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Zero-energy states in conformal field theory with sine-square deformation
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abstract
We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $|0\rangle$. We then introduce a regularized version of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a unitary transformation corresponding to the Mobius quantization. The unitary equivalence of the two Hamiltonians allows us to obtain zero-energy states of the deformed Hamiltonian in a systematic way. The regularization also provides a way to compute the expectation values of observables in zero-energy states that are not necessarily normalizable.
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Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
Under sine-square-deformed Floquet driving of a 1+1D CFT, the heating phase localizes energy and Bell-pair entanglement at two fixed-point peaks, and E scales as the exponential of the entropy.
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