A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between majorization and renormalization group irreversibility emerges from our numerical analysis.

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We simulate the t-J model in two dimensions by means of infinite projected entangled-pair states (iPEPS) generalized to arbitrary unit cells, finding results similar to those previously obtained by the density-matrix renormalization group (DMRG) for wide ladders. In particular, we show that states exhibiting stripes, i.e. a unidirectional modulation of hole-density and antiferromagnetic order with a π-phase shift between adjacent stripes, have a lower variational energy than uniform phases predicted by variational and fixed-node Monte Carlo simulations. For a fixed unit-cell size the energy per hole is minimized for a hole density ρ l ∼ 0.5 per unit length of a stripe. The superconducting order parameter is maximal around ρ l ∼ 0.75 − 0.8.

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