What is it about?
We show, within the language of tensor network states, how information about low lying excited states can be extracted from just the ground state of a low dimensional strongly correlated quantum many body system with local interactions. More specifically, we show how the eigenspectrum of the tensor network transfer matrix, a central local object in tensor network techniques, contains this information and can be extracted without any prior knowledge of the underlying Hamiltonian.
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Why is it important?
While obtaining ground states of strongly correlated many body systems already forms a formidable task by itself, extracting information about excited states is an even harder task. Our approach enables easy first access to information about low lying excited states, especially for quantum systems in 2 or higher dimensions, for which no competitive algorithms for obtaining excited states exist.
Perspectives
I think it is amazing how much information is already encoded in a local object describing the ground state of a strongly correlated quantum many body system. The fact that we can extract information about excited states from just the ground states demonstrates again how special strongly correlated systems with local interactions are. I find it particularly intriguing, how easy one can extract a first estimate of excitation energies in two dimensional systems (also with topological order) if the ground state is known in terms of a tensor network (such as PEPS).
Mr Valentin Zauner
Universitat Wien
Read the Original
This page is a summary of: Transfer matrices and excitations with matrix product states, New Journal of Physics, May 2015, Institute of Physics Publishing,
DOI: 10.1088/1367-2630/17/5/053002.
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Resources
Shadows of Anyons
We use the local 2D tensor network transfer matrix to study topological excitations and topological phase transitions in two dimensional strongly correlated quantum many body systems.
Truncating an exact Matrix Product State for the XY model
We show how knowledge about the exact quantum transfer matrix can be used to obtain an exact representation of the ground state in terms of a matrix product state (MPS) with infinite bond dimension. We show further, how the transfer matrix can be used to obtain a finite entanglement MPS approximation of the ground state with finite bond dimension.
Contributors
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