Bogdan Pirvu | Searcharxiv

arXiv2012

Variational matrix product ansatz for dispersion relations

A variational ansatz for momentum eigenstates of translation invariant quantum spin chains is formulated. The matrix product state ansatz works directly in the thermodynamic limit and allows for an efficient implementation (cubic scaling in the bond dimension) of the variational principle. Unlike previous approaches, the ansatz includes topologically non-trivial states (kinks, domain walls) for systems with symmetry breaking. The method is benchmarked using the spin-1/2 XXZ antiferromagnet and the spin-1 Heisenberg antiferromagnet and we obtain surprisingly accurate results.

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arXiv2011

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

We study a matrix product state (MPS) 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 Östlund and Rommer [1], 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 of the quantum Ising and the antiferromagnetic Heisenberg spin-1/2 model.

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