Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and particle-vortex duality, which enable a unified approach for the Laughlin states of the fractional quantum Hall system. Starting from the so-called quantum wires system, which is a semimicroscopic description in terms of
(1+1)-dimensional theories, we discuss the emergence of
(2+1)-dimensional low-energy effective field theories by using different maps connecting the microscopic degrees of freedom with the macroscopic ones. We show the origin of these maps by embedding the bosonized version of the original quantum wires model in a gauge-invariant theory and using particle vortex duality.
Fracton topological order describes a remarkable phase of matter, which can be characterized by fracton excitations with constrained dynamics and a ground-state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions, which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order [Vijay, Haah, and Fu, Phys. Rev. B 94, 235157 (2016)] but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of six sites. The model is constructed from two orthogonal stacks of
Z2 topologically ordered Kitaev honeycomb layers [Kitaev, Ann. Phys.321, 2 (2006)], which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D
Z2 topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first-order transitions.
Over the past few decades, tremendous efforts have been devoted to understanding self-duality at the quantum critical point, which enlarges the global symmetry and constrains the dynamics. A one-dimensional spin chain is an ideal platform for the theoretical investigation of these exotic phenomena, due to powerful simulation methods such as the density matrix renormalization group. Deconfined quantum criticality with self-duality at the critical point has been found in an extended short-range spin chain. In this work, we employ large-scale density matrix renormalization group simulations to investigate a critical spin chain with long-range power-law interaction $V(r)\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}}$. Remarkably, we reveal that the long-range interaction drives the original deconfined criticality towards a first-order phase transition as $\ensuremath{\alpha}$ decreases. More strikingly, the emergent self-duality leads to an enlarged symmetry and manifests at these first-order critical points. This discovery is reminiscent of self-duality protected multicritical points, and it provides an example of the critical line with generalized symmetry. Our work has far-reaching implications for ongoing experimental efforts in Rydberg atom quantum simulators.