Formation probabilities and Shannon information and their time evolution after quantum quench in transverse-field XY-chain

Abstract

We first provide a formula to calculate the probability of occurrence of different configurations (formation probabilities) in a generic free fermion system. We then study the scaling of these probabilities with respect to the size in the case of critical transverse-field XY-chain in the ${\sigma }^z$ bases. In the case of the transverse field Ising model, we show that all the "crystal" configurations follow the formulas expected from conformal field theory (CFT). In the case of critical $XX$ chain, we show that the only configurations that follow the formulas of the CFT are the ones which respect the filling factor of the system. By repeating all the calculations in the presence of open and periodic boundary conditions we find further support to our classification of different configurations. Using the developed technique, we also study Shannon information of a subregion in our system. In this respect we distinguish particular configurations that are more important in the study of the scaling limit of the Shannon information of the subsystem. Finally, we study the evolution of formation probabilities, Shannon information and Shannon mutual information after a quantum quench in free fermion system. In particular, for the intial state considered in this paper, we demonstrate that the Shannon information after quantum quench first increases with the time and then saturates at time $t^{\ast }=\frac{l}{2}$, where $l$ is the size of the subsystem.

V3: 16 pages, 14 figures. published version!

References in corpus (21)

• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Area laws in quantum systems: mutual information and correlations
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Dephasing and the steady state in quantum many-particle systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• General entanglement scaling laws from time evolution
• Evolution of entanglement after a local quench
• Rényi entropy of a line in two-dimensional Ising models
• Entanglement evolution after connecting finite to infinite quantum chains
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Universal behavior of a bipartite fidelity at quantum criticality
• Information theoretic aspects of the two-dimensional Ising model
• Universal behavior of the Shannon and Rényi mutual information of quantum critical chains
• Entanglement properties of correlated random spin chains and similarities with conformal invariant systems
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Generalized mutual informations of quantum critical chains
• On the emptiness formation probability of the open XXZ spin-$\tf{1}{2}$ chain
• Formation probabilities in quantum critical chains and Casimir effect
• Shared information in classical mean-field models

Cited by in corpus (21)

• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Full counting statistics of the subsystem energy in the free fermions and the quantum spin chains
• Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact results
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Formation probabilities and statistics of observables as defect problems in the free fermions and the quantum spin chains
• Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain
• Entanglement entropy after selective measurements in quantum chains
• Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains
• Formation probabilities in quantum critical chains and Casimir effect
• Emptiness formation probability and Painlevé V equation in the XY spin chain
• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• The non-stabilizerness of fermionic Gaussian states
• Universal logarithmic correction to Rényi (Shannon) entropy in generic systems of critical quadratic fermions
• Entanglement entropy in quantum spin chains with broken parity number symmetry
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Area law and universality in the statistics of subsystem energy
• Efficient Representation of Gaussian Fermionic Pure States in Non-Computational Bases
• Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases
• Shannon entropy in quasiparticle states of quantum chains
• Measurement-Induced Entanglement in Conformal Field Theory
• Statistical physics of principal minors: Cavity approach