$Ab$ $initio$ derivation and exact-diagonalization analysis of low-energy effective Hamiltonians for $\beta^\prime$-X[Pd(dmit)$_2$]$_2$

TL;DR

This study derives and analyzes low-energy effective Hamiltonians for $eta^\prime$-X[Pd(dmit)$_2$]$_2$ using ab initio methods and exact diagonalization, revealing temperature-dependent electronic interactions and quantum spin liquid behavior.

Contribution

The paper presents the first ab initio derivation of effective Hamiltonians for these compounds and analyzes their low-temperature properties with exact diagonalization.

Findings

Coulomb interactions and hopping anisotropy are temperature-sensitive.

Significant reduction of antiferromagnetic moment in low-temperature structure.

Results support quantum spin liquid behavior in specific compounds.

Abstract

The molecular solids $\beta^\prime$-$X$[Pd(dmit)$_2$]$_2$ (where $X$ represents a cation) are typical compounds whose electronic structures are described by single-orbital Hubbard-type Hamiltonians with geometrical frustration. Using the $ab$ $initio$ downfolding method, we derive the low-energy effective Hamiltonians for $\beta^\prime$-$X$[Pd(dmit)$_2$]$_2$ with available room- and low-temperature structures. We find that the amplitudes of the Coulomb interactions and the anisotropy of the hopping parameters in the effective Hamiltonians are sensitive to the changes in the lattice constants induced by lowering the temperature. The obtained effective Hamiltonians are analyzed using the exact diagonalization method with the boundary-condition average. We find that a significant reduction of the antiferromagnetic ordered moment occurs in the effective Hamiltonian of $\beta^\prime$-EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ with the low-temperature structure. The reduction is consistent with the quantum spin liquid behavior observed in experiments. The comprehensive derivations of the effective Hamiltonians and exact-diagonalization analyses of them will clarify the microscopic origins of the exotic quantum states of matter found in $\beta^\prime$-$X$[Pd(dmit)$_2$]$_2$ such as the quantum spin liquid behavior.