Inducing critical phenomena in spin chains through sparse alternating fields

TL;DR

This paper explores how sparse alternating magnetic fields in spin chains induce complex magnetic phases, magnetization plateaus, and entanglement effects, revealing new control mechanisms for quantum magnetic properties.

Contribution

It introduces a detailed analysis of ground states in spin-$s$ chains with $n$-alternating fields, showing how these configurations enable novel magnetic and entanglement behaviors.

Findings

Boundary of fully aligned phase analytically determined for all $n$

Magnetization plateaus obeying the OYA criterion identified

Field-induced spin polymerization explains plateau formation

Abstract

We analyze the phase diagram of the exact ground state (GS) of spin-$s$ chains with ferromagnetic $XXZ$ couplings under $n$-alternating field configurations, i.e, sparse alternating fields having nodes at $n-1$ contiguous sites. It is shown that such systems can exhibit a non-trivial magnetic behavior, which can differ significantly from that of the standard ($n=1$) alternating case and enable mechanisms for controlling their magnetic and entanglement properties. The boundary in field space of the fully aligned phase can be determined analytically $\forall\,n$, and shows that it becomes reachable only above a threshold value of the coupling anisotropy $J_z/J$, which depends on $n$ but is independent of the system size. Below this value the maximum attainable magnetization becomes much smaller. We then show that the GS can exhibit significant magnetization plateaus, persistent for large systems, at which the magnetization per site $m$ obeys the quantization rule $2n(s-m)=integer$, consistent with the Oshikawa, Yamanaka and Affleck (OYA) criterion. We also identify the emergence of field induced spin polymerization, which explains the presence of such plateaus. Entanglement and field induced frustration effects are also analyzed.