Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional Clifford circuits

Entanglement transitions in quantum dynamics present a novel class of phase transitions in nonequilibrium systems. When a many-body quantum system undergoes unitary evolution interspersed with monitored random measurements, the steady state can exhibit a phase transition between volume- and area-law entanglement. There is a correspondence between measurement-induced transitions in nonunitary quantum circuits in d spatial dimensions and classical statistical mechanical models in d + 1 dimensions. In certain limits these models map to percolation, but there is analytical and numerical evidence to suggest that away from these limits the universality class should generically be distinct from percolation. Intriguingly, despite these arguments, numerics on 1 + 1 D qubit circuits give bulk exponents which are nonetheless close to those of 2D percolation, with some possible differences in surface behavior. In the first part of this work we explore the critical properties of 2 + 1 D Clifford circuits. In the bulk, we find many properties suggested by the percolation picture, including several matching bulk exponents, and an inverse power law for the critical entanglement growth, S ( t , L ) ∼ L ( 1 − a / t ) , which saturates to an area law. We then utilize a graph-state-based algorithm to analyze in 1 + 1 D and 2 + 1 D the critical properties of entanglement clusters in the steady state. We show that in a model with a simple geometric map to percolation—the projective transverse field Ising model—these entanglement clusters are governed by percolation surface exponents. However, in the Clifford models we find large deviations in the cluster exponents from those of surface percolation, highlighting the breakdown of any possible geometric map to percolation. Given the evidence for deviations from the percolation universality class, our results raise the question of why nonetheless many bulk properties behave similarly to those of percolation

Thermodynamics of localized magnetic moments in a Dirac conductor

We show that the magnetic susceptibility of a dilute ensemble of magnetic impurities in a conductor with a relativistic electronic spectrum is non-analytic in the inverse tempertature at $1/T\to 0$. We derive a general theory of this effect and construct the high-temperature expansion for the disorder averaged susceptibility to any order, convergent at all tempertaures down to a possible ordering transition. When applied to Ising impurities on a surface of a topological insulator, the proposed general theory agrees with Monte Carlo simulations, and it allows us to find the critical temperature of the ferromagnetic phase transition.Comment: 5 pages, 1 figure, 2 tables, RevTe

Diagnostics of entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition

We utilize the concept of a measurement-induced entanglement transition to analyze the interplay and competition of processes that generate and destroy entanglement in a one-dimensional quantum spin chain evolving under a locally noisy and disordered Hamiltonian. We employ continuous measurements of variable strength to induce a transition from volume to area-law scaling of the steady-state entanglement entropy. While static background disorder systematically reduces the critical measurement strength, this critical value depends nonmonotonically on the strength of nonstatic noise. According to the extracted finite-size scaling exponents, the universality class of the transition is independent of the noise and disorder strength. We interpret the results in terms of the effect of static and nonstatic disorder on the intricate dynamics of the entanglement generation rate due to the Hamiltonian in the absence of measurement, which is fully reflected in the behavior of the critical measurement strength. Our results establish a firm connection between this entanglement growth and the steady-state behavior of the measurement-controlled systems, which therefore can serve as a tool to quantify and investigate features of transient entanglement dynamics in complex many-body systems via a steady-state phase transition

Binding energies of trions and biexcitons in two-dimensional semiconductors from diffusion quantum Monte Carlo calculations

Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional (2D) semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide statistically exact diffusion quantum Monte Carlo binding-energy data for Mott-Wannier models of excitons, trions, and biexcitons in 2D semiconductors. We also provide contact pair densities to allow a description of contact (exchange) interactions between charge carriers using first-order perturbation theory. Our data indicate that the binding energy of a trion is generally larger than that of a biexciton in 2D semiconductors. We provide interpolation formulas giving the binding energy and contact density of 2D semiconductors as functions of the electron and hole effective masses and the in-plane polarizability.</p

Diagnosing entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition

We utilize the concept of a measurement-induced entanglement transition to analyze the interplay and competition of processes that generate and destroy entanglement in a one-dimensional quantum spin chain evolving under a locally noisy and disordered Hamiltonian. We employ continuous measurements of variable strength to induce a transition from volume to area-law scaling of the steady-state entanglement entropy. While static background disorder systematically reduces the critical measurement strength, this critical value depends non-monotonically on the strength of non-static noise. According to the extracted fine-size scaling exponents, the universality class of the transition is independent of the noise and disorder strength. We interpret the results in terms of the effect of static and non-static disorder on the intricate dynamics of the entanglement generation rate due to the Hamiltonian in the absence of measurement, which is fully reflected in the behavior of the critical measurement strength. Our results establish a firm connection between this entanglement growth and the steady-state behavior of the measurement-controlled systems, which therefore can serve as a tool to quantify and investigate features of transient entanglement dynamics in complex many-body systems via a steady-state phase transition

Diffusion quantum Monte Carlo study of excitonic complexes in two-dimensional transition-metal dichalcogenides

Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide (i) statistically exact diffusion quantum Monte Carlo binding-energy data for a Mott-Wannier model of (donor/acceptor-bound) excitons, trions, and biexcitons in two-dimensional semiconductors in which charges interact via the Keldysh potential, (ii) contact pair-distribution functions to allow a perturbative description of contact interactions between charge carriers, and (iii) an analysis and classification of the different types of bright trions and biexcitons that can be seen in single-layer molybdenum and tungsten dichalcogenides. We investigate the stability of biexcitons in which two charge carriers are indistinguishable, finding that they are only bound when the indistinguishable particles are several times heavier than the distinguishable ones. Donor/acceptor-bound biexcitons have similar binding energies to the experimentally measured biexciton binding energies. We predict the relative positions of all stable free and bound excitonic complexes of distinguishable charge carriers in the photoluminescence spectra of WSe2 and MoSe2

Towards the Design of Cold-formed Steel Foam Sandwich Columns

In this paper a design method for the compressive capacity of sandwich panels comprised of steel face sheets and foamed steel cores is derived and verified. Foamed steel, literally steel with internal voids, provides the potential to mitigate many local stability issues through increasing the effective width-to thickness of the component for the same amount of material. Winter’s classical effective width expression was generalized to the case of steel foam sandwich panels. The provided analytical expressions are verified with finite element simulations employing brick elements that explicitly model the steel face sheets and steel foam cores. The closed-form design expressions are employed to conduct parametric studies of steel foam sandwich panels with various face sheet and steel foamed core configurations. The studies show the significant strength improvements possible with steel foam sandwich panels when compared with plain steel sheet/plate

Charge-carrier complexes in monolayer semiconductors

The photoluminescence (PL) spectra of monolayer (1L) semiconductors feature peaks ascribed to different charge-carrier complexes. We perform diffusion quantum Monte Carlo simulations of the binding energies of these complexes and examine their response to electric and magnetic fields. We focus on quintons (charged biexcitons), since they are the largest free charge-carrier complexes in transition-metal dichalcogenides (TMDs). We examine the accuracy of the Rytova-Keldysh interaction potential between charges by comparing the binding energies of charge-carrier complexes in 1L-TMDs with results obtained using $\textit{ab initio}$ interaction potentials. Magnetic fields$<8$T change the binding energies (BEs) by$\sim0.2$ meV,T$^{-1}$, in agreement with experiments, with the BE variations of different complexes being very similar. Our results will help identify charge complexes in the PL spectra of 1L-semiconductor