Stojevic, V;
Crowley, P;
Đurić, T;
Grey, C;
Green, A;
(2016)
Time Evolution and Deterministic Optimisation of Correlator Product States.
Physical Review B
, 94
(16)
, Article 165135. 10.1103/PhysRevB.94.165135.
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Abstract
We study a restricted class of correlator product states (CPS) for a spin-half chain in which each spin is contained in just two overlapping plaquettes. This class is also a restriction upon matrix product states (MPS) with local dimension $2^n$ ($n$ being the size of the overlapping regions of plaquettes) equal to the bond dimension. We investigate the trade-off between gains in efficiency due to this restriction against losses in fidelity. The time-dependent variational principle formulated for these states is numerically very stable. Moreover, it shows significant gains in efficiency compared to the naively related matrix product states - the evolution or optimisation scales as $2^{3n}$ for the correlator product states versus $2^{4n}$ for the unrestricted matrix product state. However, much of this advantage is offset by a significant reduction in fidelity. Correlator product states break the local Hilbert space symmetry by the explicit selection of a local basis. We investigate this dependence in detail and formulate the broad principles under which correlator product states may be a useful tool. In particular, we find that scaling with overlap/bond order may be more stable with correlator product states allowing a more efficient extraction of critical exponents - we present an example in which the use of correlator product states is several orders of magnitude quicker than matrix product states.
Type: | Article |
---|---|
Title: | Time Evolution and Deterministic Optimisation of Correlator Product States |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1103/PhysRevB.94.165135 |
Publisher version: | http://dx.doi.org/10.1103/PhysRevB.94.165135 |
Language: | English |
Additional information: | ©2016 American Physical Society. |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology |
URI: | https://discovery.ucl.ac.uk/id/eprint/1514804 |
1. | United States | 6 |
2. | United Kingdom | 2 |
3. | Russian Federation | 2 |
4. | China | 1 |
5. | Netherlands | 1 |
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