Crystalline topological defects within response theory

Lattice defects have interesting effects in some quantum Hamiltonians. Here we show how topological crystalline defects can produce qualitatively new effects by coupling to electric field probes such as Raman scattering, even when they do not appear in the low-energy Hamiltonian but rather only in the probe response theory. To show this we consider an antiferromagnetic spin-1/2 model $H_{spin}$ on a zigzag chain. Crystalline domain walls between two zigzag domains appear as at most local defects in $H_{spin}$, but as topological (not locally creatable) defects in the Raman operator $R$ of inelastic photon scattering. Using TEBD numerics, bosonization, and mean field, we show that a finite density of crystalline domain walls shifts the entire Raman signal to produce an effective gap. This lattice-defect-induced Raman gap closes and reopens in applied magnetic fields. We discuss the effect in terms of photons sensing the lattice defects within $R$ as spin-dimerization domain walls, with $Z_2$ character, and a resulting shift of the probed wavevector from $q=0$ to $\pi+\delta q$, giving an $\textit{O}(1)$ change in contrast to local defects. The magneto-Raman singularity from topological lattice defects here relies on the $H_{spin}$ spinon liquid state, suggesting future applications using lattice topological defects to modify response-theory operators independently of $H$ and thereby generate new probes of quantum phases.