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Brick Wall Quantum Circuits with Global Fermionic Symmetry
by Pietro Richelli, Kareljan Schoutens, Alberto Zorzato
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Alberto Zorzato |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202407_00034v2 (pdf) |
| Date accepted: | 2024-09-16 |
| Date submitted: | 2024-09-09 12:12 |
| Submitted by: | Zorzato, Alberto |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary $U_F$ and its, non-trivial, hamiltonian limit $H_{\gamma}$ in closed form. We find that the fermionic symmetry pins $H_{\gamma}$ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics for this class of circuits.
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- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
- clarified how the commutation relation works for the boundary matrix K
-made spin notation consistent in eq. 1.2
-corrected a typo in eq. 2.4 to clarify how parity affects local operators in graded tensor products
-enlarged fontsize for numerical plots
Published as SciPost Phys. 17, 087 (2024)