Construction of Entangled Many-body States via the Higgs Mechanism

Abstract

We provide a guiding principle to generate entanglement of quantum many-body states by applying key ideas of the Higgs mechanism to systems without gauge structures. Unitary operators associated with the Higgs mechanism are constructed, named as mean-operators, and employed to prepare entangled many-body states out of a trivial state. We uncover a symmetry-protectedtopological state with two Ising symmetries on a square lattice and find entangled states with different symmetries and lattices. Plausible applications to quantum simulators such as Rydberg atoms and trapped ions, are also discussed, interpreting the mean-operators as the Ising coupling gates.

arXiv commentMain text: 5 pages, 1 figure, Supplemental material: 6 pages

References in corpus (35)

• The theory of variational hybrid quantum-classical algorithms
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Classifying quantum phases using Matrix Product States and PEPS
• Symmetry Protected Topological phases of Quantum Matter
• Braiding statistics approach to symmetry-protected topological phases
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Amplitude / Higgs Modes in Condensed Matter Physics
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Long-range quantum entanglement in noisy cluster states
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• The Higgs Mode in Disordered Superconductors Close to a Quantum Phase Transition
• Gauging spatial symmetries and the classification of topological crystalline phases
• Higgs mode and its decay in a two dimensional antiferromagnet
• Topological phases with generalized global symmetries
• Topology and edge modes in quantum critical chains
• Gapless Symmetry Protected Topological Order
• Theory of interacting topological crystalline insulators
• Wave Function and Strange Correlator of Short Range Entangled states
• Fractal Symmetric Phases of Matter
• Robust Ising Gates for Practical Quantum Computation
• Topological color code and symmetry-protected topological phases
• Crystalline topological phases as defect networks
• Spurious Long-range Entanglement and Replica Correlation Length
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• Real-space recipes for general topological crystalline states
• Gauging the Kitaev chain
• Hofstadter's Butterfly in Quantum Geometry
• Z_N Gauge Theories on a Lattice and Quantum Memory