arXiv:2411.17877 · Physical review. B./Physical review. B

Chiral eigenbases of the XX and XY quantum spin chains

Xin Zhang, Frank Göhmann, Andreas Klümper, Vladislav Popkov

Published Mar 27, 2025• 3 citations

Abstract

We calculate the values of observables in chiral eigenstates of the XX quantum spin chain that were introduced in previous work and compare the form of the result with the respective expressions obtained in the more familiar eigenbasis of states with fixed magnetization in the $z$ direction. We carry out the diagonalization of the XY spin chain in the chiral basis. We calculate the norm of the chiral XY eigenstates, and the values of the one-point functions and some neighbor two-point correlation functions. We interpret the spectrum and the particle content of the XY chain in terms of scattering states of an even number of kink and antikink excitations that are created over a reduced Brillouin zone.

DOI: 10.1103/physrevb.111.094437

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arXiv:2411.17877 · Physical review. B./Physical review. B

Chiral eigenbases of the XX and XY quantum spin chains

Xin Zhang, Frank Göhmann, Andreas Klümper, Vladislav Popkov

Published Mar 27, 2025• 3 citations

arXiv HTML PDF

Abstract

z

direction. We carry out the diagonalization of the XY spin chain in the chiral basis. We calculate the norm of the chiral XY eigenstates, and the values of the one-point functions and some neighbor two-point correlation functions. We interpret the spectrum and the particle content of the XY chain in terms of scattering states of an even number of kink and antikink excitations that are created over a reduced Brillouin zone.

DOI: 10.1103/physrevb.111.094437

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Solitons and magnons in quantum spin chains

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The z-component dynamical spin correlation function S zz (q,w) of the s= 1 / 2 anisotropic XY chain is calculated exactly in the fermion representation. S zz consists of two parts: one (S m ) represents two fermion excitations and the other (S s ) describes scattering from thermally excited fermions. In the continuum limit, S s has the structure of the solitonic part of a classical sine-Gordon correlation function, but the soliton form factor is modified by quantum effects. S m has similarities with the spin-wave continuum form of S zz an isotropic spin chains. The continuum results are compared with those for a discrete chain.The z-component dynamical spin correlation function S zz (q,w) of the s= 1 / 2 anisotropic XY chain is calculated exactly in the fermion representation. S zz consists of two parts: one (S m ) represents two fermion excitations and the other (S s ) describes scattering from thermally excited fermions. In the continuum limit, S s has the structure of the solitonic part of a classical sine-Gordon correlation function, but the soliton form factor is modified by quantum effects. S m has similarities with the spin-wave continuum form of S zz an isotropic spin chains. The continuum results are compared with those for a discrete chain.

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A. A. Ovchinnikov

We present the new expressions for the formfactors of local operators for the XX- quantum spin chain as a Cauchy determinants. Using the known functional form of the correlator at large distances we propose the new expression for the constant for the asymptotics of the correlator as a Cauchy determinant. We calculate the momentum distribution for the general case of the XXZ- spin chain and point out that it is completely different from that for the Luttinger model (the system of fermions). For the XX chain we compare numerically the value of the lowest formfactor and the expectation value of momentum- zero operators which is determined by the functional form of the correlator. 1.Introduction. In the present paper we study the spin-spin equal-time correlator in the XX- spin chainWe present the new expressions for the formfactors of local operators for the XX- quantum spin chain as a Cauchy determinants. Using the known functional form of the correlator at large distances we propose the new expression for the constant for the asymptotics of the correlator as a Cauchy determinant. We calculate the momentum distribution for the general case of the XXZ- spin chain and point out that it is completely different from that for the Luttinger model (the system of fermions). For the XX chain we compare numerically the value of the lowest formfactor and the expectation value of momentum- zero operators which is determined by the functional form of the correlator. 1.Introduction. In the present paper we study the spin-spin equal-time correlator in the XX- spin chain

Jan 1, 20034 citations

z

κ_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^x

, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.

We calculate the vector spin chirality for

S=1/2

zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the

S=1/2

zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.