Entropy Scaling Law and the Quantum Marginal Problem
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a correction term that is independent of its size. We conjecture tha...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
American Physical Society
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/5d9e9921e48844a3855cdce4ae81f9d7 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:5d9e9921e48844a3855cdce4ae81f9d7 |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:5d9e9921e48844a3855cdce4ae81f9d72021-12-02T14:44:23ZEntropy Scaling Law and the Quantum Marginal Problem10.1103/PhysRevX.11.0210392160-3308https://doaj.org/article/5d9e9921e48844a3855cdce4ae81f9d72021-05-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021039http://doi.org/10.1103/PhysRevX.11.021039https://doaj.org/toc/2160-3308Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a correction term that is independent of its size. We conjecture that these states have an efficient dual description in terms of a set of marginal density matrices on bounded regions, obeying the same entropy scaling law locally. We prove a restricted version of this conjecture for translationally invariant systems in two spatial dimensions. Specifically, we prove that a translationally invariant marginal obeying three nonlinear constraints—all of which follow from the entropy scaling law straightforwardly—must be consistent with some global state on an infinite lattice. Moreover, we derive a closed-form expression for the maximum-entropy density compatible with those marginals, deriving a variational upper bound on the thermodynamic free energy. The main assumptions of our construction are satisfied exactly by solvable models of topological order and approximately by finite-temperature Gibbs states of certain quantum spin Hamiltonians.Isaac H. KimAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021039 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
Physics QC1-999 |
| spellingShingle |
Physics QC1-999 Isaac H. Kim Entropy Scaling Law and the Quantum Marginal Problem |
| description |
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a correction term that is independent of its size. We conjecture that these states have an efficient dual description in terms of a set of marginal density matrices on bounded regions, obeying the same entropy scaling law locally. We prove a restricted version of this conjecture for translationally invariant systems in two spatial dimensions. Specifically, we prove that a translationally invariant marginal obeying three nonlinear constraints—all of which follow from the entropy scaling law straightforwardly—must be consistent with some global state on an infinite lattice. Moreover, we derive a closed-form expression for the maximum-entropy density compatible with those marginals, deriving a variational upper bound on the thermodynamic free energy. The main assumptions of our construction are satisfied exactly by solvable models of topological order and approximately by finite-temperature Gibbs states of certain quantum spin Hamiltonians. |
| format |
article |
| author |
Isaac H. Kim |
| author_facet |
Isaac H. Kim |
| author_sort |
Isaac H. Kim |
| title |
Entropy Scaling Law and the Quantum Marginal Problem |
| title_short |
Entropy Scaling Law and the Quantum Marginal Problem |
| title_full |
Entropy Scaling Law and the Quantum Marginal Problem |
| title_fullStr |
Entropy Scaling Law and the Quantum Marginal Problem |
| title_full_unstemmed |
Entropy Scaling Law and the Quantum Marginal Problem |
| title_sort |
entropy scaling law and the quantum marginal problem |
| publisher |
American Physical Society |
| publishDate |
2021 |
| url |
https://doaj.org/article/5d9e9921e48844a3855cdce4ae81f9d7 |
| work_keys_str_mv |
AT isaachkim entropyscalinglawandthequantummarginalproblem |
| _version_ |
1718389570749333504 |