Article

# Valence bond and von Neumann entanglement entropy in Heisenberg ladders.

Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada.
Physical Review Letters (Impact Factor: 7.94). 09/2009; 103(11):117203. DOI:10.1103/PhysRevLett.103.117203
Source: arXiv

ABSTRACT We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bound on the latter. On ladder geometries, simulations with up to seven legs are sufficient to indicate that the von Neumann entropy in two dimensions obeys an area law, even though the valence bond entanglement entropy has a multiplicative logarithmic correction.

0 0
·
0 Bookmarks
·
75 Views
• Source
##### Article: Thermodynamic limit of density matrix renormalization.
[hide abstract]
ABSTRACT: The density matrix renormalization group discovered by White is investigated. In the case where renormalization eventually converges to a fixed point we show that quantum states in the thermodynamic limit with periodic boundary conditions can be simply represented by a ``matrix product ground state'' with a natural description of Bloch states of elementary excitations. We then observe that these states can be rederived through a simple variational ansatz making no reference to a renormalization construction. The method is tested on the spin-1 Heisenberg model.
Physical Review Letters 12/1995; 75(19):3537-3540. · 7.94 Impact Factor
• Source
##### Article: Violation of the entropic area law for fermions.
[hide abstract]
ABSTRACT: We investigate the scaling of the entanglement entropy in an infinite translational invariant fermionic system of any spatial dimension. The states under consideration are ground states and excitations of tight-binding Hamiltonians with arbitrary interactions. We show that the entropy of a finite region typically scales with the area of the surface times a logarithmic correction. Thus, in contrast with analogous bosonic systems, the entropic area law is violated for fermions. The relation between the entanglement entropy and the structure of the Fermi surface is discussed, and it is proven that the presented scaling law holds whenever the Fermi surface is finite. This is, in particular, true for all ground states of Hamiltonians with finite range interactions.
Physical Review Letters 02/2006; 96(1):010404. · 7.94 Impact Factor
• Source
##### Article: Criticality, the area law, and the computational power of projected entangled pair states.
[hide abstract]
ABSTRACT: The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit a very rich structure including states with critical and topological properties. We prove, in particular, that coherent versions of thermal states of any local 2D classical spin model correspond to such PEPS, which are in turn ground states of local 2D quantum Hamiltonians. This correspondence maps thermal onto quantum fluctuations, and it allows us to analytically construct critical quantum models exhibiting a strict area law scaling of the entanglement entropy in the face of power law decaying correlations. Moreover, it enables us to show that there exist PEPS which can serve as computational resources for the solution of NP-hard problems.
Physical Review Letters 07/2006; 96(22):220601. · 7.94 Impact Factor