Identifying quantum phases from the injectivity of symmetric matrix product states

Sukhwinder Singh
Phys. Rev. B 91, 115145 – Published 31 March 2015

Abstract

Given a local gapped Hamiltonian with a global symmetry on a one-dimensional lattice we describe a method to identify whether 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 equivalence classes of 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 translationally invariant Hamiltonians with a global SO(3), Z2, and Z2×Z2 symmetry on an infinite chain.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 7 November 2014
  • Revised 18 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.115145

©2015 American Physical Society

Authors & Affiliations

Sukhwinder Singh

  • Center for Engineered Quantum Systems, Department of Physics & Astronomy, Macquarie University, 2109 NSW, Australia

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 91, Iss. 11 — 15 March 2015

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×