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We develop solvable models of large-$N$ hybrid quantum circuits on qubits and fermions with long-range power-law interactions and continuous local monitoring, which provide analytical access to the entanglement phase diagram and error-correcting properties of many-body entangled non-equilibrium states generated by such dynamics. In one dimension, the long-range coupling is irrelevant for $\alpha>3/2$, where $\alpha$ is the power-law exponent, and the models exhibit a conventional measurement-induced phase transition between volume- and area-law entangled phases. For $1/2, Comment: 8+12 pages, 6 figures, v2 close to published version

We study the effect of disorder on the spacetime supersymmetry that is proposed to emerge at the quantum critical point of pair density wave transition in (2+1)D Dirac semimetals and (3+1)D Weyl semimetals. In the (2+1)D Dirac semimetal, we consider three types of disorder, including random scalar potential, random vector potential and random mass potential, while the random mass disorder is absent in the (3+1)D Weyl semimetal. Via a systematic renormalization group analysis, we find that any type of weak random disorder is irrelevant due to the couplings between the disorder potential and the Yukawa vertex. The emergent supersymmetry is thus stable for weak random potentials. Our work will pave the way for exploration supersymmetry in realistic condensed matter systems.

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

Many key features of the higher-dimensional Sachdev-Ye-Kitaev (SYK) model at {\it finite} $N$ remain unknown. Here we study the SYK chain consisting of $N$ ($N$$\ge$$2$) fermions per site with random interactions and hoppings between neighboring sites. In the limit of vanishing SYK interactions, from both supersymmetric field theory analysis and numerical calculations we find that the random hopping model exhibits Anderson localization at finite $N$, irrespective of the parity of $N$. Moreover, the localization length scales linearly with N, implying no Anderson localization \textit{only} at $N\!=\!\infty$. For finite SYK interaction $J$ , from the exact diagonalization we show that there is a dynamic phase transition between many-body localization and thermal diffusion as $J$ exceeds a critical value $J_c$. In addition, we find that the critical value $J_c$ decreases with the increase of $N$, qualitatively consistent with the analytical result of $J_c/t \!\propto\! \frac{1}{N^{5/2}\log N}$ derived from the weakly interacting limit., Published version

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an ${\mathrm{AdS}}_{2}$ chain. Specifically, by studying a double-trace deformation of a ${Z}_{2}$ scalar in an ${\mathrm{AdS}}_{2}$ chain where the ${Z}_{2}$ scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an ${\mathrm{AdS}}_{2}$ chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon ${\mathrm{AdS}}_{2}$ space-time.

It was recently shown that nonsymmorphic space group symmetries can protect novel surface states with hourglass-like dispersions. In this paper, we show that such dispersions can also appear in the bulk of three-dimensional (3D) systems which respect nonsymmorphic symmetries. Specifically, we construct 3D lattice models featuring hourglass-like dispersions in the bulk, which are protected by nonsymmorphic and time-reversal symmetries. We call such systems hourglass semimetals, as they have point or line nodes associated with hourglass-like dispersions. Hourglass nodal lines appear in glide-invariant planes, while hourglass Weyl points can occur on screw-invariant axes. The Weyl points and surface Fermi arcs in hourglass Weyl semimetals are stable against weak perturbations breaking those nonsymmorphic symmetries. Our results may shed light on searching for exotic Weyl semimetals in nonsymmorphic materials., 6 pages, 5 figures + Supplemental Material, published versioin

We study the fate of double-Weyl fermions in three-dimensional systems in the presence of long-range Coulomb interactions. By employing the momentum-shell renormalization-group approach, we find that the fixed point of noninteracting double-Weyl fermions is unstable against Coulomb interactions and flows to a nontrivial stable fixed point with anisotropic screening effect. Moreover, experimentally measurable quantities such as specific heat obtain unusual logarithmic corrections. We also discuss implications of our results to three-dimensional materials ${\mathrm{HgCr}}_{2}{\mathrm{Se}}_{4}$ and ${\mathrm{SrSi}}_{2}$, candidate materials of hosting double-Weyl fermions.