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

Cécile Monthus (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Domains: Physics [physics]

Cécile Monthus. Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder. Physica A: Statistical Mechanics and its Applications, 2021, ⟨10.1016/j.physa.2021.126040⟩. ⟨cea-02571099⟩