Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
arXiv:2001.10731 · doi:10.1016/j.physa.2021.126040
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.
arXiv commentv2=revised version with simplified notations, 25 pages, 1 figure
References in corpus (41)
- Quantum entanglement
- The density-matrix renormalization group in the age of matrix product states
- The density-matrix renormalization group
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- A class of quantum many-body states that can be efficiently simulated
- Quantum entanglement in condensed matter systems
- Tensor networks for complex quantum systems
- Renormalization and tensor product states in spin chains and lattices
- Strong disorder RG approach of random systems
- Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
- Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
- Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field
- Strong Disorder RG approach - a short review of recent developments
- Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems
- Renormalization Group and Probability Theory
- Treelike interactions and fast scrambling with cold atoms
- Eigenfunction entropy and spectral compressibility for critical random matrix ensembles
- Anderson localization transition and eigenfunction multifractality in ensemble of ultrametric random matrices
- Quantum Criticality and the Kondo Lattice
- The Hierarchical Random Energy Model
- Quantum spin chains with site dissipation
- Ensemble renormalization group for disordered systems
- Random transverse-field Ising chain with long-range interactions
- Numerical renormalization-group study of spin correlations in one-dimensional random spin chains
- Self-assembling tensor networks and holography in disordered spin chains
- Quantum criticality in spin chains with non-ohmic dissipation
- Long-range random transverse-field Ising model in three dimensions
- Real space Renormalization Group analysis of a non-mean field spin-glass
- Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study
- Entanglement renormalization for disordered systems
- Long-range epidemic spreading in a random environment
- Monte Carlo simulations of dissipative quantum Ising models
- Lifshits tails in the hierarchical Anderson model
- Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
- One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
- Dyson hierarchical quantum ferromagnetic Ising chain with pure or random transverse fields
- Dynamical Barriers in the Dyson Hierarchical model via Real Space Renormalization
- Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
- Foundations and Applications of Entanglement Renormalization
- On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain