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

2011/04/30 by Hosho Katsura · 2 citations
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1088/1751-8113/44/25/252001

published as J. Phys. A: Math. Theor. 44 (2011) 252001 · 10 pages

arxiv created 2011/05/15 · arxiv updated 2011/07/05

Abstract

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 = sin² [π/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. Rev. B 83 060414(R)] based on numerical evidence.

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• Two dimensional inhomogeneous classical systems at criticality
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