Quantum Monte Carlo simulations revisited: The case of anisotropic Heisenberg chains

Localizable entanglement of isotropic antiferromagnetic spin-1/2 chain

“…Thermal entanglement measurements based on concurrence of isotropic XY model zero-field, provide maximized entanglement in ground state whereas strong external magnetic field was the main reason for extinction of entanglement at T = 0 [11]. As stated in [19], the second order QPT under zero-field and revival phenomena were observed for AF spin-1/2 chain in the lack of dipole-dipole interaction. DaSilva found that entanglement increased with increasing exchange constant J of spin-1/2 particles located at adjacent sites of the lattice [20].…”

“…x, y, z and β = z) , using a loop algorithm [25,26]-based simulator which was already included in the ALPS package [22]. Note that the spin chain corresponds to an infinite chain between 10-100 spins [18,19]. We deemed 2 × 10 7 steps suitable for the measurement process (correlations and thermodynamic quantities) and 2 × 10 6 steps for the thermalization process, respectively.…”

“…Heisenberg model is an appropriate candidate to study entanglement due to its literal and simplistic structure [8][9][10]. A wide range of studies have focused on both isotropic, anisotropic, AF (antiferromagnetic), and mixed Heisenberg systems with either absence or presence of external fields by neglecting dipole-dipole interactions [11][12][13][14][15][16][17][18][19][20]. Various entanglement measurement methods allow investigations in both bipartite and multipartite entanglement such as concurrence, entanglement witness, entanglement entropy, and localizable entanglement (LE) which are used to reveal the dependence of entanglement on certain physical quantities, e.g., anisotropy and magnetic field [11][12][13][14][15][16][17][18][19][20][21].…”