Evidence of valence bond solid and quantum paramagnetism in the $J_1$--$J_2$--$J_3$ Heisenberg model from pseudofermion functional renormalization group

Abstract

Motivated by recent tensor network studies reporting a quantum spin liquid (QSL) within the quantum paramagnetic (QP) regime, we investigate numerically the zero-temperature phase diagram of the $J_1$--$J_2$--$J_3$ Heisenberg model on the square lattice using the pseudofermion functional renormalization group (pf-fRG). Thanks to improved frequency resolution and larger lattice truncations, we are able to explore a significantly larger parameter space than previous pf-fRG work to map out the phase boundary of an extended QP region. We further resolve possible bond order within the QP regime by measuring the dimer response to small deformations in $J_1$, i.e. bond anisotropy that breaks the point-group symmetry of the Hamiltonian. The functional renormalization group flow of the dimer susceptibility suggests that the QP window splits into two: a region where it grows continuously down to the lowest energy scale to signal valence bond solid (VBS) order, and another region where it reaches a peak at a finite scale and is subsequently suppressed to indicate a QSL.