Diverging scaling with converging multisite entanglement in odd and even quantum Heisenberg ladders

TL;DR

This study explores how multisite entanglement scales in quantum Heisenberg ladders, revealing divergent finite-size scaling behaviors for odd and even-legged systems despite similar asymptotic entanglement levels.

Contribution

It demonstrates that the finite-size scaling exponents of multisite entanglement distinguish odd and even Heisenberg ladders, even when their entanglement measures converge.

Findings

GGMs increase with odd rungs and decrease with even rungs for different ladder types.

As the number of rungs grows, odd and even ladders' GGMs converge to a single value.

Finite-size scaling exponents diverge for odd and even ladders, serving as a distinguishing feature.

Abstract

We investigate finite-size scaling of genuine multisite entanglement in the ground state of quantum spin-1/2 Heisenberg ladders. We obtain the ground states of odd- and even-legged Heisenberg ladder Hamiltonians and compute genuine multisite entanglement, the generalized geometric measure (GGM), which shows that for even rungs, GGM increases for odd-legged ladder while it decreases for even ones. Interestingly, the ground state obtained by short-range dimer coverings, under the resonating valence bond (RVB) ansatz, encapsulates the qualitative features of GGM for both the ladders. We find that while the GGMs for higher legged odd- and even-ladders converge to a single value in the asymptotic limit of a large number of rungs, the finite-size scaling exponents of the same tend to diverge. The scaling exponent of GGM obtained by employing density matrix recursion method is therefore a reliable quantity in distinguishing the odd-even dichotomy in Heisenberg ladders, even when the corresponding multisite entanglements merge.