Exact ground state of the sine-square deformed XY spin chain

Understand

We study the sine-square deformed quantum XY chain with open boundary conditions, in which the interaction strength at the position $x$ in the chain of length $L$ is proportional to the function $f_x = \sin^2 [\pi/L (x-1/2)]$.

• The model can be mapped onto a free spinless fermion model with site-dependent hopping amplitudes and on-site potentials via the Jordan-Wigner transformation.
• Although the single-particle eigenstates of this system cannot be obtained in closed form, it is shown that the many-body ground state is identical to that of the uniform XY chain with periodic boundary conditions.
• This proves a conjecture of Hikihara and Nishino [Hikihara T and Nishino T 2011 {\it Phys.