Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets

TL;DR

For two vacua, it is demonstrated that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics.

Abstract

In a spontaneously dimerized quantum antiferromagnet, spin-1/2 excitations (spinons) are confined in pairs by strings akin to those confining quarks in non-abelian gauge theories. The system has multiple degenerate ground states (vacua) and domain walls between regions of different vacua. For two vacua, we demonstrate that spinons on a domain wall are liberated, in a mechanism strikingly similar to domain-wall deconfinement of quarks in variants of quantum chromodynamics. This observation not only establishes a novel phenomenon in quantum magnetism, but also provides a new direct link between particle physics and condensed-matter physics. The analogy opens doors to improving our understanding of particle confinement and deconfinement by computational and experimental studies in quantum magnetism.

Figures (4)

• Figure 1: Deconfinement on domain walls. A quark-confining string (a) composed out of two strands (domain walls) separating two vacua Anber:2015kea allow deconfinement on a domain wall (b). Confinement in a VBS with $Z_2$ degeneracy, where two domain walls form between unpaired spins (c). A domain wall absorbs the string completely, liberating the spinons (d).
• Figure 2: The vacua of a $Z_4$ VBS, illustrated with short valence bonds (singlets). Petterns with a relative shift of one lattice spacing are colored with blue and green. The four phases meet at an unpaired spin (red circle). A spinon can be thought of as such a nexus of four different kinds of domain walls (dashed lines labeled by the numbers 1-4) with a spin in the core. Spinons are then not confined by a single string (inlay A), but by four string-like domain lines (inlay B).
• Figure 3: The $J$-$Q$ model and domain walls. (a) The singlet projectors $P_{ij}$ of the $J$ and $Q$ terms. (b) Using periodic boundaries in the $y$-direction and open boundaries in the $x$-direction, a $\pi$ domain wall is enforced when $L_x$ is odd and $Q_x>Q_y$. The $y$-direction is compactified.
• Figure 4: Correlations in the presence of a domain wall. The $x$ boundaries of the $(L+1)\times L$$J$-$Q$ lattice ($L$ even) are open, which forces a domain wall in the $y$-direction. The coupling $Q_x=1$. (a) Spin correlations transverse to the domain wall at $Q_y=0.6$ and $L=32$. Averaging has been performed over all spin pairs separated by $(\Delta x=r,\Delta y=0)$. The inset shows the VBS (dimer) order parameter vs the lateral system coordinate. (b) Correlations parallel to the domain wall at $r=L/2$ fitted to the critical Heisenberg form. The inset shows the behavior in three different phases of the model: Néel-ordered ($J=5.0$, $Q_y=0.6$), $Z_2$ VBS ($J=0.5$, $Q_y=0.6$), and $Z_4$ VBS ($J=0.0$, $Q_y=1.0$).