[Paper Review] Dynamical Signatures of Symmetry Broken and Liquid Phases in an $S=1/2$ Heisenberg Antiferromagnet on the Triangular Lattice

Markus Drescher, Laurens Vanderstraeten+2 more|arXiv (Cornell University)|Sep 7, 2022

Advanced Condensed Matter Physics80 references7 citations

TL;DR

This study uses large-scale matrix-product state simulations to compute the dynamical spin structure factor of the S=1/2 J1-J2 Heisenberg model on a triangular lattice, revealing distinct dynamical signatures in the 120° ordered phase and a candidate spin-liquid phase at J2/J1=0.125. It demonstrates avoided magnon decay in the ordered phase and identifies low-energy excitations at the Brillouin zone corners in the spin-liquid phase, supporting the presence of gapless Dirac spin liquid behavior with triplet monopole excitations.

ABSTRACT

We present the dynamical spin structure factor of the antiferromagnetic spin-$\frac{1}{2}$ $J_1-J_2$ Heisenberg model on a triangular lattice obtained from large-scale matrix-product state simulations. The high frustration due to the combination of antiferromagnetic nearest and next-to-nearest neighbour interactions yields a rich phase diagram. We resolve the low-energy excitations both in the $120^{\circ}$-ordered phase and in the putative spin liquid phase at $J_2/J_1 = 0.125$. In the ordered phase, we observe an avoided decay of the lowest magnon-branch, demonstrating the robustness of this phenomenon in the presence of gapless excitations. Our findings in the spin-liquid phase chime with the field-theoretical predictions for a gapless Dirac spin liquid, in particular the picture of low-lying monopole excitations at the corners of the Brillouin zone. We comment on possible practical difficulties of distinguishing proximate liquid and solid phases based on the dynamical structure factor.

Motivation & Objective

• To identify dynamical fingerprints of symmetry-broken and quantum spin-liquid phases in the frustrated S=1/2 J1-J2 Heisenberg model on a triangular lattice.
• To resolve low-energy excitations in both the 120° ordered phase (J2=0) and the putative spin-liquid phase at J2/J1=0.125.
• To test the robustness of avoided quasiparticle decay in the presence of gapless excitations in the ordered phase.
• To compare numerical results with field-theoretical predictions for a U(1) Dirac spin liquid, particularly regarding monopole excitations at the Brillouin zone corners.
• To assess the practical challenges in distinguishing proximate quantum phases using the dynamical structure factor.

Proposed method

• Large-scale matrix-product state (MPS) time-evolution simulations are used to compute the dynamical spin structure factor on infinite cylinders with L_y=6.
• The quasiparticle ansatz is applied as a complementary method to target excited states on top of the MPS ground state.
• The spectral function is computed for two key points: J2=0 (120° ordered phase) and J2/J1=0.125 (candidate spin-liquid phase).
• The results are compared with analytical calculations and variational Monte Carlo data for a U(1) Dirac spin liquid ansatz.
• Finite-cylinder effects are accounted for by comparing DMRG results with analytical predictions for the static structure factor χ(k).
• Field-theoretical predictions for triplet monopole excitations at the K and K' points of the Brillouin zone are used as a benchmark for the spin-liquid phase.

Experimental results

Research questions

• RQ1 Does the lowest magnon branch in the 120° ordered phase exhibit avoided decay despite kinematic decay channels?
• RQ2 What dynamical features characterize the candidate spin-liquid phase at J2/J1=0.125, and how do they compare to field-theoretical predictions?
• RQ3 Are low-energy excitations localized at the corners of the Brillouin zone in the spin-liquid phase, as predicted for a U(1) Dirac spin liquid?
• RQ4 To what extent do the dynamical structure factors of the ordered and spin-liquid phases exhibit similar finite-time and short-distance correlations, complicating experimental distinction?
• RQ5 Can the MPS approach validate the variational Monte Carlo description of a U(1) Dirac spin liquid without prior assumptions about the ground state wave function?

Key findings

• The lowest magnon branch in the 120° ordered phase exhibits avoided decay, confirming its robustness even when kinematically allowed, consistent with previous findings in anisotropic models.
• In the candidate spin-liquid phase at J2/J1=0.125, prominent low-energy excitations are observed at the K and K' points of the Brillouin zone, matching predictions for triplet monopole excitations in a U(1) Dirac spin liquid.
• The static spin structure factor χ(k) in the spin-liquid phase shows broad, diffuse maxima at the K points, in qualitative agreement with analytical predictions for a U(1) Dirac spin liquid, despite finite-cylinder effects.
• Excellent agreement is found between time-evolution and quasiparticle ansatz methods, validating both as reliable tools for studying dynamical correlations in quantum spin systems.
• The dynamical structure factors of the ordered and spin-liquid phases share striking similarities in finite-time and short-distance correlations, highlighting the challenge of experimentally distinguishing such proximate phases.
• The MPS results support the U(1) Dirac spin liquid description without prior wave function assumptions, lending strong validation to variational Monte Carlo approaches.