Entanglement spectra & Hamiltonians at criticality
Entanglement spectra and Hamiltonians reveal aspects of criticality that are invisible to entropy scaling alone. I study how conformal operator content appears in entanglement levels, how the level spacings scale, and what the spatial form of the entanglement Hamiltonian says about locality. Time evolution, temperature, and measurements provide ways to test which of these structures are robust and which can change independently.
Papers
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A critical state under weak measurement is not critical
Journal of High Energy Physics 09 (2025) 168
We show that weak measurement of a critical free-fermion ground state can preserve logarithmic entanglement entropy while breaking conformal symmetry. Treating the measurement as a conformal defect at a fixed time gives an analytic mapping between the original and measured entanglement Hamiltonians. Even arbitrarily weak measurement opens an entanglement gap and generates long-range couplings, while unchanged spatial eigenfunctions explain the surviving entropy scaling.
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Critical Scaling Behaviors of Entanglement Spectra
Chinese Physics Letters 37, 010301 (2020)
Following a global quench from a short-range correlated state to the Ising critical point, we find that the late-time entanglement spectrum organizes into conformal towers. Conformal mapping predicts level spacings that scale as the inverse subsystem size, compared with inverse-logarithmic scaling in the critical ground state. Real-time simulations verify this scaling and recover the operator content of the Ising CFT.
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Thermal correction to entanglement spectrum for conformal field theories
Journal of High Energy Physics 08 (2022) 239
For a single interval in a CFT, we determine how the entanglement spectrum changes at low temperature. The leading correction depends on the scaling dimension and degeneracy of the lowest excited state, allowing thermal changes to reveal conformal data. We obtain analytical results for small and large intervals, verify them in a free-fermion model, and extend the analysis to entanglement spectra resolved by symmetry sector.