Matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions

Autor(en)

Bogdan Corneliu Pirvu, Jutho Haegeman, Frank Verstraete

Abstrakt

We study a matrix product state algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of Ostlund and Rommer [see S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 ( 1995); S. Rommer and S. Ostlund, Phys. Rev. B 55, 2164 (1997)], we separate the Hilbert space of the system into subspaces with different momentum. This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation. Surprisingly, many branches of the dispersion relation are approximated to a very good precision. We benchmark the accuracy of the algorithm by comparison with the exact solutions and previous numerical results for the quantum Ising, the antiferromagnetic Heisenberg spin-1/2, and the bilinear-biquadratic spin-1 models.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Ghent University

Journal

Physical Review B

Band

85

Anzahl der Seiten

13

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.85.035130

Publikationsdatum

01-2012

Peer-reviewed

Ja

ÖFOS 2012

103026 Quantenoptik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/868a91ec-e763-4387-b271-d61d65ec3ea3