Entanglement negativity and replica symmetry breaking in general holographic states
Abstract The entanglement negativity E $$ \mathcal{E} $$ (A : B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity E 2...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-01-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2025)022 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832595076003397632 |
|---|---|
| author | Xi Dong Jonah Kudler-Flam Pratik Rath |
| author_facet | Xi Dong Jonah Kudler-Flam Pratik Rath |
| author_sort | Xi Dong |
| collection | DOAJ |
| description | Abstract The entanglement negativity E $$ \mathcal{E} $$ (A : B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity E 2 k $$ {\mathcal{E}}^{(2k)} $$ generically break the ℤ 2k replica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumed ℤ 2k replica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing E 2 k $$ {\mathcal{E}}^{(2k)} $$ indeed break the ℤ 2k replica symmetry. Our argument involves an identity relating E 2 k $$ {\mathcal{E}}^{(2k)} $$ to the k-th Rényi entropy on subregion AB ∗ in the doubled state ρ AB A A ∗ BB ∗ $$ {\left.|{\rho}_{AB}\right\rangle}_{A{A}^{\ast }{BB}^{\ast }} $$ , from which we see that the ℤ 2k replica symmetry is broken down to ℤ k . For k < 1, which includes the case of E $$ \mathcal{E} $$ (A : B) at k = 1/2, we use a modified cosmic brane proposal to derive a new holographic prescription for E 2 k $$ {\mathcal{E}}^{(2k)} $$ and show that it is given by a new saddle with multiple cosmic branes anchored to subregions A and B in the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations near k = 1. Moreover, we argue that the ℤ 2k symmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity. |
| format | Article |
| id | doaj-art-d1c7e28c852f4deda05d9022f5b60891 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d1c7e28c852f4deda05d9022f5b608912025-01-19T12:07:02ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025114110.1007/JHEP01(2025)022Entanglement negativity and replica symmetry breaking in general holographic statesXi Dong0Jonah Kudler-Flam1Pratik Rath2Department of Physics, University of CaliforniaSchool of Natural Sciences, Institute for Advanced StudyCenter for Theoretical Physics and Department of Physics, University of CaliforniaAbstract The entanglement negativity E $$ \mathcal{E} $$ (A : B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity E 2 k $$ {\mathcal{E}}^{(2k)} $$ generically break the ℤ 2k replica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumed ℤ 2k replica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing E 2 k $$ {\mathcal{E}}^{(2k)} $$ indeed break the ℤ 2k replica symmetry. Our argument involves an identity relating E 2 k $$ {\mathcal{E}}^{(2k)} $$ to the k-th Rényi entropy on subregion AB ∗ in the doubled state ρ AB A A ∗ BB ∗ $$ {\left.|{\rho}_{AB}\right\rangle}_{A{A}^{\ast }{BB}^{\ast }} $$ , from which we see that the ℤ 2k replica symmetry is broken down to ℤ k . For k < 1, which includes the case of E $$ \mathcal{E} $$ (A : B) at k = 1/2, we use a modified cosmic brane proposal to derive a new holographic prescription for E 2 k $$ {\mathcal{E}}^{(2k)} $$ and show that it is given by a new saddle with multiple cosmic branes anchored to subregions A and B in the original state. Using our prescription, we reproduce known results for the PSSY model and show that our saddle dominates over previously proposed CFT calculations near k = 1. Moreover, we argue that the ℤ 2k symmetric configurations previously proposed are not gravitational saddles, unlike our proposal. Finally, we contrast holographic calculations with those arising from RTNs with non-maximally entangled links, demonstrating that the qualitative form of backreaction in such RTNs is different from that in gravity.https://doi.org/10.1007/JHEP01(2025)022AdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Xi Dong Jonah Kudler-Flam Pratik Rath Entanglement negativity and replica symmetry breaking in general holographic states Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | Entanglement negativity and replica symmetry breaking in general holographic states |
| title_full | Entanglement negativity and replica symmetry breaking in general holographic states |
| title_fullStr | Entanglement negativity and replica symmetry breaking in general holographic states |
| title_full_unstemmed | Entanglement negativity and replica symmetry breaking in general holographic states |
| title_short | Entanglement negativity and replica symmetry breaking in general holographic states |
| title_sort | entanglement negativity and replica symmetry breaking in general holographic states |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP01(2025)022 |
| work_keys_str_mv | AT xidong entanglementnegativityandreplicasymmetrybreakingingeneralholographicstates AT jonahkudlerflam entanglementnegativityandreplicasymmetrybreakingingeneralholographicstates AT pratikrath entanglementnegativityandreplicasymmetrybreakingingeneralholographicstates |