Entanglement entropy after selective measurements in quantum chains
arXiv:1608.04074 · doi:10.1007/JHEP12(2016)124
Abstract
We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.
Published version: 71 pages, 36 figures. added new references!
References in corpus (32)
- Towards a derivation of holographic entanglement entropy
- Entanglement negativity in quantum field theory
- Entanglement versus Correlations in Spin Systems
- Measuring entanglement growth in quench dynamics of bosons in an optical lattice
- Entanglement spectrum in one-dimensional systems
- Dephasing and the steady state in quantum many-particle systems
- Diverging Entanglement Length in Gapped Quantum Spin Systems
- Entanglement entropy of two disjoint intervals in conformal field theory II
- Relative entropy and the Bekenstein bound
- Localizable Entanglement
- Measuring entanglement entropy of a generic many-body system with a quantum switch
- Entanglement of low-energy excitations in Conformal Field Theory
- Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
- Finite temperature entanglement negativity in conformal field theory
- Entanglement entropy of two disjoint blocks in XY chains
- Entanglement negativity in the harmonic chain out of equilibrium
- Entanglement Entropy and Twist Fields
- Unusual Corrections to Scaling in Entanglement Entropy
- Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality
- Measuring entanglement using quantum quenches
- Comments on Entanglement Negativity in Holographic Field Theories
- Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
- Negativity spectrum of one-dimensional conformal field theories
- Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
- Entanglement entropy and negative energy in two dimensions
- Entanglement entropy in quantum spin chains with finite range interaction
- Universal behavior of the Shannon and Rényi mutual information of quantum critical chains
- Boundary Entropy Can Increase Under Bulk RG Flow
- Beyond Logarithmic Corrections to Cardy Formula
- Generalized mutual informations of quantum critical chains
- Entanglement entropy scaling in solid-state spin arrays via capacitance measurements
- Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories