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Tensor Network Representation of Strongly Correlated States of Matter

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Topological chiral phases are ubiquitous in the physics of the Fractional Quantum Hall Effect. Non-chiral topological spin liquids are also well known. Here, using the framework of projected entangled pair states (PEPS), one constructs the spin-1/2 Resonating Valence Bond (RVB) on the kagome lattice and a family of chiral spin liquids on the square lattice which are generalized RVB states obtained from deformed local tensors with d+id symmetry. Using the PEPS formalism, one explicitly derives (orthogonal) “minimally entangled” PEPS RVB states in disconnected topological sectors. A simple bulk-edge correspondence, enables one to investigate the Entanglement Spectrum (and the corresponding Topological Hamiltonian) of those topological states. The chiral spin liquid is shown to exhibit chiral edge modes, which are confronted to predictions of Conformal Field Theory. I argue the state is a magnetic analogue of the nu=1/2 (bosonic) Laughlin state.

This talk is part of the Theory of Condensed Matter series.

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