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Physics Letters A

From uniform to staggered gamma coupling: Reconstructing the phase landscape of spin-1/2 XXZ chains

D. Liu, M. Abbasi, Yan-Wei Dai, M. Motamedifar, S. Mahdavifar

Published Sep 16, 2026• 0 citations
Publisher
DOI
10.1016/j.physleta.2026.132189

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In this study, we delve into the intricate ground state phase diagram of anisotropic spin-1/2 XXZ chains under the uniform Gamma interaction. Employing the robust infinite time evolving block decimation (iTEBD) technique and the Lanczos technique, we meticulously obtain the model's ground state properties. Complementing our numerical analysis, we derive analytical approximations through a mean-field framework, transposed into the fermionic representation. Our investigation rigorously scrutinizes the energy spectrum, distinguishing between gapped and gapless domains at absolute zero. Furthermore, we thoroughly examine various order parameters including magnetization, staggered magnetization, chirality, and spin nematicity, which demarcate the diverse phases within the ground state phase diagram, each characterized by its unique long-range order.
We study the spin-1/2 XX chain with a modulated Gamma interaction (GI), which results from the superposition of uniform and staggered Gamma terms. We diagonalize the Hamiltonian of the model exactly using the Fermionization technique. We then probe the energy gap and identify the gapped and gapless regions. We also examine the staggered chiral, staggered nematic and dimer order parameters to determine the different phases of the ground state phase diagram with their respective long-range orders. Our findings indicate that the model undergoes first-order, second-order, gapless-gapless, and gapped-gapped phase transitions.
The continuous imaginary-time quantum Monte Carlo method with the worm update algorithm is applied to explore the ground-state properties of the spin-1/2 Heisenberg model with antiferromagnetic (AF) coupling J>0 and ferromagnetic (F) coupling J^{'}<0 along zigzag and armchair directions, respectively, on honeycomb lattice. It is found that by enhancing the F coupling J^{'} between zigzag AF chains, the system is smoothly crossover from one-dimensional zigzag spin chains to a two-dimensional magnetic ordered state. In absence of an external field, the system is in a stripe-ordered phase. In the presence of uniform and staggered fields, the uniform and staggered out-of-plane magnetizations appear while the stripe order remains in the xy plane, and a second-order quantum phase transition (QPT) at a critical staggered field is observed. The critical exponents of correlation length for QPTs induced by a staggered field for the cases with J>0, J^{'}<0 and J<0, J^{'}>0 are obtained to be ν=0.70046(1) and 0.7086(3), respectively, indicating that both cases belong to O(3) universality. The corresponding dynamic and susceptibility exponent z and γ/ν are fitted to be 1.006572(9), 1.9412(2) and 1.004615(8), 1.96121(9) for the two cases, respectively. The scaling behavior in a staggered field is analyzed, and the ground-state phase diagrams in the plane of coupling ratio and staggered field are presented for two cases. The temperature dependence of susceptibility and specific heat of both systems in external magnetic fields is also discussed. A Kosterlitz-Thouless phase transition is found for the present system in a uniform field.