Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large-$$\mathcal{z}$$ limit
Abstract
The Mott metal-insulator transition in the Hubbard model is studied here by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number $$\mathcal{z}$$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in $$1/ \sqrt{z}$$ and becomes exact on the infinite-$$\mathcal{z}$$ Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard $$U_c$$ and the corresponding doublon density $$n^c_d$$, hopping $$χ^c_d$$ and doublon-holon pairing $$Δ^c_d$$ amplitudes. We find $$U_c = U_{\text{BR}}[1 – 2n^c_d – \sqrt{z}(χ^c_d + Δ^c_d)] ≃ 0.8U_{\text{BR}}$$ , where $$U_{\text{BR}}$$ is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a $$\textit{U}$$(1) quantum spin liquid with nonzero intersite spinon hopping that survives the large-$$\mathcal{z}$$ limit and lifts the $2^N$ -fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact $$\textit{U}$$(1) gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.
- Authors:
-
[1];
[2];
- Chinese Academy of Sciences (CAS), Beijing (China); University of Chinese Academy of Sciences, Beijing (China)
- Aalto Univ., Otaniemi (Finland). School of Science
- Boston College, Chestnut Hill, MA (United States)
- Publication Date:
- Research Org.:
- Boston College, Chestnut Hill, MA (United States)
- Sponsoring Org.:
- Chinese Academy of Sciences (CAS); National Natural Science Foundation of China (NSFC); Academy of Finland; USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
- OSTI Identifier:
- 1800970
- Grant/Contract Number:
- FG02-99ER45747; QYZDB-SSW-SYS012; XDB28000000; 11847612; 11974362; PHY-1066293
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 101; Journal Issue: 3; 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
Citation Formats
Zhou, Sen, Liang, Long, and Wang, Ziqiang. Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large-$\mathcal{z}$ limit. United States: N. p., 2020.
Web. doi:10.1103/physrevb.101.035106.
Zhou, Sen, Liang, Long, & Wang, Ziqiang. Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large-$\mathcal{z}$ limit. United States. https://doi.org/10.1103/physrevb.101.035106
Zhou, Sen, Liang, Long, and Wang, Ziqiang. Mon .
"Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large-$\mathcal{z}$ limit". United States. https://doi.org/10.1103/physrevb.101.035106. https://www.osti.gov/servlets/purl/1800970.
@article{osti_1800970,
title = {Dynamical slave-boson mean-field study of the Mott transition in the Hubbard model in the large-$\mathcal{z}$ limit},
author = {Zhou, Sen and Liang, Long and Wang, Ziqiang},
abstractNote = {The Mott metal-insulator transition in the Hubbard model is studied here by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number $\mathcal{z}$ that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in $1/ \sqrt{z}$ and becomes exact on the infinite-$\mathcal{z}$ Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard $U_c$ and the corresponding doublon density $n^c_d$, hopping $χ^c_d$ and doublon-holon pairing $Δ^c_d$ amplitudes. We find $U_c = U_{\text{BR}}[1 – 2n^c_d – \sqrt{z}(χ^c_d + Δ^c_d)] ≃ 0.8U_{\text{BR}}$ , where $U_{\text{BR}}$ is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a $\textit{U}$(1) quantum spin liquid with nonzero intersite spinon hopping that survives the large-$\mathcal{z}$ limit and lifts the $2^N$ -fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact $\textit{U}$(1) gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.},
doi = {10.1103/physrevb.101.035106},
journal = {Physical Review B},
number = 3,
volume = 101,
place = {United States},
year = {Mon Jan 06 00:00:00 EST 2020},
month = {Mon Jan 06 00:00:00 EST 2020}
}
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