Topology meets symmetry breaking: Hidden order, intrinsically gapless topological states and finite-temperature topological transitions

Abstract

Since the discovery of phase transitions driven by topological defects, the classification of phases of matter has been significantly extended beyond Ginzburg and Landau's paradigm of spontaneous symmetry breaking (SSB). In particular, intrinsic and symmetry-protected topological (SPT) orders have been discovered in (mostly gapped) quantum many-body ground states. However, these are commonly viewed as zero-temperature phenomena, and their robustness in a gapless ground state or against thermal fluctuations remains challenging to tackle. Here we introduce an explicit construction for SPT-type states with hidden order associated with SSB: They feature (quasi) long-range correlations along appropriate edges, but short-range order in the bulk; ground state degeneracy associated with SSB; and non-local string order in the bulk. We apply our construction to predict two types of finite-temperature SPT transitions, in the Ising and BKT class respectively, where the usual signs of criticality appear despite the absence of a diverging correlation length in the bulk. While the state featuring hidden Ising order is gapped, the other SPT state associated with the BKT-SPT transition has hidden $U(1)$, or XY-order and constitutes an intrinsically gapless SPT state, associated with a gapless Goldstone mode. Specifically, in this work we discuss spins with global ${\mathbb{Z}}_2$ or $U(1)$ symmetry coupled to link variables constituting a loop gas model. By mapping this system to an Ising-gauge theory, we demonstrate that one of the SPT phases we construct corresponds to the Higgs-SPT phase at $T=0$ -- which we show here to remain stable at finite temperature. Our work paves the way for a more systematic search for hidden order SPT phases, including in gapless systems, and raises the question if a natural (finite-$T$) spin liquid candidate exists that realizes hidden order in the Higgs-SPT class.

arXiv comment12 pages, 6 figures

References in corpus (61)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Probing many-body dynamics on a 51-atom quantum simulator
• Topological entanglement entropy
• Persistent entanglement in arrays of interacting particles
• Quantum Spin Liquids
• Topological quantum memory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Braiding statistics approach to symmetry-protected topological phases
• Topology by Dissipation in Atomic Quantum Wires
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Detection of Symmetry Protected Topological Phases in 1D
• Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Symmetry protected topological phases from decorated domain walls
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Revealing Hidden Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum phases of Rydberg atoms on a kagome lattice
• Statistical localization: from strong fragmentation to strong edge modes
• Competing orders in a magnetic field: spin and charge order in the cuprate superconductors
• Gapless topological phases and symmetry-enriched quantum criticality
• Intrinsically Gapless Topological Phases
• Gapless Symmetry Protected Topological Order
• Perfect Sampling with Unitary Tensor Networks
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Topology of density matrices
• Average Symmetry-Protected Topological Phases
• Density Matrix Topological Insulators
• Probing the topology of density matrices
• Topological indices for open and thermal systems via Uhlmann's phase
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Phase diagram of the toric code model in a parallel magnetic field
• Topological Luttinger Liquids from Decorated Domain Walls
• Geometry and the Hidden Order of Luttinger Liquids: the Universality of Squeezed Space
• Symmetry protected topological order at nonzero temperature
• The hidden symmetry-breaking picture of symmetry-protected topological order
• Realistic scheme for quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical matter in $(2+1)$D
• Gauging the Kitaev chain
• Stabilizing lattice gauge theories through simplified local pseudo generators
• Properties and Detection of Spin Nematic Order in Strongly Correlated Electron Systems
• Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Topological order of mixed states in quantum many-body systems
• Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories
• Snapshot based characterization of particle currents and the Hall response in synthetic flux lattices
• Topological phase transitions at finite temperature
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Interaction-induced topological phase transition at finite temperature
• Percolation as a confinement order parameter in ${\mathbb{Z}}_2$ lattice gauge theories
• Coherent information as a mixed-state topological order parameter of fermions
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Independent e- and m-anyon confinement in the parallel field toric code on non-square lattices
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• Percolation renormalization group analysis of confinement in ${\mathbb{Z}}_2$ lattice gauge theories
• Quantum Restored Symmetry Protected Topological Phases
• Mean-field theory of 1+1D ${\mathbb{Z}}_2$ lattice gauge theory with matter