In a critical free-fermion chain, after partial projective measurements the entanglement Hamiltonian is a local grand-canonical operator: a measurement-independent inverse temperature times a local chemical potential that encodes the induced charge density.
Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals
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abstract
We consider free-fermion chains in the ground state and the entanglement Hamiltonian for a subsystem consisting of two separated intervals. In this case, one has a peculiar long-range hopping between the intervals in addition to the well-known and dominant short-range hopping. We show how the continuum expressions can be recovered from the lattice results for general filling and arbitrary intervals. We also discuss the closely related case of a single interval located at a certain distance from the end of a semi-infinite chain and the continuum limit for this problem. Finally, we show that for the double interval in the continuum a commuting operator exists which can be used to find the eigenstates.
fields
cond-mat.stat-mech 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
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Measurement-induced entanglement Hamiltonian
In a critical free-fermion chain, after partial projective measurements the entanglement Hamiltonian is a local grand-canonical operator: a measurement-independent inverse temperature times a local chemical potential that encodes the induced charge density.