TY - JOUR

T1 - Comparative Study of State-of-the-Art Matrix-Product-State Methods for Lattice Models with Large Local Hilbert Spaces without U(1) symmetry

AU - Stolpp, Jan

AU - Köhler, Thomas

AU - Manmana, Salvatore R.

AU - Jeckelmann, Eric

AU - Heidrich-Meisner, Fabian

AU - Paeckel, Sebastian

N1 - Funding Information: We thank K. Harms and D. Jansen for insightful discussions. TK acknowledges financial support by the ERC Starting Grant from the European Union's Horizon 2020 research and innovation program under grant agreement No. 758935 . This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 207383564 ; 217133147 , via FOR 1807 (projects P4 and P7) and CRC 1073 (projects B03 and B09), respectively. SP acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy-426 EXC-2111-390814868 . We thank the TU Clausthal for providing access to the Nuku computational cluster.

PY - 2021/12

Y1 - 2021/12

N2 - Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size-scaling analysis of relevant ground-state observables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches.

AB - Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size-scaling analysis of relevant ground-state observables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches.

KW - DMRG

KW - Lattice phonons

KW - MPS

KW - Quantum lattice models

KW - Quantum physics

UR - http://www.scopus.com/inward/record.url?scp=85113354426&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2021.108106

DO - 10.1016/j.cpc.2021.108106

M3 - Article

VL - 269

JO - Computer physics communications

JF - Computer physics communications

SN - 0010-4655

M1 - 108106

ER -