This webpage collects resources regarding the rainbow state, a quantum many-body state presenting very interesting entanglement properties. Here you can see a snapshot.

• From conformal to volume-law for the entanglement entropy in exponentially deformed critical chains, G. Ramírez, J. Rodríguez-Laguna, G. Sierra, JSTAT P10004 (2014) or ArXiv:1407.3456.
  The original article introducing the term rainbow, and discussing its origin from the strong disorder renormalization group.
• Entanglement over the rainbow, G. Ramírez, J. Rodríguez-Laguna, G. Sierra, JSTAT P06002 (2015) or ArXiv:1503.02695.
  First weak inhomogeneity analysis of the rainbow state, conjecturing the relation to conformal field theory.

• More on the rainbow chain: entanglement, space-time geometry and thermal states, J. Rodríguez-Laguna, J. Dubail, G. Ramirez, P. Calabrese, G. Sierra, J. Phys. A 50, 164001 (2017) or ArXiv:1611.08559.
  Description of the rainbow system as a conformal field theory on hyperbolic spacetime.
• Entanglement Hamiltonian and entanglement contour in inhomogeneous 1D systems, E. Tonni, J. Rodríguez-Laguna, G. Sierra, JSTAT 043105 (2018) or ArXiv:1712.03557.
  Evaluation of the entanglement contour, hamiltonian y spectrum for a CFT on a curved spacetime, using the rainbow system as an example.
• Piercing the rainbow: entanglement on an inhomogeneous spin chain with a defect, N. Samos Sáenz de Buruaga, S.N. Santalla, J. Rodríguez-Laguna, G. Sierra, Phys. Rev. B 101, 205121 (2020) or ArXiv:1912.10788
  Entanglement transitions can be found by tuning the central hopping of a rainbow system.
• Symmetry protected phases in inhomogeneous spin chains, N. Samos Sáenz de Buruaga, S.N. Santalla, J. Rodríguez-Laguna, G. Sierra, JSTAT 093102 (2019) or ArXiv:1812.04869.
  Folding the rainbow state, and introducing symmetry protected topological phases by inserting a spare site at the center.
• Casimir forces on deformed fermionic chains, B. Mula, S.N. Santalla, J. Rodríguez-Laguna, Phys. Rev. Research 3, 013062 (2021) or ArXiv:2004.12456.
  Extension of Cardy's expression for the Casimir force in a conformal system to inhomogeneous 1+1D systems, using the rainbow system as an example.
• Entanglement in non-critical inhomogeneous quantum chains, N. Samos Sáenz de Buruaga, S.N. Santalla, J. Rodríguez-Laguna, G. Sierra, Phys. Rev. B 104, 195147 (2021) or ArXiv:2107.12113.
  The rainbow state in presence of a mass, showing that it preserves its entanglement properties within a correlation length of the center.
• Depletion in fermionic chains with inhomogeneous hoppings, B. Mula, N. Samos Sáenz de Buruaga, G. Sierra, S.N. Santalla, J. Rodríguez-Laguna, Phys. Rev. B 106, 224204 (2022) or ArXiv:2209.10624.
  The fermionic rainbow state away from half-filling presents regions of depletion, which we characterize using an effective Schrödinger equation.

• Entanglement in correlated random spin chains, RNA folding and kinetic roughening, J. Rodríguez-Laguna, S.N. Santalla, G. Ramírez, G. Sierra, New J. Phys. 18, 073025 (2016) or ArXiv:1601.03408.
  Phase diagram of the fermionic chains with strongly correlated disorder, showing that in a certain regime they approach the rainbow state.
• Unusual area-law violation in random inhomogeneous systems, V. Alba, S.N. Santalla, P. Ruggiero, J. Rodríguez-Laguna, P. Calabrese, G. Sierra, JSTAT 023105 (2019) or ArXiv:1807.04179.
  Rainbow chain with disordered hoppings, showing the appearance of a new phase.

• Engineering large end-to-end correlations in finite fermionic chains, H. Santos, J.E. Alvarellos, J. Rodríguez-Laguna, Phys. Rev. B 98, 245121 (2018) or ArXiv:1809.06246.
  Analysing the tradeoff between energy gap and end-to-end correlation in fermionic chains with inhomogeneous hoppings.

• Entanglement as geometry and flow, S. Singha Roy, S.N. Santalla, J. Rodríguez-Laguna, G. Sierra, Phys. Rev. B 101, 195134 (2020) or ArXiv:1906.05146.
  Introducing the entanglement links.
• Link representation of the entanglement entropies for all bipartitions, S. Singha Roy, S.N. Santalla, G. Sierra, J. Rodríguez-Laguna, J. Phys. A: Math. Theor. 54, 305301 (2021) or ArXiv:2103.08929.
  Numerical algorithms in order to evaluate the entanglement links, for gaussian states and matrix product states.
• Entanglement links and the quasiparticle picture, S.N. Santalla, G. Ramírez, S. Singha Roy, G. Sierra, J. Rodríguez-Laguna, Phys.Rev. B 107, L121114 (2023) or ArXiv:2208.03766.
  Dynamics of the rainbow state under a quench to a homogeneous Hamiltonian, using the entanglement links in order to interpret the evolution of the entanglement entropy.

STATPHYS 28, Tokyo: Entanglement over the rainbows

STATPHYS 27, Buenos Aires: Entanglement over the rainbow: statistical mechanics of the area law