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{"Abstract":["The data in this repository appear in Figs. 2 and 3 in the manuscript titled "Symmetry Fragmentation" (arXiv:2510.06333, to appear in PRL). Fig. 2 has two time series, one colored orange and one colored green; the data for each time series are stored as separate files with corresponding names.\n\n\n\n\n "]} 

Data associated with the plots for the paper “Post-selected Criticality of Measurement-Induced Phase Transitions.”Each dataset used to generate a figure in the paper is organized into a folder named after the corresponding figure number. Within each figure folder, there are two subfolders containing data for: random quantum circuits (RQC), and random tensor networks (RTN). The github repository with the codes to generate the data is https://github.com/dollynambi/Codes-for-Post-selected-MIPT. For any questions, please contact: dazhak1@lsu.edu 

This repository contains the codes for the figures generated in the article Post-selected Criticality in Measurement-induced Phase Transitions. If you use these codes, please cite it as below. 

{"Abstract":["This repository contains the data used to produce Figure 2 in the manuscript titled "Profusion of Symmetry-Protected Qubits from Stable Ergodicity Breaking" (arXiv:2512.20393, to appear in PRB). The data are stored in an h5 file, and the included Python notebook reads in the h5 file and reproduces the published figure."]} 

We consider a recently discovered mathematical correspondence between the spectra of a naively discretized lattice fermion and that of a periodically driven (i.e., Floquet) quantum system and enhance it into an infrared equivalence between the two systems. The equivalence can be framed as a duality relation, allowing us to simulate a two-flavor discrete-time fermion theory on the lattice side, where the two flavors arise from time discretization, using a single-flavor fermion theory on the Floquet side. Our demonstration establishes an equivalence between (i) the fermion content, (ii) the correlation functions, and consequently (iii) observables of the two theories in the infrared, going substantially beyond the previously discovered spectral equivalence. We also show how interactions may be incorporated into this enhanced infrared equivalence. 

Confinement is a prominent phenomenon in condensed-matter and high-energy physics that has recently become the focus of quantum-simulation experiments of lattice gauge theories (LGTs). As such, a theoretical understanding of the effect of confinement on LGT dynamics is not only of fundamental importance but also can lend itself to upcoming experiments. Here we show how confinement in a ${\mathbb{Z}}_2$LGT can be avoided by proximity to a resonance between the fermion mass and the electric field strength. Furthermore, we show that this local deconfinement can become global for certain initial conditions, where information transport occurs over the entire chain. In addition, we show how this can lead to strong quantum many-body scarring starting in different initial states. Our findings provide deeper insights into the nature of confinement in ${\mathbb{Z}}_2$LGTs and can be tested on current and near-term quantum devices. 

Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a conserved density, require a notion of spatially local interactions. We study the transport of the energy, the most basic conserved density, in few-body and 1D chains of nearest-neighbor random matrix terms that square to one, which we dub the “Haar-Ising” local random matrix model. In the few-body but large local Hilbert space dimension case, we develop a mapping for the energy dynamics to a single-particle hopping picture. This allows for the computation of the energy density autocorrelators and an out-of-time-ordered correlator of the energy density. In the 1D chain, we numerically study the energy transport for a small local Hilbert space dimension. Throughout, we discuss the density of states and touch upon the relation to free probability theory. 

Adaptive quantum circuits—where a quantum many-body state is controlled using measurements and conditional unitary operations—are a powerful paradigm for state preparation and quantum error-correction tasks. They can support two types of nonequilibrium quantum phase transitions: measurement-induced transitions between volume- and area-law-entangled steady states and control-induced transitions where the system falls into an absorbing state or, more generally, an orbit visiting several absorbing states. Within this context, nonlocal conditional operations can alter the critical properties of the two transitions and the topology of the phase diagram. Here, we consider the scenario where the measurements are , in order to engineer efficient control onto dynamical trajectories. Motivated by Rydberg-atom arrays, we consider a locally constrained model with global sublattice magnetization measurements and local correction operations to steer the system’s dynamics onto a many-body orbit with finite recurrence time. The model has a well-defined classical limit, which we leverage to aid our analysis of the control transition. As a function of the density of local correction operations, we find control and entanglement transitions with continuously varying critical exponents. For sufficiently high densities of local correction operations, we find that both transitions acquire a dynamical critical exponent $z<1$, reminiscent of criticality in long-range power-law interacting systems. At low correction densities, we find that the criticality reverts to a short-range nature with $z\gtrsim 1$. In the long-range regime, the control and entanglement transitions are indistinguishable to within the resolution of our finite-size numerics, while in the short-range regime we find evidence that the transitions become distinct. We conjecture that the effective long-range criticality mediated by collective measurements is essential in driving the two transitions together. Published by the American Physical Society2025