Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems

Abstract

We propose that the properties of the capacity of entanglement (COE) in gapless systems can efficiently be investigated through the use of the distribution of eigenvalues of the reduced density matrix (RDM). The COE is defined as the fictitious heat capacity calculated from the entanglement spectrum. Its dependence on the fictitious temperature can reflect the low-temperature behavior of the physical heat capacity, and thus provide a useful probe of gapless bulk or edge excitations of the system. Assuming a power-law scaling of the COE with an exponent $\alpha$ at low fictitious temperatures, we derive an analytical formula for the distribution function of the RDM eigenvalues. We numerically test the effectiveness of the formula in relativistic free scalar boson in two spatial dimensions, and find that the distribution function can detect the expected $\alpha =3$ scaling of the COE much more efficiently than the raw data of the COE. We also calculate the distribution function in the ground state of the half-filled Landau level with short-range interactions, and find a better agreement with the $\alpha =2/3$ formula than with the $\alpha =1$ one, which indicates a non-Fermi-liquid nature of the system.

arXiv comment9 pages, 4 figures

References in corpus (71)

• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Calculation of reduced density matrices from correlation functions
• Quantum entanglement in condensed matter systems
• Reduced density matrices and entanglement entropy in free lattice models
• Entanglement entropy in free quantum field theory
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Violation of the entropic area law for Fermions
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Hidden Fermi surfaces in compressible states of gauge-gravity duality
• Entanglement spectrum in one-dimensional systems
• Entanglement spectrum of topological insulators and superconductors
• Is the Composite Fermion a Dirac Particle?
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Holographic Fermi Surfaces and Entanglement Entropy
• Entanglement Entropy and the Fermi Surface
• The entanglement gap and a new principle of adiabatic continuity
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Entanglement Entropy in the O(N) model
• Bulk-Edge Correspondence in the Entanglement Spectra
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• The half-filled Landau level: the case for Dirac composite fermions
• A geometric proof of the equality between entanglement and edge spectra
• Universal entanglement entropy in 2D conformal quantum critical points
• Entanglement entropy of critical spin liquids
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• Real-Space Entanglement Spectrum of Quantum Hall States
• How universal is the entanglement spectrum?
• Renyi Entropies for Free Field Theories
• Real-space entanglement spectrum of quantum Hall systems
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Universal crossovers between entanglement entropy and thermal entropy
• Negativity spectrum of one-dimensional conformal field theories
• Composite fermi liquids in the lowest Landau level
• Renyi Entropy of the Interacting Fermi Liquid
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• A Holographic Proof of Rényi Entropic Inequalities
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Operator content of real-space entanglement spectra at conformal critical points
• Conformal Field Theory on the Fermi Surface
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Entanglement Thermodynamics
• Negativity spectrum in 1D gapped phases of matter
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Quantum Entanglement and Thermal Reduced Density Matrices in Fermion and Spin Systems on Ladders
• Particle-hole symmetry and electromagnetic response of a half-filled Landau level
• Entanglement Entropy of Annulus in Three Dimensions
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula
• Specific heat and validity of quasiparticle approximation in the half-filled Landau level
• Probing Critical Surfaces in Momentum Space Using Real-Space Entanglement Entropy: Bose versus Fermi

Cited by in corpus (10)

• Probing Hawking radiation through capacity of entanglement
• Aspects of capacity of entanglement
• Replica wormholes and capacity of entanglement
• Negativity Spectrum in the Random Singlet Phase
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Eigenstate capacity and Page curve in fermionic Gaussian states
• Capacity of Entanglement in Local Operators
• Capacity of entanglement in random pure state
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair
• Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair