Free fermionic and parafermionic quantum spin chains with multispin interactions. ALCARAZ, Francisco Castilho; PIMENTA, Rodrigo Alves.
Abstract: We introduce a family of Z (N) multispin quantum chains with a free fermionic (N = 2) or free parafermionic (N > 2) eigenspectrum. The models have (p + 1) interacting spins (p = 1 , 2 ,... ), which are Hermitian in the Z (2) (Ising) case and non-Hermitian for N > 2 . We construct a set of mutually commuting charges that allows us to derive the eigenenergies in terms of the roots of polynomials generated by a recurrence relation of order (p + 1) . In the critical limit we identify these polynomials with certain hypergeometric polynomials (p + 1) Fp . Also in the critical regime, we calculate the ground-state energy in the bulk limit and verify that they are given in terms of the Lauricella hypergeometric series. The models with special couplings are self-dual and at the self-dual point show a critical behavior with a dynamical critical exponent Zc = (p + 1)/ N .
Physical Review B
v. 102, n. 12, p. 121101-1-121101-6 - Ano: 2020
Fator de Impacto: 3,575
@article={003005634,author = {ALCARAZ, Francisco Castilho; PIMENTA, Rodrigo Alves.},title={Free fermionic and parafermionic quantum spin chains with multispin interactions},journal={Physical Review B},note={v. 102, n. 12, p. 121101-1-121101-6},year={2020}}
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Abstract: We introduce a family of Z (N) multispin quantum chains with a free fermionic (N = 2) or free parafermionic (N > 2) eigenspectrum. The models have (p + 1) interacting spins (p = 1 , 2 ,... ), which are Hermitian in the Z (2) (Ising) case and non-Hermitian for N > 2 . We construct a set of mutually commuting charges that allows us to derive the eigenenergies in terms of the roots of polynomials generated by a recurrence relation of order (p + 1) . In the critical limit we identify these polynomials with certain hypergeometric polynomials (p + 1) Fp . Also in the critical regime, we calculate the ground-state energy in the bulk limit and verify that they are given in terms of the Lauricella hypergeometric series. The models with special couplings are self-dual and at the self-dual point show a critical behavior with a dynamical critical exponent Zc = (p + 1)/ N .
@article={003005634,author = {ALCARAZ, Francisco Castilho; PIMENTA, Rodrigo Alves.},title={Free fermionic and parafermionic quantum spin chains with multispin interactions},journal={Physical Review B},note={v. 102, n. 12, p. 121101-1-121101-6},year={2020}}