Universal logarithmic correction to Rényi (Shannon) entropy in generic systems of critical quadratic fermions

Abstract

The Rényi (Shannon) entropy, i.e. $R{e}_{\alpha }(Sh)$, of the ground state of quantum systems in local bases normally show a volume-law behavior. For a subsystem of quantum chains at critical point there is an extra logarithmic subleading term with a coefficient which is universal. In this paper we study this coefficient for generic time-reversal translational invariant quadratic critical free fermions. These models can be parameterized by a complex function which has zeros on the unit circle. When the zeros on the unit circle do not have degeneracy and there is no zero outside of the unit circle we are able to classify the coefficient of the logarithm. In particular, we numerically calculate the Rényi (Shannon) entropy in configuration basis for wide variety of these models and show that there are two distinct classes. For systems with $U(1)$ symmetry the coefficient is proportional to the central charge, i.e. one half of the number of points that one can linearize the dispersion relation of the system; for all the values of $\alpha$ with transition point at $\alpha =4$. For systems without this symmetry, when $\alpha >1$ this coefficient is again proportional to the central charge. However, the coefficient for $\alpha \le 1$ is a new universal number. Finally, by using the discrete version of Bisognano-Wichmann modular Hamiltonian of the Ising chain we show that these coefficients are universal and dependent on the underlying CFT.

arXiv commentv2: 16 pages, 10 figures published version

References in corpus (36)

• Renormalization Group Approach to Interacting Fermions
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Reduced density matrices and entanglement entropy in free lattice models
• Area laws in quantum systems: mutual information and correlations
• Notes on Some Entanglement Properties of Quantum Field Theory
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Topology and edge modes in quantum critical chains
• Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
• Universal behavior beyond multifractality in quantum many-body systems
• Rényi entropy of a line in two-dimensional Ising models
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Shannon and Rényi mutual information in quantum critical spin chains
• Analytical results for the entanglement Hamiltonian of a free-fermion chain
• Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain
• Universal behavior of the Shannon mutual information of critical quantum chains
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Entanglement, combinatorics and finite-size effects in spin-chains
• Properties of the entanglement Hamiltonian for finite free-fermion chains
• Entanglement entropy in quantum spin chains with finite range interaction
• Shannon-Rényi entropies and participation spectra across 3d $O(3)$ criticality
• Information theoretic aspects of the two-dimensional Ising model
• Emptiness formation probability, Toeplitz determinants, and conformal field theory
• Universal behavior of the Shannon and Rényi mutual information of quantum critical chains
• Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
• Entanglement Hamiltonian of quantum critical chains and conformal field theories
• Entanglement properties of correlated random spin chains and similarities with conformal invariant systems
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Generalized mutual informations of quantum critical chains
• Formation probabilities and Shannon information and their time evolution after quantum quench in transverse-field XY-chain
• Measuring von Neumann entanglement entropies without wave functions
• 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
• Emptiness formation probability and Painlevé V equation in the XY spin chain
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain

Cited by in corpus (6)

• The non-stabilizerness of fermionic Gaussian states
• Topological physics in quantum critical systems
• Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases
• Efficient Representation of Gaussian Fermionic Pure States in Non-Computational Bases
• Shannon entropy in quasiparticle states of quantum chains
• Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains