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We introduce a half-filled Hamiltonian of spin-half lattice fermions that canbe studied with the efficient meron-cluster algorithm in any dimension. As withthe usual bipartite half-filled Hubbard models, the na\"ive $U(2)$ symmetry isenhanced to $SO(4)$. On the other hand our model has a novel spin-charge flip${\mathbb Z}^C_2$ symmetry which is an important ingredient of free masslessfermions. In this work we focus on one spatial dimension, and show that ourmodel can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveumodel. Our model remains solvable in the presence of the Hubbard coupling $U$,which maps to a combination of Gross-Neveu and Thirring couplings in onedimension. Using the meron-cluster algorithm we find that the ground state ofour 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 interestingfrustration between spin and charge sectors in the renormalization group flowenforced by the ${\mathbb Z}^C_2$ symmetry. This state spontaneously breakstranslation symmetry by one lattice unit, which can be identified with a$\mathbb{Z}_2^\chi$ 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 thesetwo phases is known to exhibit a novel symmetry enhancement between spin anddimer. Here we verify the scaling relations of these correlation functions nearthe critical point numerically. Our study opens up the exciting possibility ofnumerical access to similar novel phase transitions in higher dimensions infermionic lattice models using the meron-cluster algorithm.

Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm