Weicheng Ye, Meng Guo, Yin-Chen He, Chong Wang, Liujun Zou
SciPost Phys. 13, 066 (2022) ·
published 26 September 2022
|
· pdf
Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the
emergibility problem, i.e. whether a quantum phase or phase transition can
emerge in a many-body system. We derive the topological partition functions
that characterize the LSM constraints in spin systems with $G_s\times G_{int}$
symmetry, where $G_s$ is an arbitrary space group in one or two spatial
dimensions, and $G_{int}$ is any internal symmetry whose projective
representations are classified by $\mathbb{Z}_2^k$ with $k$ an integer. We then
apply these results to study the emergibility of a class of exotic quantum
critical states, including the well-known deconfined quantum critical point
(DQCP), $U(1)$ Dirac spin liquid (DSL), and the recently proposed
non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the
competition between a magnetic state and a non-magnetic state. We identify all
possible realizations of these states on systems with $SO(3)\times
\mathbb{Z}_2^T$ internal symmetry and either $p6m$ or $p4m$ lattice symmetry.
Many interesting examples are discovered, including a DQCP adjacent to a
ferromagnet, stable DSLs on square and honeycomb lattices, and a class of
quantum critical spin-quadrupolar liquids of which the most relevant spinful
fluctuations carry spin-$2$. In particular, there is a realization of
spin-quadrupolar DSL that is beyond the usual parton construction. We further
use our formalism to analyze the stability of these states under
symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete
example, we find that a DSL can be stable in a recently proposed candidate
material, NaYbO$_2$.
SciPost Phys. 12, 196 (2022) ·
published 14 June 2022
|
· pdf
We study the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary. We calculate various edge properties in an $N\to\infty$ limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as "fractional" degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the quantum spin Hall state but with the full $SU(2)$ spin rotation symmetry, which cannot be realized if the bulk is gapped.
