Abstract
An efficient scheme for computing the geometric entanglement (GE) per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on matrix product state representations. It has been systematically tested for three prototypical critical quantum spin chains, which belong to the same Ising universality class. The simulation results lend strong support to the previous claim (Shi et al 2010 New J. Phys.12 025008; Stéphan et al 2010 Phys. Rev. B 82 180406R) that the leading finite-size correction to the GE per lattice site is universal, with its remarkable connection to the celebrated Affleck–Ludwig boundary entropy corresponding to a conformally invariant boundary condition.
Highlights
In the last decade, significant progress has been made in the investigation of quantum phase transitions (QPTs) from a novel perspective-quantum entanglement [1]
A remarkable result is achieved for the von Neumann entropy that quantifies the bipartite entanglement when a finite-size spin chain is partitioned into two disjoint parts: it scales logarithmically with the subsystem’s size, with a prefactor proportional to the central charge, a fundamental quantity in conformal field theory, as long as the system is at criticality [2,3,4,5]
We have developed a scheme to efficiently compute the geometric entanglement (GE) per lattice site for quantum manybody spin systems on a periodic finite-size chain in the context of a tensor network algorithm based on the matrix product state representations
Summary
An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state representations. It is systematically tested for three prototypical critical quantum spin chains, which belong to the same Ising universality class. Rev. B 82, 180406R (2010)] that the leading finite-size correction to the geometric entanglement per lattice site is universal, with its remarkable connection to the celebrated AffleckLudwig boundary entropy corresponding to a conformally invariant boundary condition. PACS numbers: 03.67.-a, 03.65.Ud, 03.67.Hk arXiv:1106.2110v1 [cond-mat.stat-mech] 10 Jun 2011
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