2009
DOI: 10.1103/physreva.80.032102
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XYmodel on the circle: Diagonalization, spectrum, and forerunners of the quantum phase transition

Abstract: We exactly diagonalize the finite-size XY model with periodic boundary conditions and analytically determine the ground state energy. We show that there are two types of fermions: singles and pairs, whose dispersion relations have a completely arbitrary gauge-dependent sign. It follows that the ground state is determined by a competition between the vacuum states (with a suitable gauge) of two parity sectors. We finally exhibit some points in finite size systems that forerun criticality. They are associated to… Show more

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Cited by 36 publications
(79 citation statements)
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“…The exact values of the elements of the density matrix (48) can be obtained, for any size n or separation L, through the Jordan-Wigner fermionization of the model [85] and its analytic parity-dependent diagonalization [55,86,87] (see the Appendix).…”
Section: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…The exact values of the elements of the density matrix (48) can be obtained, for any size n or separation L, through the Jordan-Wigner fermionization of the model [85] and its analytic parity-dependent diagonalization [55,86,87] (see the Appendix).…”
Section: Resultsmentioning
confidence: 99%
“…We briefly discuss here the exact solution of the finite cyclic XY chain with first neighbor couplings, which requires one to take into account exactly the parity effects [55,[85][86][87]. The Jordan-Wigner transformation [85] allows one to rewrite the Hamiltonian (46) …”
Section: A Appendixmentioning
confidence: 99%
“…[24], where the comprehensive study of this problem in a finite Ising chain is presented (see also Ref. [25] for the discussion of the finite-size effects in the XY model).…”
Section: Quantum Ising Modelmentioning
confidence: 99%
“…This is done using the socalled Jordan-Wigner transformation and a subsequent Fourier transform 54 .…”
Section: Many-particle Eigenstatesmentioning
confidence: 99%