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arXiv · 1207.6752

Entanglement Spectra of the quantum hard-square model: Holographic minimal models

Shu Tanaka·Ryo Tamura·Hosho Katsura
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Abstract

We study the entanglement properties of a quantum lattice-gas model for which we can find the exact ground state (of the Rokhsar-Kivelson type). The ground state can be expressed as a superposition of states, each of which is characterized by a particle configuration with nearest-neighbor exclusion. We show that the reduced density matrix of the model on a ladder is intimately related to the transfer matrix of the classical hard-square model. The entanglement spectra of the model on square and triangular ladders are critical when parameters are chosen so that the corresponding classical hard-square models are critical. A detailed analysis reveals that the critical theories for the entanglement Hamiltonians are $c<1$ minimal conformal field theories. We further show that the entanglement Hamiltonian for the triangular ladder is integrable despite the fact that the original quantum lattice-gas model is non-integrable.

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Shu Tanaka, Ryo Tamura, Hosho Katsura. 2012-07-29. Entanglement Spectra of the quantum hard-square model: Holographic minimal models. https://doi.org/10.1103/physreva.86.032326

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