Zero Curvature Condition for Quantum Criticality
arXiv:2303.09591 · doi:10.1103/l3d5-lnr7
Abstract
Quantum criticality often lies beyond the scope of the conventional Landau paradigm, and a unifying framework has yet to emerge, due in part to the wide variety of quantum orders. We propose a geometric approach to quantum phase transitions (QPTs) that shifts focus from microscopic order to the competition between non-commuting operators. This competition is encoded in the boundary geometry of their expectation values, defining a quantum observable space (QOS). We show that QPTs occur at zero-curvature points on the QOS boundary, signaling maximal commutativity and suggesting an underlying integrable structure at criticality.
References in corpus (21)
- Anyons in an exactly solved model and beyond
- Topological Field Theory of Time-Reversal Invariant Insulators
- Entanglement in quantum critical phenomena
- The physics of exceptional points
- "Deconfined" quantum critical points
- Entanglement renormalization
- Quantum Orders and Symmetric Spin Liquids
- Zoo of quantum-topological phases of matter
- Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
- Ground state overlap and quantum phase transitions
- Dynamics of a Quantum Phase Transition
- Quantum phase transitions
- Fidelity approach to quantum phase transitions
- Entanglement and Extreme Spin Squeezing
- Quantum Criticality: competing ground states in low dimensions
- Topological characterization of quantum phase transitions in a S=1/2 spin model
- Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
- Choreographed entangle dances: topological states of quantum matter
- A c-theorem for the entanglement entropy
- Frozen deconfined quantum criticality
- Quantum Geometry of Expectation Values