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X-FROM-URL:https://eom.sdu.dk/events/ical/b87c33c2-98c0-4db4-8775-d1a17bc0
 e524
X-WR-CALNAME:QM Research Seminar: Spontaneously Broken Non-Invertible Symm
 etries in Transverse-Field Ising Qudit Chains
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TZID:Europe/Copenhagen
X-LIC-LOCATION:Europe/Copenhagen
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DTSTAMP:20260602T163402Z
DTSTART:20261028T030000
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DTSTART:20260325T020000
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DESCRIPTION:Recent developments have revealed that symmetries need not for
 m a group\, but instead can be non-invertible. I will use analytical argu
 ments and numerical evidence to illuminate how spontaneous symmetry break
 ing of a non-invertible symmetry is similar yet distinct from ordinary sy
 mmetry breaking. I will consider one-dimensional chains of group-valued q
 udits\, whose local Hilbert space is spanned by elements of a finite grou
 p $G$ (reducing to ordinary qubits when $G=\mathbbm{Z}_2$). I will constr
 uct Ising-type transverse-field Hamiltonians with Rep($G$) symmetry whose
  generators multiply according to the tensor product of irreducible repre
 sentations (irreps) of the group $G$. For non-Abelian $G$\, the symmetry 
 is non-invertible. In the symmetry broken phase there is one ground state
  per irrep on a closed chain. The symmetry breaking can be detected by lo
 cal order parameters but\, unlike the invertible case\, different ground 
 states have distinct entanglement patterns. I will show that for each irr
 ep of dimension greater than one the corresponding ground state exhibits 
 string order\, entanglement spectrum degeneracies\, and has gapless edge 
 modes on an open chain -- features usually associated with symmetry-prote
 cted topological order. Consequently\, domain wall excitations behave as 
 one-dimensional non-Abelian anyons with non-trivial internal Hilbert spac
 es and fusion rules. This work identifies properties of non-invertible sy
 mmetry breaking that existing quantum hardware can probe and raises new q
 uestions in quantum computing.
DTEND:20251006T123000Z
DTSTAMP:20260602T163402Z
DTSTART:20251006T113000Z
LOCATION:Syddansk Universitet\, Campusvej 55\, 5230\, Odense M
SEQUENCE:0
SUMMARY:QM Research Seminar: Spontaneously Broken Non-Invertible Symmetrie
 s in Transverse-Field Ising Qudit Chains
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