Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics
Abstract
In the study of strongly correlated, many-electron systems, the Hubbard-Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multiband in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground-state auxiliary field quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximate those observed in ruthenates, rhodates, and other materials exhibiting Hund's physics. Unlike previous studies, the constrained path and phaseless approximations are used to respectively control the sign and phase problems, which enables high-accuracy modeling of the HK model's ground-state properties within parameter regimes of experimental interest. We demonstrate that, after careful consideration of the Hubbard-Stratonovich transformations and trial wave functions employed, relative errors in the energy of less than 1% can routinely be achieved for moderate to large values of the Hund's coupling constant. Crucially, our methodology also accurately predicts magnetic ordering and phase transitions. Furthermore, the results presented open the door to more predictive modeling of Hund's physics within a wide range of strongly correlated materials usingmore »
- Authors:
-
- Brown Univ., Providence, RI (United States)
- Flatiron Institute, New York, NY (United States)
- Publication Date:
- Research Org.:
- Brown Univ., Providence, RI (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1613232
- Alternate Identifier(s):
- OSTI ID: 1546243
- Grant/Contract Number:
- SC0019441
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 23; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Strongly correlated systems; Hubbard model; Quantum Monte Carlo
Citation Formats
Hao, Hongxia, Rubenstein, Brenda M., and Shi, Hao. Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics. United States: N. p., 2019.
Web. doi:10.1103/physrevb.99.235142.
Hao, Hongxia, Rubenstein, Brenda M., & Shi, Hao. Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics. United States. https://doi.org/10.1103/physrevb.99.235142
Hao, Hongxia, Rubenstein, Brenda M., and Shi, Hao. Thu .
"Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics". United States. https://doi.org/10.1103/physrevb.99.235142. https://www.osti.gov/servlets/purl/1613232.
@article{osti_1613232,
title = {Auxiliary field quantum Monte Carlo for multiband Hubbard models: Controlling the sign and phase problems to capture Hund's physics},
author = {Hao, Hongxia and Rubenstein, Brenda M. and Shi, Hao},
abstractNote = {In the study of strongly correlated, many-electron systems, the Hubbard-Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multiband in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground-state auxiliary field quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximate those observed in ruthenates, rhodates, and other materials exhibiting Hund's physics. Unlike previous studies, the constrained path and phaseless approximations are used to respectively control the sign and phase problems, which enables high-accuracy modeling of the HK model's ground-state properties within parameter regimes of experimental interest. We demonstrate that, after careful consideration of the Hubbard-Stratonovich transformations and trial wave functions employed, relative errors in the energy of less than 1% can routinely be achieved for moderate to large values of the Hund's coupling constant. Crucially, our methodology also accurately predicts magnetic ordering and phase transitions. Furthermore, the results presented open the door to more predictive modeling of Hund's physics within a wide range of strongly correlated materials using AFQMC.},
doi = {10.1103/physrevb.99.235142},
journal = {Physical Review. B},
number = 23,
volume = 99,
place = {United States},
year = {Thu Jun 20 00:00:00 EDT 2019},
month = {Thu Jun 20 00:00:00 EDT 2019}
}
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