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.

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

References in corpus (8)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Matrix product states represent ground states faithfully
• String order and symmetries in quantum spin lattices
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Entropy and Entanglement in Quantum Ground States
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• On topological phases of spin chains
• A discriminating string order parameter for topological phases of gapped SU(N) spin chains

Cited by in corpus (4)

• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Entanglement renormalization and symmetry fractionalization
• Persistent Haldane Phase in Carbon Tetris Chains