Infinite boundary conditions for matrix product state calculations

Abstract

We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been eliminated. For one-dimensional systems, infinite boundary conditions are obtained by attaching two boundary sites to a finite system, where each of these two sites effectively represents a semi-infinite extension of the system. One can then use standard finite-size matrix product state techniques to study a region of the system while avoiding many of the complications normally associated with finite-size calculations such as boundary Friedel oscillations. We illustrate the technique with an example of time evolution of a local perturbation applied to an infinite (translationally invariant) ground state, and use this to calculate the spectral function of the S=1 Heisenberg spin chain. This approach is more efficient and more accurate than conventional simulations based on finite-size matrix product state and density-matrix renormalization-group approaches.

10 pages

References in corpus (9)

• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The iTEBD algorithm beyond unitary evolution
• From density-matrix renormalization group to matrix product states
• Matrix Product States for dynamical simulation of infinite chains
• Applying matrix product operators to model systems with long-range interactions
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Symmetry breaking and criticality in tensor-product states

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• Topological phases arising from attractive interaction and pair hopping in the Extended Hubbard Model
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