Formation probabilities in quantum critical chains and Casimir effect

Abstract

We find a connection between logarithmic formation probabilities of two disjoint intervals of quantum critical spin chains and the Casimir energy of two aligned needles in two dimensional classical critical systems. Using this connection we provide a formula for the logarithmic formation probability of two disjoint intervals in generic $1+1$ dimensional critical systems. The quantity is depenedent on the full structure of the underlying conformal field theory and so useful to find the universality class of the critical system. The connection that we find also provides a very efficient numerical method to calculate the Casimir energy between needles using quantum critical chains. The agreement between numerical results performed on critical transverse field Ising model and XX chain with our exact results is very good. We also comment on the mutual Rényi information of two disjoint intervals.

v2: 8 pages, 3 figures

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Cited by in corpus (13)

• Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact results
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Characterizing quantum correlations in spin chains
• Formation probabilities and Shannon information and their time evolution after quantum quench in transverse-field XY-chain
• Formation probabilities and statistics of observables as defect problems in the free fermions and the quantum spin chains
• Entanglement entropy after selective measurements in quantum chains
• Emptiness formation probability and Painlevé V equation in the XY spin chain
• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• Classification of the sign of the critical Casimir force in two dimensional systems at asymptotically large separations
• Casimir interaction of rod-like particles in a two-dimensional critical system
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Area law and universality in the statistics of subsystem energy
• Shannon entropy in quasiparticle states of quantum chains