Classifying quantum phases using matrix product states and projected entangled pair states

By Norbert Schuch, David Pérez-García, I. Cirac. 2011

592 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/a843c846dd18344fdd13da2c003c3cf9c81d1a91

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Stability of Frustration-Free Hamiltonians (2011, methodology): “Hamiltonians with a unique Matrix Product State as their groundstate, or injective PEPS [38,42,43]) to modify a frustration-free Hamiltonian H0 to a different Hamiltonian H1, satisfying Local-TQO without changing the global ground state subspace, or closing the gap.”
Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect (2012, background): “In these phases, the bulk appears to local probes as a rather conventional gapped state.”
Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states (2012, background): “[60] Norbert Schuch, David Perez-Garcia, and Ignacio Cirac, Classifying Quantum Phases Using Matrix Product States and Projected Entangled Pair States, Phys.”
Pre-thermal phases of matter protected by time-translation symmetry (2016, background): “[7] Norbert Schuch, David Pérez-Garćıa, and Ignacio Cirac, “Classifying quantum phases using matrix product states and projected entangled pair states,” Phys.”
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems (2014, background): “In addition, the theoretical underpinning of tensor-network states in terms of the area law of entanglement entropy [38,39] makes them suitable for theoretical results as profound as the complete classification of gapped quantum phases [40,41].”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “…2009), it was realized that the local symmetries of the tensors are of primordial importance for describing long range topological order, and in (Schuch et al., 2011) this was formalized by the crucial concept of Ginjectivity and later by the more general concept of MPOinjectivity (Bultinck et…”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “In particular, one can ‘push’ physical symmetries through to the ‘virtual’ level 12 [3, 22, 25, 92, 124]: There exists an operator V g such that In other words, we see that the physical operator U g is equivalent to acting with V g and V † g at the virtual level.”