Competing symmetry breaking and topology in quantum spin chains

arXiv:2610.10694 · cond-mat.str-el · Submitted 2026-10-07 · Read on arXiv

cond-mat.str-el

Submitted: 2026-10-07

Updated: 2026-10-07

Terminology

• Degeneracy — 56× in this paper · explained in 3 episodes
• Entanglement — 46× in this paper · explained in 3 episodes
• Anisotropy — 34× in this paper · explained in 3 episodes
• Entanglement Entropy — 19× in this paper · explained in 2 episodes
• Bosonization — 16× in this paper · explained in 2 episodes
• Phase Transitions — 12× in this paper · explained in 2 episodes
• Symmetry Breaking — 12× in this paper · explained in 3 episodes
• Spectral Gap — 11× in this paper · explained in 5 episodes
• First-Order Transition — 10× in this paper · explained in 2 episodes
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Lifshitz transition — 9× in this paper · explained in 2 episodes
• Effective Hamiltonian — 7× in this paper · explained in 2 episodes
• Domain Walls — 4× in this paper · explained in 2 episodes
• Hubbard Model — 4× in this paper · explained in 3 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Consistency — 3× in this paper · explained in 3 episodes
• Self-consistency — 3× in this paper · explained in 2 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Frustration — 1× in this paper · explained in 2 episodes
• Gauge Freedom — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Redundancy — 1× in this paper · explained in 2 episodes

Sources

• Topology and edge states survive quantum criticality between topological insulators
• Absence of Friedel oscillations in the entanglement entropy profile of one-dimensional intrinsically gapless topological phases
• Stability and fine structure of symmetry-enriched quantum criticality in a spin ladder triangular model
• Gauging on the lattice and gapped/gapless topological phases
• Continuous symmetry breaking in 1D spin chains and 1+1D field theory
• Theory of criticality-enabled U(1) symmetry breaking in a class of 1+1D systems
• Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions
• Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions
• On the Strength of First Order Phase Transitions
• Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains

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