Entanglement negativity and conformal field theory: a Monte Carlo study

Abstract

We investigate the behavior of the moments of the partially transposed reduced density matrix ρ^{T_2}_A in critical quantum spin chains. Given subsystem A as union of two blocks, this is the (matrix) transposed of ρ_A with respect to the degrees of freedom of one of the two. This is also the main ingredient for constructing the logarithmic negativity. We provide a new numerical scheme for calculating efficiently all the moments of ρ_A^{T_2} using classical Monte Carlo simulations. In particular we study several combinations of the moments which are scale invariant at a critical point. Their behavior is fully characterized in both the critical Ising and the anisotropic Heisenberg XXZ chains. For two adjacent blocks we find, in both models, full agreement with recent CFT calculations. For disjoint ones, in the Ising chain finite size corrections are non negligible. We demonstrate that their exponent is the same governing the unusual scaling corrections of the mutual information between the two blocks. Monte Carlo data fully match the theoretical CFT prediction only in the asymptotic limit of infinite intervals. Oppositely, in the Heisenberg chain scaling corrections are smaller and, already at finite (moderately large) block sizes, Monte Carlo data are in excellent agreement with the asymptotic CFT result.

31 pages, 10 figures. Minor changes, published version

References in corpus (19)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement negativity in quantum field theory
• Entropy scaling and simulability by Matrix Product States
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Scaling of entanglement support for Matrix Product States
• A holographic proof of the strong subadditivity of entanglement entropy
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Remarks on the entanglement entropy for disconnected regions
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• Entanglement Entropy and Twist Fields
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Scaling of entanglement between separated blocks in spin chains at criticality
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• Holographic entanglement entropy for disconnected regions
• Finite Temperature Critical Behavior of Mutual Information
• The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
• Holographic entanglement entropy: near horizon geometry and disconnected regions
• Entanglement of two blocks of spins in the critical Ising model

Cited by in corpus (59)

• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Finite temperature entanglement negativity in conformal field theory
• Partial time-reversal transformation and entanglement negativity in fermionic systems
• Entanglement negativity and topological order
• Negativity and topological order in the toric code
• On the partial transpose of fermionic Gaussian states
• The entanglement negativity in random spin chains
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Entanglement negativity after a local quantum quench in conformal field theories
• Entanglement negativity bounds for fermionic Gaussian states
• Symmetry decomposition of negativity of massless free fermions
• Twisted and untwisted negativity spectrum of free fermions
• Negativity spectrum of one-dimensional conformal field theories
• Disentangling Theorem and Monogamy for Entanglement Negativity
• Entanglement negativity via replica trick: a Quantum Monte Carlo approach
• Entanglement negativity in two-dimensional free lattice models
• Entanglement Renyi negativity across a finite temperature transition: a Monte Carlo study
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Out-of-equilibrium protocol for Rényi entropies via the Jarzynski equality
• Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution
• Mixed state entanglement measures as probe for confinement
• Negativity Spectrum in the Random Singlet Phase
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Entanglement negativity in free-fermion systems: An overlap matrix approach
• Multi-charged moments of two intervals in conformal field theory
• Geometric mutual information at classical critical points
• Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case
• Entanglement negativity between separated regions in quantum critical systems
• Entanglement entropy from non-equilibrium Monte Carlo simulations
• The Early Universe as an Open Quantum System: Complexity and Decoherence
• Decoherence, Entanglement Negativity and Circuit Complexity for Open Quantum System
• Entanglement of two disjoint intervals in conformal field theory and the 2D Coulomb gas on a lattice
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Holographic confining/deconfining gauge theories and entanglement measures with a magnetic field
• Entanglement entropy after selective measurements in quantum chains
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Entanglement Microscopy: Tomography and Entanglement Measures via Quantum Monte Carlo
• Klein bottle entropy of compactified boson conformal field theory
• Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
• Distilling topological entropy from single entanglement measures on projected systems
• Multipartite entanglement and quantum Fisher information in conformal field theories
• Tracking the variation of entanglement Rényi negativity: a quantum Monte Carlo study
• Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations
• The classical mutual information in mean-field spin glass models
• An entropy perspective on the thermal crossover in a fermionic Hubbard chain
• Holographic Entanglement negativity in flat space generalized minimal massive gravity
• Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Quench dynamics of Rényi negativities and the quasiparticle picture
• Entanglement Negativity and Defect Extremal Surface
• Symmetry protected entanglement in random mixed states
• Entanglement in Lifshitz Fermion Theories
• Rényi entropy of quantum anharmonic chain at non-zero temperature
• Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point
• Quench dynamics of negativity Hamiltonians
• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d
• A contour for the entanglement negativity of bosonic Gaussian states