Symmetry Protected Quantum State Renormalization

TL;DR

This paper introduces a modified quantum state renormalization algorithm that incorporates symmetry protection, enabling the identification of symmetry protected topological (SPT) phases in strongly interacting systems using tensor network methods.

Contribution

The authors develop a symmetry-protected quantum state renormalization algorithm that effectively detects SPT order by analyzing fixed point entanglement patterns in ground states.

Findings

Successfully identifies SPT phases in AKLT states in 1D and 2D.

Demonstrates the algorithm's effectiveness in numerical simulations.

Provides a practical method for studying SPT phases without local order parameters.

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.