Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling

Abstract

Quantum circuits offer a versatile platform for simulating digital quantum dynamics and uncovering novel states of non-equilibrium quantum matter. One principal example are measurement-induced phase transitions arising from non-unitary dynamics in monitored circuits, which employ mid-circuit measurements as an essential building block next to standard unitary gates. Although a comprehensive understanding of dynamics in generic circuits is still evolving, we contend that monitored quantum circuits yield robust phases of dynamic matter, which -- akin to Hamiltonian ground state phases -- can be categorized based on symmetries and spatial dimensionality. To illustrate this concept, we focus on quantum circuits within symmetry classes BDI and D, which are measurement-only adaptations of the paradigmatic Kitaev and Yao-Kivelson models, embodying particle-hole-symmetric Majorana fermions with or without time-reversal. We establish a general framework -- Majorana loop models -- for both symmetry classes to provide access to the phenomenology of the entanglement dynamics in these circuits, displaying both an area-law phase of localized Majorana loops and a delocalized, highly entangled Majorana liquid phase. The two phases are separated by a continuous transition displaying quantum Lifshitz scaling, albeit with critical exponents of two distinct universality classes. The loop model framework provides not only analytical understanding of these universality classes in terms of non-linear sigma models, but also allows for highly efficient numerical techniques capable of simulating excessively large circuits with up to $10^8$ qubits. We utilize this framework to accurately determine universal probes that distinguish both the entangled phases and the critical points of the two symmetry classes. Our work thereby further solidifies the concept of emergent circuit phases and their phase transitions.

References in corpus (90)

• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Quantum Spin Liquids
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Random Quantum Circuits
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Violation of the entropic area law for Fermions
• Interacting anyons in topological quantum liquids: The golden chain
• Stim: a fast stabilizer circuit simulator
• An exact chiral spin liquid with non-Abelian anyons
• Topological Order and Conformal Quantum Critical Points
• Scalable probes of measurement-induced criticality
• Measurement-Only Topological Quantum Computation
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Entanglement phase transitions in measurement-only dynamics
• Vaporization of Kitaev spin liquids
• Measurement-induced criticality in (2+1)-d hybrid quantum circuits
• Entanglement Entropy and the Fermi Surface
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Bond and Site Percolation in Three Dimensions
• Dynamically Generated Logical Qubits
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Quantum criticality under decoherence or weak measurement
• Classification of gapless Z2 spin liquids in three-dimensional Kitaev models
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Entanglement Transition in the Projective Transverse Field Ising Model
• The two-dimensional random-bond Ising model, free fermions and the network model
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Anomalies in the Entanglement Properties of the Square Lattice Heisenberg Model
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Simultaneous analysis of three-dimensional percolation models
• Topological order and criticality in (2+1)D monitored random quantum circuits
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Ground state projection of quantum spin systems in the valence bond basis
• Theory of free fermions under random projective measurements
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• Entanglement Negativity at Measurement-Induced Criticality
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Chiral Symmetry Breaking, Deconfinement and Entanglement Monotonicity
• Nonlinear sigma models for monitored dynamics of free fermions
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• 3D loop models and the CP^{n-1} sigma model
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
• Field theory of compact polymers on the square lattice
• Floquet codes without parent subsystem codes
• Entanglement transitions with free fermions
• Analysis of a fully packed loop model arising in a magnetic Coulomb phase
• Degeneracy and criticality from emergent frustration in artificial spin ice
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Loop models with crossings
• Phase transitions in 3D loop models and the $C{P}^{n-1}$ $\sigma$ model
• Entanglement at a Two-Dimensional Quantum Critical Point: a T=0 Projector Quantum Monte Carlo Study
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• From discrete to continuous percolation in dimensions 3 to 7
• Majorana Loop Models for Measurement-Only Quantum Circuits
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Entanglement in gapless resonating valence bond states
• Universal statistics of vortex lines
• Length Distributions in Loop Soups
• Loop models and their critical points
• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
• Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
• Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
• Rényi entanglement entropies in quantum dimer models : from criticality to topological order
• Engineering 3D Floquet codes by rewinding
• Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model
• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra
• Kitaev model and dimer coverings on the honeycomb lattice
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions
• Scaling of entanglement in $2+1$-dimensional scale-invariant field theories
• A Bionic Coulomb Phase on the Pyrochlore Lattice
• Quantum Network Models and Classical Localization Problems
• On the universality of compact polymers
• Frustrated colloidal ordering and fully packed loops in arrays of optical traps
• A numerical study of the 3D random interchange and random loop models
• Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits
• Entanglement entropy and particle number cumulants of disordered fermions
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Quantum criticality of loops with topologically constrained dynamics
• Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• Critical spin chains and loop models with $PSU(n)$ symmetry
• Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions

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