Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder

Abstract

The simplest Tree-Tensor-States (TTS) respecting the Parity and the Time-Reversal symmetries are studied in order to describe the ground states of Long-Ranged Quantum Spin Chains with or without disorder. Explicit formulas are given for the one-point and two-point reduced density matrices that allow to compute any one-spin and two-spin observable. For Hamiltonians containing only one-body and two-body contributions, the energy of the TTS can be then evaluated and minimized in order to obtain the optimal parameters of the TTS. This variational optimization of the TTS parameters is compared with the traditional block-spin renormalization procedure based on the diagonalization of some intra-block renormalized Hamiltonian.

Entanglement equipartition in critical random spin chains

“…We mention that SDRG methods can be used also to derive predictions for the entanglement scaling in other phases of matter more complicated than RSP [74][75][76][77][78][79][80][81][82][83] .…”

“…Different symbols and colors correspond to different symmetry sectors s = 0, 1/2, 1, 3/2, 2. The dashed lines represent the theory prediction (83) in which a has been adjusted to fit the data.…”