Phases and phase transtions in one-dimensional alternating mixed spin (1/2-1) chain: effects of frustration and anisotropy

TL;DR

This work analyzes a one-dimensional alternating chain of $S_1=\tfrac{1}{2}$ and $S_2=1$ with competing NN and NNN antiferromagnetic couplings and on-site single-ion anisotropy. Using ED, DMRG, LSWT, and TEBD, it maps a ground-state phase diagram featuring a commensurate ferrimagnetic phase that transitions to an incommensurate antiferromagnetic phase as the NNN frustration $J_2$ increases past about 0.23, accompanied by a gap opening in the AFM phase. Easy-plane anisotropy ($D>0$) suppresses ferrimagnetism and, at strong frustration, yields a SDW-like state with spin-1/2 sites magnetized while spin-1 sites remain nearly nonmagnetic. Finite-temperature calculations confirm the persistence of these phases with distinct thermodynamic signatures, offering insights into the behavior of frustrated mixed-spin quantum systems and potential routes to experimental realization in synthetic quantum magnets and cold-atom setups.

Abstract

We investigate the phases and phase-transitions in one-dimensional alternating mixed-spin (1/2-1) chain in the presence of both frustration and anisotropy. Frustration is introduced via next-nearest-neighbor interactions, while single-ion anisotropy is incorporated at each lattice site. Our results show that moderate frustration can drive a phase transition from a ferrimagnetic state to an anti-ferromagnetic ground state. Remarkably, the presence of a weak easy-plane anisotropy destabilizes the ferrimagnetic order, also leading to the emergence of an antiferromagnetic phase. Interestingly, under strong frustration and anisotropy, the system exhibits signatures of a novel phase with spin density wave (SDW)-like modulation . We explore these anomalous phase transitions by employing exact diagonalization (ED) for small system sizes and the density matrix renormalization group (DMRG) method to characterize ground state properties for larger system sizes. We also investigate the finite-temperature behavior across various phases using the ancilla-based time-evolving block decimation (TEBD) approach. The primary objective of this work is to elucidate the phase structure of alternating mixed-spin chains under the combined effects of frustration and anisotropy. The primary objective of this work is to elucidate the intricate interplay between frustration and anisotropy in identifying the exotic phases and phase-transitions in alternating mixed-spin chains. Our findings contribute to a deeper understanding of mixed-spin quantum systems and may offer insights for future theoretical and experimental studies.

Figures (8)

• Figure 1: (Color online). Schematic diagram of a spin $\frac{1}{2}$-spin $1$ alternate spin chain model, where nearest-neighbor interactions are $J_1$, and next-nearest-neighbor interactions are $J_2$.
• Figure 2: (Color online). The two spin-wave excitation branches, $\epsilon_{1k}$ and $\epsilon_{2k}$, expressed in units of $J_1$, are displayed for the alternating spin-($\frac{1}{2},1$) chain varying NNN coupling $J_2$.
• Figure 3: (Color online). Site-resolved expectation value of the $z$-component of the spin, $\langle S_z(i)\rangle$, for (a) $J_2=0.1$ and (b) $J_2=0.5$.
• Figure 4: (Color online). Spin–spin correlation function $C^z(|i-j|)$ (defined in Eq. \ref{['eq2']}) as a function of the distance $|i-j|$ between two spins. (a) Corresponds to the phase with $J_2=0.1$, and (b) corresponds to the phase with $J_2=0.5$.
• Figure 5: (Color online). The static spin structure factor $S(q)$ as a function of $q$ (defined in Eq. \ref{['eq21']}); (a) for $J_2 = 0.1$ and (b) for $J_2=0.5$.