[Paper Review] First-order transition between the plaquette valence bond solid and antiferromagnetic phases of the Shastry-Sutherland model

Ning Xi, Hongyu Chen+2 more|arXiv (Cornell University)|Nov 14, 2021

Advanced Condensed Matter Physics47 references4 citations

TL;DR

This study uses infinite tensor network states to demonstrate a weakly first-order transition between the plaquette valence bond solid (VBS) and antiferromagnetic (AFM) phases in the Shastry-Sutherland model. It identifies a competing full plaquette (FPL) state with energy within 10⁻⁴J of the empty plaquette (EPL) ground state, and proposes a deconfined quantum critical point (DQCP) at the triple point where EPL, FPL, and AFM phases meet, stabilized by a symmetry-preserving staggered ring exchange interaction.

ABSTRACT

We study the ground state phase diagram of the Shastry-Sutherland model by using the variational optimization of the infinite tensor network states, and find a weakly first-order transition between the plaquette and the antiferromagnetic states. The full plaquette state strongly competes with the empty plaquette ground state, with an energy difference less than $10^{-4}J$. We show a staggered ring exchange interaction that preserves the Shastry-Sutherland lattice symmetry can stabilize the full plaquette ground state. In light of this, we propose the triple point where the full plaquette, empty plaquette, and antiferromagnetic phases meet as a deconfined quantum critical point.

Motivation & Objective

• To resolve the long-standing debate on the nature of the plaquette-AFM transition in the Shastry-Sutherland model.
• To clarify whether the intermediate phase is an empty plaquette (EPL) or full plaquette (FPL) state, given conflicting theoretical and experimental reports.
• To investigate whether a deconfined quantum critical point (DQCP) can emerge at the intersection of EPL, FPL, and AFM phases.
• To explore how symmetry-preserving perturbations can stabilize the FPL state over the EPL state in the absence of lattice symmetry breaking.

Proposed method

• Employed variational optimization of infinite projected entangled simplex states (PESS) with a 16-PESS tensor network construction on the Shastry-Sutherland lattice.
• Used the PESS ansatz to compute ground-state energies and order parameters for the plaquette and antiferromagnetic phases with high accuracy.
• Introduced a staggered ring exchange interaction in the Hamiltonian that preserves the lattice symmetry of the Shastry-Sutherland model.
• Tracked the energy derivative dE/dQ and discontinuities in the first-order transition to detect critical behavior near the triple point.
• Performed systematic calculations across different bond ratio J/J′ and tensor bond dimension D to ensure convergence and accuracy.
• Constructed a global phase diagram of the generalized model to map the EPL, FPL, and AFM phases and identify the triple point.

Experimental results

Research questions

• RQ1 Is the plaquette-AFM transition in the Shastry-Sutherland model first-order or continuous, and what is the nature of the intermediate phase?
• RQ2 Can the full plaquette (FPL) state be stabilized as the ground state without breaking the lattice symmetry of the Shastry-Sutherland model?
• RQ3 What is the role of a staggered ring exchange interaction in tuning the ground state between EPL and FPL configurations?
• RQ4 Does a deconfined quantum critical point (DQCP) exist at the triple point where EPL, FPL, and AFM phases meet?
• RQ5 How do the energy differences between competing FPL and EPL states influence the possibility of a quantum spin liquid phase?

Key findings

• The plaquette-AFM transition in the standard Shastry-Sutherland model is weakly first-order, with a transition point at J/J′ ≈ 0.79.
• The empty plaquette (EPL) state is the ground state in the standard model, with energy lower than previous iPEPS and DMRG results at comparable bond dimensions.
• The full plaquette (FPL) state is energetically nearly degenerate with the EPL state, differing by less than 10⁻⁴J.
• A staggered ring exchange interaction that preserves the SS lattice symmetry stabilizes the FPL state as the ground state.
• The discontinuity in the energy derivative dE/dQ vanishes at the triple point, indicating a continuous transition consistent with a DQCP.
• The proposed DQCP at the EPL-FPL-AFM triple point exhibits enhanced SO(5) symmetry, supporting the deconfined quantum criticality scenario.