Entanglement entropies of inhomogeneous Luttinger liquids

Abstract

We develop a general framework to compute the scaling of entanglement entropy in inhomogeneous one-dimensional quantum systems belonging to the Luttinger liquid universality class. While much insight has been gained in homogeneous systems by making use of conformal field theory techniques, our focus is on systems for which the Luttinger parameter $K$ depends on position, and conformal invariance is broken. An important point of our analysis is that contributions stemming from the UV cutoff have to be treated very carefully, since they now depend on position. We show that such terms can be removed either by considering regularized entropies specifically designed to do so, or by tabulating numerically the cutoff, and reconstructing its contribution to the entropy through the local density approximation. We check our method numerically in the spin-1/2 XXZ spin chain in a spatially varying magnetic field, and find excellent agreement.

19 pages, 4 figures

References in corpus (22)

• Bosonizing one-dimensional cold atomic gases
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Relaxation in the XX quantum chain
• Universal correlations of trapped one-dimensional impenetrable bosons
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Connecting distant ends of one-dimensional critical systems by a sine-square deformation
• Entanglement entropy and negative energy in two dimensions
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Entanglement in spin chains with gradients
• Front dynamics and entanglement in the XXZ chain with a gradient
• More on the rainbow chain: entanglement, space-time geometry and thermal states
• Exact ground state of the sine-square deformed XY spin chain
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Free fermions at the edge of interacting systems
• Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
• Front dynamics in the XY chain after local excitations
• Hydrodynamic description of Hard-core Bosons on a Galileo ramp
• General finite-size effects for zero-entropy states in one-dimensional quantum integrable models
• Rényi entanglement entropies for the compactified massless boson with open boundary conditions

Cited by in corpus (25)

• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Boundary effects on symmetry resolved entanglement
• Domain-wall melting in the spin-$1/2$ XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Experimental Observation of Curved Light-Cones in a Quantum Field Simulator
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• Time evolution of entanglement negativity across a defect
• Multi-charged moments of two intervals in conformal field theory
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Entanglement spreading and quasiparticle picture beyond the pair structure
• Scaling of fronts and entanglement spreading during a domain wall melting
• Entanglement entropies of an interval for the massless scalar field in the presence of a boundary
• Exact Dirac-Bogoliubov-de Gennes Dynamics for Inhomogeneous Quantum Liquids
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Holographic Entanglement Entropy of the Coulomb Branch
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Probing universal critical scaling with scan-DMRG
• One-body correlations and momentum distributions of trapped one-dimensional Bose gases at finite temperature
• Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Electrostatic solution of massless quenches in Luttinger liquids
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain