Projected entangled-pair states (PEPS) provide a framework for the construction of models where a single tensor gives rise to both Hamiltonian and ground state wave function on the same footing. A key problem is to characterize the behavior which emerges in the system in terms of the properties of the tensor, and thus of the Hamiltonian. In this paper, we consider PEPS models with ${\mathbb{Z}}_{2}$ on-site symmetry and study the occurrence of long-range order and spontaneous symmetry breaking. We show how long-range order is connected to a degeneracy in the spectrum of the PEPS transfer operator, and how the latter gives rise to spontaneous symmetry breaking under perturbations. We provide a succinct characterization of the symmetry-broken states in terms of the PEPS tensor, and find that using the symmetry-broken states we can derive a local entanglement Hamiltonian, thereby restoring locality of the entanglement Hamiltonian for all gapped phases.Projected entangled-pair states (PEPS) provide a framework for the construction of models where a single tensor gives rise to both Hamiltonian and ground state wave function on the same footing. A key problem is to characterize the behavior which emerges in the system in terms of the properties of the tensor, and thus of the Hamiltonian. In this paper, we consider PEPS models with ${\mathbb{Z}}_{2}$ on-site symmetry and study the occurrence of long-range order and spontaneous symmetry breaking. We show how long-range order is connected to a degeneracy in the spectrum of the PEPS transfer operator, and how the latter gives rise to spontaneous symmetry breaking under perturbations. We provide a succinct characterization of the symmetry-broken states in terms of the PEPS tensor, and find that using the symmetry-broken states we can derive a local entanglement Hamiltonian, thereby restoring locality of the entanglement Hamiltonian for all gapped phases.

arXiv:1505.04217Physical Review BOct 20, 201518 citations

Long-Range Order and Spontaneous Symmetry Breaking in the Classical and Quantum Ising Models

Hal Tasaki

Graduate texts in physicsJan 1, 20200 citations

QUANTUM ENTANGLEMENT AND SYMMETRIES

Marek Kuś

International Symposium on Quantum Theory and Symmetries (QTS)Jun 1, 20020 citations

Spontaneous Symmetry Breaking, Off-diagonal Long-range Order, and Nucleation of Quantum State

Yu Shi

Spontaneous symmetry breaking originats in quantum mechanical measurement of the relevant observable defining the physical situation, order parameter is the average of this observable. A modification is made on the random-phase postulate validating the ensemble description. Off-diagonal long-range order, macroscopic wavefunction and interference effects in many-particle systems present when there is a so-called nucleation of quantum state, which is proposed to be the origin of spontaneous gauge symmetry breaking, for which nonconservation of particle number N is not essential. The approach based on nonvanishing expectation of the field operator, $$, is only a coherent-state approximation in thermodynamic limit. When $N \to \infty$, this approach is equivalent, but $$ is not the macroscopic wavefunction.Spontaneous symmetry breaking originats in quantum mechanical measurement of the relevant observable defining the physical situation, order parameter is the average of this observable. A modification is made on the random-phase postulate validating the ensemble description. Off-diagonal long-range order, macroscopic wavefunction and interference effects in many-particle systems present when there is a so-called nucleation of quantum state, which is proposed to be the origin of spontaneous gauge symmetry breaking, for which nonconservation of particle number N is not essential. The approach based on nonvanishing expectation of the field operator, $$, is only a coherent-state approximation in thermodynamic limit. When $N \to \infty$, this approach is equivalent, but $$ is not the macroscopic wavefunction.

arXiv:quant-ph/9702026Feb 11, 19970 citations

Disentangling Quantum Entanglement

Luis de la Peña, Ana Marı́a Cetto, Andrea Valdés Hernández

Springer eBooksJul 15, 20141 citation

{\mathbb{Z}}_{2}

on-site symmetry and study the occurrence of long-range order and spontaneous symmetry breaking. We show how long-range order is connected to a degeneracy in the spectrum of the PEPS transfer operator, and how the latter gives rise to spontaneous symmetry breaking under perturbations. We provide a succinct characterization of the symmetry-broken states in terms of the PEPS tensor, and find that using the symmetry-broken states we can derive a local entanglement Hamiltonian, thereby restoring locality of the entanglement Hamiltonian for all gapped phases.