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Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains
Kristian Tyn Kai Chung1,2, Umberto Borla3,4,5, Andriy H Nevidomskyy2,6,7
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Physical Review Letters
|June 12, 2026
Summary
Symmetries can be noninvertible, leading to distinct spontaneous symmetry breaking. This study explores these noninvertible symmetries in quantum systems, revealing unique ground states and excitations with potential for quantum hardware investigation.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Group theory in physics
Background:
- Traditional symmetry in physics assumes invertibility, forming mathematical groups.
- Recent theoretical advancements suggest symmetries can be noninvertible.
- Understanding noninvertible symmetries is crucial for exploring new quantum phases.
Purpose of the Study:
- To investigate spontaneous symmetry breaking (SSB) for noninvertible symmetries.
- To compare and contrast SSB of noninvertible symmetries with traditional invertible symmetries.
- To identify observable signatures of noninvertible symmetry breaking using quantum hardware.
Main Methods:
- Analytical arguments and numerical evidence were employed.
- The study considered one-dimensional chains of group-valued qudits.
- Ising-type transverse-field Hamiltonians with Rep(G) symmetry were constructed.
Main Results:
- Non-Abelian groups G lead to noninvertible symmetries.
- Symmetry breaking yields one ground state per irreducible representation (irrep) on a closed chain.
- Distinct ground states exhibit unique entanglement patterns, string order, and gapless edge modes for irreps > 1 dimension.
- Domain wall excitations behave as 1D non-Abelian anyons.
Conclusions:
- Noninvertible symmetry breaking presents unique characteristics compared to invertible cases.
- Features like string order and non-Abelian anyonic excitations are associated with symmetry-protected topological order.
- The identified properties are experimentally accessible with current quantum hardware.
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