The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion ${\cal S}\sim \ln\ln(L)$ , where $L$ is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance $l$ from the contact point as $\sim l^{-\kappa}$ . For $\kappa<1/2$ , the entropy scales as ${\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)$ , while for $\kappa \ge 1/2$ , when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion ${\cal S}\sim \ln\ln(L)$, where $L$ is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance $l$ from the contact point as $\sim l^{-\kappa}$. For $\kappa<1/2$, the entropy scales as ${\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)$, while for $\kappa \ge 1/2$, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.

Jan 1, 20172 citations

Two-channel Kondo behavior in the quantum XX chain with a boundary defect

Yicheng Tang, Pradip Kattel, J. H. Pixley +1 more

We demonstrate that a boundary defect in the single spin- $\frac{1}{2}$ quantum $XX$ chain exhibits two-channel Kondo physics. Due to the presence of the defect, the edge spin fractionalizes into two Majorana fermions, out of which one decouples, and one is overscreened by the free fermion in bulk, leading to non-trivial boundary behavior characteristic of the two-channel Kondo model. When the ratio of boundary to bulk coupling exceeds a critical value of $\sqrt{2}$ , a massive boundary-bound mode is exponentially localized near the impurity site for strong impurity coupling. This leads to unusual behavior in physical quantities, such as the $g$ -function not being monotonic. We compute the $g-$ function of the impurity from both thermodynamic and entanglement entropy calculations and show that it takes a non-integer value of $\sqrt{2}$ just as in the two-channel Kondo problem.We demonstrate that a boundary defect in the single spin-$\frac{1}{2}$ quantum $XX$ chain exhibits two-channel Kondo physics. Due to the presence of the defect, the edge spin fractionalizes into two Majorana fermions, out of which one decouples, and one is overscreened by the free fermion in bulk, leading to non-trivial boundary behavior characteristic of the two-channel Kondo model. When the ratio of boundary to bulk coupling exceeds a critical value of $\sqrt{2}$, a massive boundary-bound mode is exponentially localized near the impurity site for strong impurity coupling. This leads to unusual behavior in physical quantities, such as the $g$-function not being monotonic. We compute the $g-$function of the impurity from both thermodynamic and entanglement entropy calculations and show that it takes a non-integer value of $\sqrt{2}$ just as in the two-channel Kondo problem.

arXiv:2501.16415Physical review. B./Physical review. BJul 14, 20254 citations

Entanglement Entropy in Gapped Quantum Spin Chains

Hosho Katsura, Takaaki Hirano, Yasuhiro Hatsugai

Bulletin of the American Physical SocietyMar 8, 20070 citations

Entanglement between random and clean quantum spin chains

Róbert Juhász, István A Kovács, Gergő Roósz +1 more

Abstract The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean subsystem and a random subsystem, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion S ∼ ln ln ⁡ ( L ) , where L is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance l from the contact point as ∼ l − κ . For κ < 1 / 2 , the entropy scales as S ( κ ) ≃ ln ⁡ 2 ( 1 − 2 κ ) 6 ln ⁡ L , while for κ ⩾ 1 / 2 , when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.Abstract The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean subsystem and a random subsystem, both being critical. In the composite, antiferromagnetic XX-chain with a sharp interface, the entropy is found to grow in a double-logarithmic fashion S ∼ ln ln ⁡ ( L ) , where L is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance l from the contact point as ∼ l − κ . For κ < 1 / 2 , the entropy scales as S ( κ ) ≃ ln ⁡ 2 ( 1 − 2 κ ) 6 ln ⁡ L , while for κ ⩾ 1 / 2 , when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.

arXiv:1704.07444Journal of Physics A Mathematical and TheoreticalJun 20, 20175 citations

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

{\cal S}\sim \ln\ln(L)

, where

L

is the length of the chain. We have also considered an extended defect at the interface, where the disorder penetrates into the homogeneous region in such a way that the strength of disorder decays with the distance

l

from the contact point as

\sim l^{-\kappa}

. For

\kappa<1/2

, the entropy scales as

{\cal S}(\kappa) \simeq (1-2\kappa){\cal S}(\kappa=0)

, while for

\kappa \ge 1/2

, when the extended interface defect is an irrelevant perturbation, we recover the double-logarithmic scaling. These results are explained through strong-disorder RG arguments.

We demonstrate that a boundary defect in the single spin-

\frac{1}{2}

quantum

XX

chain exhibits two-channel Kondo physics. Due to the presence of the defect, the edge spin fractionalizes into two Majorana fermions, out of which one decouples, and one is overscreened by the free fermion in bulk, leading to non-trivial boundary behavior characteristic of the two-channel Kondo model. When the ratio of boundary to bulk coupling exceeds a critical value of

\sqrt{2}

, a massive boundary-bound mode is exponentially localized near the impurity site for strong impurity coupling. This leads to unusual behavior in physical quantities, such as the

g

-function not being monotonic. We compute the

g-

function of the impurity from both thermodynamic and entanglement entropy calculations and show that it takes a non-integer value of

\sqrt{2}

just as in the two-channel Kondo problem.