We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the naïve U(2) symmetry is enhanced to SO(4). On the other hand, our model has a novel spin-charge flip Z2C symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of the Hubbard coupling U, which maps to a combination of Gross-Neveu and Thirring couplings in one dimension. Using the meron-cluster algorithm we find that the ground state of our model is a valence bond solid when U=0. From our field theory analysis, we argue that the valence bond solid forms inevitably because of an interesting frustration between spin and charge sectors in the renormalization group flow enforced by the Z2C symmetry. This state spontaneously breaks translation symmetry by one lattice unit, which can be identified with a Z2χ chiral symmetry in the continuum. We show that increasing U induces a quantum phase transition to a critical phase described by the SU(2)1 Wess-Zumino-Witten theory. The quantum critical point between these two phases is known to exhibit a novel symmetry enhancement between spin and dimer. Here we verify the scaling relations of these correlation functions near the critical point numerically. Our study opens up the exciting possibility of numerical access to similar novel phase transitions in higher dimensions in fermionic lattice models using the meron-cluster algorithm.
|Journal||Physical Review D|
|State||Published - Mar 25 2021|
Bibliographical noteFunding Information:
We thank Emilie Huffman and Hersh Singh for helpful discussions and pointing us to the literature on interesting fermionic quantum critical behavior. S. C. thanks Uwe-Jens Wiese for discussions. H. L. thanks Zhe Wang for sharing his computer codes on the coordinate descend method and Xin Zhang for helpful discussions. The material presented here is supported by the U.S. Department of Energy, Office of Science, Nuclear Physics program under Award No. DE-FG02-05ER41368. R. K. K. was supported in part by NSF Grant No. DMR-1611161.
© 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)