More on the rainbow chain: entanglement, space-time geometry and thermal states

Abstract

The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature $R=-h^2$ ($h$ is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature $T_R$ and the physical temperature $T$.

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Cited by in corpus (29)

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• Quantum information geometry of driven CFTs
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Entanglement of inhomogeneous free fermions on hyperplane lattices
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• Link representation of the entanglement entropies for all bipartitions
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• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Local fermion density in inhomogeneous free-fermion chains: a discrete WKB approach
• A formula for the overlap between Generalized Coherent States of any rank one simple Lie algebra
• Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble
• Comparing quantum complexity and quantum fidelity
• Creating long-range entangled Majorana pairs: from spin-1/2 twisted Kitaev to generalized XY chains
• Optimal bound on long-range distillable entanglement
• Emergent geometry from entanglement structure