Symmetry Protected Quantum State Renormalization

Abstract

Symmetry protected topological (SPT) phases with gapless edge excitations have been shown to exist in principle in strongly interacting bosonic/fermionic systems and it is highly desirable to find practical systems to realize such phases through numerical calculation. A central question to be addressed is how to determine the SPT order in the system given the numerical simulation result while no local order parameter can be measured to distinguish the phases from a trivial one. In the tensor network approach to simulate strongly interacting systems, the quantum state renormalization algorithm has been demonstrated to be effective in identifying the intrinsic topological orders. Here we show that a modified algorithm can identify SPT orders by extracting the fixed point entanglement pattern in the ground state wave function which is essential for the existence of SPT order. The key to this approach is to add symmetry protection to the quantum state renormalization process and we demonstrate the effectiveness of this algorithm with the example of AKLT states in both 1D and 2D.

References in corpus (9)

• Classification of topological insulators and superconductors in three spatial dimensions
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Tensor renormalization group approach to 2D classical lattice models
• The iTEBD algorithm beyond unitary evolution
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Quantum computational capability of a 2D valence bond solid phase
• Symmetry protected entanglement renormalization

Cited by in corpus (16)

• Quantum Convolutional Neural Networks
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Detection of Symmetry Enriched Topological Phases
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Symmetry-Protected Topological Entanglement
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Quantum computational advantage with string order parameters of 1D symmetry-protected topological order
• Two-dimensional Valence Bond Solid (AKLT) states from $t_{2g}$ electrons
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Jones index, secret sharing and total quantum dimension
• Continuum limits of homogeneous binary trees and the Thompson group
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems