Area-Law Study of Quantum Spin System on Hyperbolic Lattice Geometries |
| A. Gendiar
Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11 Bratislava, Slovakia |
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| Magnetic properties of the transverse-field Ising model on curved (hyperbolic) lattices are studied by a tensor product variational formulation that we have generalized for this purpose. First we identify the quantum phase transition for each hyperbolic lattice by calculating the magnetization. We study the entanglement entropy at the phase transition in order to analyze the correlations of various subsystems located at the center with the rest of the lattice. We confirm that the entanglement entropy satisfies the area law at the phase transition for fixed coordination number, i.e., it scales linearly with increasing size of the subsystems. On the other hand, the entanglement entropy decreases as power-law with respect to the increasing coordination number. |
DOI:10.12693/APhysPolA.137.589 topics: quantum magnetism in spin systems, phase transitions, tensor-network methods |