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We propose a procedure to derive quantum spectral curves of AdS/CFT type byrequiring that a specially designed analytic continuation around the branchpoint results in an automorphism of the underlying algebraic structure. In thisway we derive four new curves. Two are based on SU(2|2) symmetry, and we showthat one of them, under the assumption of square root branch points, describesHubbard model. Two more are based on SU(2|2) x SU(2|2). In the special subcaseof zero central charge, they both reduce to the unique nontrivial curve whichfurthermore has analytic properties compatible with PSU(1,1|2) x PSU(1,1|2)real form. A natural conjecture follows that this is the quantum spectral curveof AdS/CFT integrable system with AdS3 x S3 x T4 background supported byRR-flux. We support the conjecture by verifying its consistency with themassive sector of asymptotic Bethe equations in the large volume regime. Forthis spectral curve, it is compulsory that branch points are not of the squareroot type which qualitatively distinguishes it from the previously known cases.

Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2