Perfect Particle Transmission through Duality Defects

TL;DR

The paper investigates how wavepackets can achieve perfect transmission across duality defects that couple dual theories, providing a lattice realization of the monopole paradox. By representing dualities and generalized symmetries as matrix product operator (MPO) algebras, it identifies the impurity degree of freedom with the dangling virtual space of the MPO and shows that a unitary duality MPO can be moved without altering the spectrum, while dressing the scattered excitation with a topological string. The main contributions include explicit lattice constructions exhibiting universal perfect transmission across duality defects, MPO-based mechanisms linking impurity states to virtual spaces, and generalizations to higher dimensions via PEPOs with connections to toric-code-like gauging. These results offer both an operational interpretation of topological interfaces and a practical framework for simulating and understanding dualities in strongly interacting quantum spin systems. The work thus deepens the connection between duality, topological strings, and unitarity in many-body dynamics, with potential implications for DMRG algorithms and lattice realizations of field-theoretic dualities.

Abstract

We study wavepackets that propagate across (a) topological interfaces in quantum spin systems exhibiting non-invertible symmetries and (b) duality defects coupling dual theories. We demonstrate that the transmission is always perfect, and that a particle traversing the interface is converted into a nonlocal string-like excitation. We give a systematic way of constructing such a defect by identifying its Hilbert space with the virtual bond dimension of the matrix product operator representing defect lines. Our work both gives an operational meaning to topological interfaces, and provides a lattice analogue of recent results solving the monopole paradox in quantum field theory.

Figures (7)

• Figure 1: $(a)$ Chiral fermion scattered by a Dirac monopole. $(b)$ Fermion rotor model. $(c)$ A schematic illustration of the system. Two systems with different Hamiltonians interact through the impurity, denoted by a black diamond. $(d)$ We create a right-moving particle/wave packet in the left medium on top of the many-body ground state. $(e)$ When $H_L$ and $H_R$ are related by duality and separated by a topological impurity, the excitation propagates with perfect transmittance. The outgoing particle on the right appears to be a different particle, but can be described by the same particle with a topological string attached to the impurity.
• Figure 2: The time evolution of the local magnetization $\langle Z_x\rangle$ for $(a)$$(g_L,g_R)=(4.0,2.0)$ and $(b)$$(g_L,g_R)=(4.0,4.0)$ with $(L,x_0,k) = (50, 15,0.7\pi)$. The impurity site is represented by a gray shaded strip. $(c)$ Transmittance rate of the wave packet. The scattering is purely reflective for $g_R<2$ and $g_R>6$ as can be seen from the exact solution.$(d)$ Perfect transmission of a domain wall of a ferromagnet to a Haldane chain. The video versions are available in Supplemental Material and https://github.com/dartsushi/Video_scattering.
• Figure 3: Equivalence between perfect transmittance and topological defects. Moving the topological impurity is a unitary transformation and does not alter the Hamiltonian spectrum.
• Figure 4: The time evolution for the $\mathsf{Rep}(\mathcal{S}_3)$ model with with $(g_L,g_R)=(4.0,4.0)$ of (a) the local energy and (b) the local magnetization $\braket{Z_x}$. Total transmittance is visible, as well as the spin flip on the impurity. The topological string is invisible due to the symmetry respecting ground state.
• Figure 5: The Kramers-Wannier duality in two dimensions. This maps the transverse-field Ising model on a square lattice to the model on links.