Entanglement entropy and quantum field theory
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρAT 2 of the reduced density matrix of a subsystem A=A 1A 2, and introducing a replica approach to o...
| Main Authors: | , |
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| Format: | Journal article |
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2004
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| _version_ | 1797057622932717568 |
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| author | Calabrese, P Cardy, J |
| author_facet | Calabrese, P Cardy, J |
| author_sort | Calabrese, P |
| collection | OXFORD |
| description | We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρAT 2 of the reduced density matrix of a subsystem A=A 1A 2, and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=lnρAT 2. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E∼(c/4)ln[ 12/( 1+ 2)] for the case of two adjacent intervals of lengths 1, 2 in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain. © 2012 American Physical Society. |
| first_indexed | 2024-03-06T19:39:02Z |
| format | Journal article |
| id | oxford-uuid:2003e669-ba3e-4605-bc7c-7fb6930cddd9 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:39:02Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:2003e669-ba3e-4605-bc7c-7fb6930cddd92022-03-26T11:25:11ZEntanglement entropy and quantum field theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2003e669-ba3e-4605-bc7c-7fb6930cddd9Symplectic Elements at Oxford2004Calabrese, PCardy, JWe develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρAT 2 of the reduced density matrix of a subsystem A=A 1A 2, and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=lnρAT 2. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E∼(c/4)ln[ 12/( 1+ 2)] for the case of two adjacent intervals of lengths 1, 2 in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain. © 2012 American Physical Society. |
| spellingShingle | Calabrese, P Cardy, J Entanglement entropy and quantum field theory |
| title | Entanglement entropy and quantum field theory |
| title_full | Entanglement entropy and quantum field theory |
| title_fullStr | Entanglement entropy and quantum field theory |
| title_full_unstemmed | Entanglement entropy and quantum field theory |
| title_short | Entanglement entropy and quantum field theory |
| title_sort | entanglement entropy and quantum field theory |
| work_keys_str_mv | AT calabresep entanglemententropyandquantumfieldtheory AT cardyj entanglemententropyandquantumfieldtheory |