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We show that a class of $\mathcal{PT}$ symmetric non-Hermitian Hamiltonians realizing the Yang-Lee edge singularity exhibits an entanglement transition in the long-time steady state evolved under the Hamiltonian. Such a transition is induced by a level crossing triggered by the critical point associated with the Yang-Lee singularity and hence is first-order in nature. At the transition, the entanglement entropy of the steady state jumps discontinuously from a volume-law to an area-law scaling. We exemplify this mechanism using a one-dimensional transverse field Ising model with additional imaginary fields, as well as the spin-1 Blume-Capel model and the three-state Potts model. We further make a connection to the forced-measurement induced entanglement transition in a Floquet non-unitary circuit subject to continuous measurements followed by post-selections. Our results demonstrate a new mechanism for entanglement transitions in non-Hermitian systems harboring a critical point., Updated to published version

We study the stability of the Wilson-Fisher fixed point of the quantum $\text{O}(2N)$ vector model to quenched disorder in the large-$N$ limit. While a random mass is strongly relevant at the Gaussian fixed point, its effect is screened by the strong interactions of the Wilson-Fisher fixed point. This enables a perturbative renormalization group study of the interplay of disorder and interactions about this fixed point. We show that, in contrast to the spiralling flows obtained in earlier double-$\ensuremath{\epsilon}$ expansions, the theory flows directly to a quantum critical point characterized by finite disorder and interactions. The critical exponents we obtain for this transition are in remarkable agreement with numerical studies of the superfluid-Mott glass transition. We additionally discuss the stability of this fixed point to scalar and vector potential disorder and use proposed boson-fermion dualities to make conjectures regarding the effects of weak disorder on dual Abelian Higgs and Chern-Simons-Dirac fermion theories when $N=1$.

In the last few years a lot of exotic and anomalous topological phases were constructed by proliferating the vortexlike topological defects on the surface of the $3d$ topological insulator (TI) [Fidkowski et al., Phys. Rev. X 3, 041016 (2013); Chen et al., Phys. Rev. B 89, 165132 (2014); Bonderson et al., J. Stat. Mech. (2013) P09016; Wang et al., Phys. Rev. B 88, 115137 (2013); Metlitski et al., Phys. Rev. B 92, 125111 (2015)]. In this work, rather than considering topological phases at the boundary, we will study quantum critical points driven by vortexlike topological defects. In general, we will discuss a $(2+1)d$ quantum phase transition described by the following field theory: $\mathcal{L}=\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}_{\ensuremath{\mu}}({\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{-}i{a}_{\ensuremath{\mu}})\ensuremath{\psi}+|({\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{-}ik{a}_{\ensuremath{\mu}}){\ensuremath{\phi}|}^{2}+{r|\ensuremath{\phi}|}^{2}+g{|\ensuremath{\phi}|}^{4}$, with tuning parameter $r$, arbitrary integer $k$, Dirac fermion $\ensuremath{\psi}$, and complex scalar bosonic field $\ensuremath{\phi}$, which both couple to the same $(2+1)d$ dynamical noncompact U(1) gauge field ${a}_{\ensuremath{\mu}}$. The physical meaning of these quantities/fields will be explained in the text. Making use of the new duality formalism developed in [Metlitski et al., Phys. Rev. B 93, 245151 (2016); Wang et al., Phys. Rev. X 5, 041031 (2015); Wang et al., Phys. Rev. B 93, 085110 (2016); D. T. Son, Phys. Rev. X 5, 031027 (2015)], we demonstrate that this quantum critical point has a quasi-self-dual nature. And at this quantum critical point, various universal quantities such as the electrical conductivity and scaling dimension of gauge-invariant operators, can be calculated systematically through a $1/{k}^{2}$ expansion, based on the observation that the limit $k\ensuremath{\rightarrow}+\ensuremath{\infty}$ corresponds to an ordinary $3d XY$ transition.

In this paper we systematically classify and describe bosonic symmetry protected topological (SPT) phases in all physical spatial dimensions using semiclassical nonlinear Sigma model (NLSM) field theories. All the SPT phases on a $d-$dimensional lattice discussed in this paper can be described by the same NLSM, which is an O(d+2) NLSM in $(d+1)-$dimensional space-time, with a topological $\Theta-$term. The field in the NLSM is a semiclassical Landau order parameter with a unit length constraint. The classification of SPT phases discussed in this paper based on their NLSMs is consistent with the more mathematical classification based on group cohomology. Besides the classification, the formalism used in this paper also allows us to explicitly discuss the physics at the boundary of the SPT phases, and it reveals the relation between SPT phases with different symmetries. For example, it gives many of these SPT states a natural "decorated defect" construction., Comment: 16 pages

We demonstrate that the anyon statistics and three-loop statistics of various 2d and 3d topological phases can be derived using semiclassical nonlinear Sigma model field theories with a topological $\Theta$-term. In our formalism, the braiding statistics has a natural geometric meaning: The braiding process of anyons or loops leads to a nontrivial field configuration in the space-time, which will contribute a braiding phase factor due to the $\Theta$-term., Comment: 4 pages, 3 figures

A 3d symmetry protected topological phase, by definition must have symmetry protected nontrivial boundary states, namely its 2d boundary must be either gapless or degenerate. In this work we demonstrate that once we couple a 3d SPT phase to a lattice dynamical Z2 gauge field, in many cases the Z2 vison loop excitation (line defect) can be viewed as a "1d boundary" of the 3d SPT phase, and this line defect is guaranteed to have gapless or degenerate spectrum, which is also protected by the symmetry of the SPT phase., Comment: 5 pages, 2 figures