Entanglement Hamiltonian of the quantum Néel state

Abstract

Two-dimensional Projected Entangled Pair States (PEPS) provide a unique framework giving access to detailed entanglement features of correlated (spin or electronic) systems. For a bi-partitioned quantum system, it has been argued that the Entanglement Spectrum (ES) is in a one-to-one correspondence with the physical edge spectrum on the cut and that the structure of the corresponding Entanglement Hamiltonian (EH) reflects closely bulk properties (finite correlation length, criticality, topological order, etc...). However, entanglement properties of systems with spontaneously broken continuous symmetry are still not fully understood. The spin-1/2 square lattice Heisenberg antiferromagnet provides a simple example showing spontaneous breaking of SU(2) symmetry down to U(1). The ground state can be viewed as a "quantum Néel state" where the classical (Néel) staggered magnetization is reduced by quantum fluctuations. Here I consider the (critical) Resonating Valence Bond state doped with spinons to describe such a state, that enables to use the associated PEPS representation (with virtual bond dimension $D=3$) to compute the EH and the ES for a partition of an (infinite) cylinder. In particular, I find that the EH is (almost exactly) a chain of a dilute mixture of heavy ($\downarrow$ spins) and light ($\uparrow$ spins) hardcore bosons, where light particles are subject to long-range hoppings. The corresponding ES shows drastic differences with the typical ES obtained previously for ground states with restored SU(2)-symmetry (on finite systems).

arXiv comment6 pages, final version to be published in J. Stat. Mech. (2014), Special Issue on "Quantum Entanglement in Condensed Matter Physics"

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Cited by in corpus (8)

• Quantum entanglement in condensed matter systems
• Quantum critical phase with infinite projected entangled paired states
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Entanglement Hamiltonians for chiral fermions with zero modes
• Entanglement Hamiltonians and entropy in 1+1D chiral fermion systems
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
• Locality at the boundary implies gap in the bulk for 2D PEPS