Identifying quantum phases from injectivity of symmetric matrix product states

Abstract

Given a local gapped Hamiltonian with a global symmetry on a one dimensional lattice we describe a method to identify if the Hamiltonian belongs to a quantum phase in which the symmetry is spontaneously broken in the ground states or to a specific symmetry protected phase, without using local or string order parameters. We obtain different matrix product state (MPS) descriptions of the symmetric ground state(s) of the Hamiltonian by restricting the MPS matrices to transform under different projective representations of the symmetry. The phase of the Hamiltonian is identified by examining which MPS descriptions, if any, are injective, namely, whether the largest eigenvalue of the "transfer matrix" obtained from the MPS is unique. We demonstrate the method for translation invariant Hamiltonians with a global SO(3), Z_2 and Z_2 x Z_2 symmetry on an infinite chain.

arXiv comment9 pages, 6 figures, 1 table (minor changes from previous version)

References in corpus (27)

• Topological entanglement entropy
• Efficient classical simulation of slightly entangled quantum computations
• Detecting topological order in a ground state wave function
• Entanglement spectrum of a topological phase in one dimension
• An Area Law for One Dimensional Quantum Systems
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classifying quantum phases using Matrix Product States and PEPS
• Matrix product states represent ground states faithfully
• Detection of Symmetry Protected Topological Phases in 1D
• Tensor network decompositions in the presence of a global symmetry
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• String order and symmetries in quantum spin lattices
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• Entropy and Entanglement in Quantum Ground States
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• An order parameter for symmetry-protected phases in one dimension
• On topological phases of spin chains
• Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy
• Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains
• Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains
• Matrix product states for anyonic systems and efficient simulation of dynamics
• Identifying Symmetry-Protected Topological Order by Entanglement Entropy

Cited by in corpus (9)

• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S=1 Haldane chain
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Holographic spin networks from tensor network states
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries
• Entanglement renormalization and symmetry fractionalization
• Persistent Haldane Phase in Carbon Tetris Chains