Quantum Restored Symmetry Protected Topological Phases
arXiv:2410.02689 · doi:10.1038/s42005-025-02385-7
Abstract
Symmetry protected topological (SPT) phases are fundamental quantum many-body states of matter beyond Landau's paradigm. Here, we introduce the concept of quantum restored SPTs (QRSPTs), where the protecting symmetry is spontaneously broken at each instance in time, but restored after time average over quantum fluctuations, so that topological features re-emerge. To illustrate the concept, we study a one-dimensional fermionic Su-Schrieffer-Heeger model with fluctuating superconducting order. We solve this problem in several limiting cases using a variety of analytical methods and compare them to numerical (density matrix renormalization group) simulations which are valid throughout the parameter regime. We thereby map out the phase diagram and identify a QRSPT phase with topological features which are reminiscent from (but not identical to) the topology of the underlying free fermion system. The QRSPT paradigm thereby stimulates a new perspective for the constructive design of novel topological quantum many-body phases.
7 pages, 6 pages supplement, 10 figures
References in corpus (51)
- Topological insulators and superconductors
- Classification of topological insulators and superconductors in three spatial dimensions
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Quantum Spin Liquids
- Periodic table for topological insulators and superconductors
- Entanglement spectrum of a topological phase in one dimension
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Topological phases of fermions in one dimension
- Symmetry Protected Topological phases of Quantum Matter
- The effects of interactions on the topological classification of free fermion systems
- Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
- Quantum magnetism and criticality
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
- Complete classification of 1D gapped quantum phases in interacting spin systems
- Interacting topological insulators: a review
- Single particle Green's functions and interacting topological insulators
- Detection of Symmetry Protected Topological Phases in 1D
- Long-range interacting quantum systems
- Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear models and a special group supercohomology theory
- Interacting fermionic topological insulators/superconductors in three dimensions
- One-Dimensional Symmetry Protected Topological Phases and their Transitions
- Intertwined vestigial order in quantum materials: nematicity and beyond
- Entanglement entropy and the Berry phase in solid states
- Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
- Quantum criticality and minimal conductivity in graphene with long-range disorder
- Topological invariants and interacting one-dimensional fermionic systems
- A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
- Symmetry Protected Topological States of Interacting Fermions and Bosons
- Quantum criticality of quasi one-dimensional topological Anderson insulators
- Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
- An order parameter for symmetry-protected phases in one dimension
- Symmetric Mass Generation
- Topology vs. Anderson localization: non-perturbative solutions in one dimension
- Mott insulators with boundary zeros
- Particle-Hole Symmetries in Condensed Matter
- Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
- Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
- Interaction Enabled Topological Crystalline Phases
- Electronic properties, correlated topology and Green's function zeros
- Topological Goldstone phases of matter
- Interacting topological quantum chemistry of Mott atomic limits
- Ground state stability, symmetry, and degeneracy in Mott insulators with long range interactions
- Number conserving analysis of measurement-based braiding with Majorana zero modes
- Phase diagram of an interacting staggered Su-Schrieffer-Heeger two-chain ladder close to a quantum critical point
- Topological Green's function zeros in an exactly solved model and beyond
- Quantum phase transition in the one-dimensional extended Peierls-Hubbard model
- Topological symplectic Kondo effect
- Long distance coherence of Majorana wires
- Topological Kondo effect with spinful Majorana fermions
- Weakly interacting one-dimensional topological insulators: a bosonization approach