### Abstract

Original language | English |
---|---|

Number of pages | 22 |

Publication status | Submitted - 12 Dec 2019 |

### Keywords

- computational
- strongly-correlated
- quantum
- physics
- chemistry
- tensor networks
- time evolution
- simulation
- long-range interactions
- magnetism
- TDVP
- DMRG
- MPS
- MPI
- OpenMP
- parallelisation
- spin chains
- Ising model

### ASJC Scopus subject areas

- Software
- Condensed Matter Physics
- Atomic and Molecular Physics, and Optics
- Computational Mathematics
- Mathematical Physics
- Modelling and Simulation

### Cite this

*Parallel time-dependent variational principle algorithm for matrix product states*.

**Parallel time-dependent variational principle algorithm for matrix product states.** / Secular, Paul; Gourianov, Nikita; Lubasch, Michael; Dolgov, Sergey; Clark, Stephen; Jaksch, Dieter.

Research output: Working paper

}

TY - UNPB

T1 - Parallel time-dependent variational principle algorithm for matrix product states

AU - Secular, Paul

AU - Gourianov, Nikita

AU - Lubasch, Michael

AU - Dolgov, Sergey

AU - Clark, Stephen

AU - Jaksch, Dieter

PY - 2019/12/12

Y1 - 2019/12/12

N2 - Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving one-dimensional (1D) quantum systems with long-range interactions. We benchmark the accuracy and performance of our implementation by simulating quenches in the long-range Ising and XY models. We show that our code scales well up to 32 processes with parallel efficiencies as high as 86%. Finally, we calculate the dynamical correlation function of a 201-site Heisenberg XXX chain with 1/r² interactions, which is challenging to compute sequentially. These results pave the way for the application of MPS to increasingly complex systems.

AB - Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state (MPS) algorithm capable of time evolving one-dimensional (1D) quantum systems with long-range interactions. We benchmark the accuracy and performance of our implementation by simulating quenches in the long-range Ising and XY models. We show that our code scales well up to 32 processes with parallel efficiencies as high as 86%. Finally, we calculate the dynamical correlation function of a 201-site Heisenberg XXX chain with 1/r² interactions, which is challenging to compute sequentially. These results pave the way for the application of MPS to increasingly complex systems.

KW - computational

KW - strongly-correlated

KW - quantum

KW - physics

KW - chemistry

KW - tensor networks

KW - time evolution

KW - simulation

KW - long-range interactions

KW - magnetism

KW - TDVP

KW - DMRG

KW - MPS

KW - MPI

KW - OpenMP

KW - parallelisation

KW - spin chains

KW - Ising model

M3 - Working paper

BT - Parallel time-dependent variational principle algorithm for matrix product states

ER -