Scaling of entanglement entropy for chains of arbitrary spin

We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin $S$ . Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block, and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude $S$ of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer-spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin- $3∕2$ chains using an asymptotically exact real-space renormalization group approach.We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin $S$. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block, and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude $S$ of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer-spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-$3∕2$ chains using an asymptotically exact real-space renormalization group approach.

arXiv:quant-ph/0703028Physical Review AMay 22, 200719 citations

Generalized Entanglement Entropy in New Spin Chains

Fumihiko Sugino, V. E. Korepin

Springer proceedings in physicsJan 1, 20201 citation

Entanglement Entropy in Quantum Spin Chains with Finite Range Interaction

Alexander Rudol'fovich Its, Francesco Mezzadri, M. Y. Mo

arXiv:0708.0161Communications in Mathematical PhysicsAug 11, 200847 citations

Valence-bond entanglement entropy of frustrated spin chains

Fabien Alet, Ian P. McCulloch, Sylvain Capponi +1 more

We extend the definition of the recently introduced valence-bond entanglement entropy to arbitrary SU(2) wave functions of $S=1/2$ spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a ``good'' bipartition should be chosen, for instance, according to the Marshall sign.We extend the definition of the recently introduced valence-bond entanglement entropy to arbitrary SU(2) wave functions of $S=1/2$ spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a ``good'' bipartition should be chosen, for instance, according to the Marshall sign.

arXiv:1005.0787Physical Review BSep 29, 201019 citations

Entanglement Entropy in Gapped Quantum Spin Chains

Hosho Katsura, Takaaki Hirano, Yasuhiro Hatsugai

Bulletin of the American Physical SocietyMar 8, 20070 citations

We discuss the scaling of entanglement entropy in the random singlet phase (RSP) of disordered quantum magnetic chains of general spin

S

. Through an analysis of the general structure of the RSP, we show that the entanglement entropy scales logarithmically with the size of a block, and we provide a closed expression for this scaling. This result is applicable for arbitrary quantum spin chains in the RSP, being dependent only on the magnitude

S

of the spin. Remarkably, the logarithmic scaling holds for the disordered chain even if the pure chain with no disorder does not exhibit conformal invariance, as is the case for Heisenberg integer-spin chains. Our conclusions are supported by explicit evaluations of the entanglement entropy for random spin-1 and spin-

3∕2

chains using an asymptotically exact real-space renormalization group approach.

We extend the definition of the recently introduced valence-bond entanglement entropy to arbitrary SU(2) wave functions of

S=1/2

spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a ``good'' bipartition should be chosen, for instance, according to the Marshall sign.