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Abstract |
Quantum Chromodynamics (QCD) -- the theory of strong nuclear forces -- has baffled the physics
community and remains one of the poorly understood parts of the standard model. Its quintessential
property: the confinement of quarks into protons, neutrons and mesons, while verified both experimentally
and numerically, remains an elusive theoretical problem. The various cousins of QCD are however possible
to understand to varying degrees and precision. In some of these theories the vacuum state is degenerate,
and hence allows for domain walls -- a surface excitation which interpolates between two vacua of the
theory. These domain walls have a remarkable property that quarks become liberated on them, and the
domain wall excitation spectrum is very different from that of the bulk. Such QCD cousins are,
unfortunately, not the physical theory, and they do not occur in nature. QCD however has another unlikely
cousin: the Valence Bond Solid (VBS) state of the quantum anti-ferromagnet, where spin 1/2 excitations
(or spinons) are bound into spin 1 excitations by a mechanism very similar to confinement of quarks.
Perhaps surprisingly the low energy theory describing the behavior of the VBS phase is virtually identical
to its QCD cousins under certain conditions. Further the VBS phase may have multiple vacua, and thus
support domain walls, which in turn support liberated spinon excitations absent in the bulk. This has been
verified numerically in the so-called J-Q model. These domain wall modes can in fact be seen as edge
modes akin to those of the symmetry protected topological state. A multidisciplinary effort is slowly
emerging to understand such phenomena, from the theoretical aspects of fundamental and condensed
matter physics, to the numerical efforts in trying to understand QCD and quantum magnets. |
