Effective hopping in holographic Bose and Fermi-Hubbard models

Fujita, Mitsutoshi; Meyer, René; Pujari, Sumiran; Tezuka, Masaki

doi:10.1007/jhep01(2019)045

Effective hopping in holographic Bose and Fermi-Hubbard models

Journal Article · Fri Jan 04 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2019)045· OSTI ID:1610114

^[1]; Meyer, René ^[2]; Pujari, Sumiran ^[3]; Tezuka, Masaki ^[4]

Sun Yat-Sen Univ., Guangzhou (China); DOE/OSTI
Univ. of Wurzburg (Germany)
Univ. of Kentucky, Lexington, KY (United States); IIT Bombay, Mumbai, Maharastra (India)
Kyoto Univ. (Japan)

In this paper, we analyze a proposed gravity dual to a SU(N) Bose-Hubbard model, as well as construct a holographic dual of a SU(N) Fermi-Hubbard model from D-branes in string theory. In both cases, the SU(N) is dynamical, i.e. the hopping degrees of freedom are strongly coupled to SU(N) gauge bosons which themselves are strongly interacting. The vacuum expectation value (VEV) of the hopping term (i.e. the hopping energy) is analyzed in the gravity dual as a function of the bulk mass of the field dual to the hopping term, as well as of the coupling constants of the model. The bulk mass controls the anomalous dimension (i.e. the critical exponent) of the hopping term in the SU(N) Bose-Hubbard model. We compare the hopping energy to the corresponding result in a numerical simulation of the ungauged SU(N) Bose-Hubbard model. We find agreement when the hopping parameter is smaller than the other couplings. Our analysis shows that the kinetic energy increases as the bulk mass increases, due to increased contributions from the IR. The holographic Bose-Hubbard model is then compared with the string theory construction of a SU(N) Fermi-Hubbard model. The string theory construction makes it possible to describe fluctuations around a half-filled state in the supergravity limit, which map to O(1) occupation number fluctuations in the Fermi-Hubbard model at half filling. Finally, the VEV of the Bose-Hubbard model is shown to agree with the one of the fermionic Hubbard model with the help of a two-site version of the Jordan-Wigner transformation.

View Accepted Manuscript (DOE)

Research Organization:: State Univ. of New York (SUNY), Albany, NY (United States); Stony Brook Univ., NY (United States)

Sponsoring Organization:: JSPS KAKENHI; National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: FG02-88ER40388

OSTI ID:: 1610114

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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