state to the case of the self-conjugate

\mathbf{6}

representation of SU(4). As for the case of SU(2) [J.-Y. Chen and D. Poilblanc, Phys. Rev. B 97, 161107(R) (2018)], we use the projected entangled pair state (PEPS) formalism to derive a simple (two-dimensional) family of generalized SU(4) RVB states on the square lattice. We show that, when longer-range SU(4)-singlet bonds are included, a local gauge symmetry is broken down from U(1) to

{\mathbb{Z}}_{2}

, leading to the emergence of a short-range spin liquid. Evidence for the topological nature of this spin liquid is provided by the investigation of the Renyi entanglement entropy of infinitely long cylinders and of the modular matrices. Relevance to microscopic models and experiments of ultracold atoms is discussed.

Starting from the large-U Hubbard model combining the intersite Coulomb interaction V, we investigate the competition, on a square lattice, between the d-wave resonating-valence-bond (RVB) state and the staggered-flux-phases (SFP) state on the basis of F. C. Zhang's earlier work [Phys. Rev. Lett. 64, 974 (1990)]. We find that a very small V (0.1U) may help stabilize the SFP state by effectively suppressing the d-wave pairing amplitude and enhance the particle-hole correlation. We show in the phase diagram of V-\ensuremath{\delta} (the doping concentration) the critical curve of

{\mathit{V}}_{\mathit{c}}

(\ensuremath{\delta}) below which the RVB state is energetically favored while beyond this point a mixed state of SFP and RVB occurs, which has the lowest energy. We also find that the pure SFP state is not the most stable state in the whole V region.

We study a short-range resonating valence bond (RVB) wave function with diagonal links on the square lattice that permits sign-problem free wave function Monte Carlo studies. Special attention is given to entanglement properties, in particular, the study of minimum entropy states (MES) according to the method of Zhang et al. [Phys. Rev. B 85, 235151 (2012)]. We provide evidence that the MES associated with the RVB wave functions can be lifted from an associated quantum dimer picture of these wave functions, where MES states are certain linear combinations of eigenstates of a 't Hooft ``magnetic loop''-type operator. From this identification, we calculate a value consistent with

ln(2)

for the topological entanglement entropy directly for the RVB states via wave function Monte Carlo. This corroborates the

{\mathbb{Z}}_{2}

nature of the RVB states. We furthermore define and elaborate on the concept of a ``pre-Kasteleyn'' orientation that may be useful for the study of lattices with nonplanar topology in general.