DMRG studies on linear-exchange quantum spin models in one dimension

TL;DR

This paper investigates linear-exchange quantum spin chains with varying interaction ranges using DMRG, revealing that even-range models exhibit spin gaps and dimer correlations, expanding understanding beyond exactly solvable cases.

Contribution

The study provides numerical analysis of even-range linear-exchange spin models, showing they have spin gaps and MG-like correlations, which were previously unknown.

Findings

Even R models are spin-gapped.

Strong dimer-dimer correlations observed.

Rapid decay of spin-spin correlations with weak revivals.

Abstract

We study a class of spin-1/2 quantum antiferromagnetic chains using DMRG technique. The exchange interaction in these models decreases linearly as a function of the separation between the spins, $J_{ij} = R-|i-j|$ for $|i-j| \le R$. For the separations beyond $R$, the interaction is zero. The range parameter $R$ takes positive integer values. The models corresponding to all the odd values of $R$ are known to have the same exact doubly degenerate dimer ground state as for the Majumdar-Ghosh (MG) model. In fact, R=3 is the MG model. For even $R$, the exact ground state is not known in general, except for R=2 (the Bethe ansatz solvable Heisenberg chain) and in the asymptotic limit of $R$ where the two MG dimer states again emerge as the exact ground state. In the present work, we numerically investigate the even-$R$ models whose ground state is not known analytically. In particular, for R=4, 6 and 8, we have computed a number of ground state properties. We find that, unlike R=2, the higher even-$R$ models are spin-gapped, and show strong dimer-dimer correlations of the MG type. Moreover, the spin-spin correlations decay very rapidly, albeit showing weak periodic revivals.