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arXiv:2204.12147 · Physical review. B./Physical review. B

Quantum phase transitions from competing short- and long-range interactions on a π -flux lattice

Xingchuan Zhu, Yiqun Huang, Huaiming Guo, Shiping Feng

Published Aug 3, 2022• 7 citations
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Abstract

Quantum phase transitions from the cluster-charge interaction, which is composed of competing short- and long-range interactions, are investigated on a $\ensuremath{\pi}$-flux lattice by using the mean-field theory and determinant quantum Monte Carlo (DQMC) simulations. Both methods identify a plaquette-dimer phase, which develops from a finite interaction strength. While its signature in DQMC is relatively weak, an obvious antiferromagnetic transition is revealed in the spin structure factor instead. The corresponding critical interaction and exponents are readily obtained by finite-size scalings, with the plaquette-dimer structure factor that can also be well scaled. These results suggest a possible deconfined quantum critical point between the plaquette-dimer and antiferromagnetic phases driven by the cluster-charge interaction on a $\ensuremath{\pi}$-flux lattice.

DOI
10.1103/physrevb.106.075109

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Quantum phase transitions from the cluster-charge interaction, which is composed of competing short- and long-range interactions, are investigated on a \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux lattice by using the mean-field theory and determinant quantum Monte Carlo (DQMC) simulations. Both methods identify a plaquette-dimer phase, which develops from a finite interaction strength. While its signature in DQMC is relatively weak, an obvious antiferromagnetic transition is revealed in the spin structure factor instead. The corresponding critical interaction and exponents are readily obtained by finite-size scalings, with the plaquette-dimer structure factor that can also be well scaled. These results suggest a possible deconfined quantum critical point between the plaquette-dimer and antiferromagnetic phases driven by the cluster-charge interaction on a \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux lattice.
The plaquette phase of the square-lattice quantum dimer model is studied using a continuous-time reptation quantum Monte Carlo method for lattices of sizes up to $48\ifmmode\times\else\texttimes\fi{}48$ sites. We determine the location of the phase transition between the columnar and plaquette phases to occur at ${V}_{c}∕J=0.60\ifmmode\pm\else\textpm\fi{}0.05$ which is significantly larger than inferred from previous exact diagonalization studies on smaller lattices. Off diagonal correlation functions are obtained. They exhibit long-range order in the plaquette phase but not at the Rokhsar-Kivelson point. We also observe significant finite-size corrections to scaling for the transition between the plaquette phase and the critical resonating valence bond liquid. This study demonstrates the importance of understanding finite-size effects when considering critical properties of the square-lattice quantum dimer model.
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Using quantum Monte Carlo and numerical analytic continuation methods, we study the dynamic spin structure factor and the single-hole spectral function of a two-dimensional quantum magnet (JJJ-QQQ model) at its quantum phase transition separating Néel antiferromagnetic and spontaneously dimerized ground states. At this putative deconfined quantum-critical point, we find a broad continuum of spinon excitations that can be accounted for by the fermionic πππ-flux state; a known mean-field model for deconfined quantum criticality. We find that the best description of the two-spinon continuum is with a version of the model with a 2×22\times 22×2 unit cell, reflecting non-trivial mutual statistics of spinons and anti-spinons. The single-hole spectral function can be described by the same spinon dispersion relation and an independently propagating holon. Thus, the system exhibits spin-charge separation and will likely evolve into an extended holon metal phase at finite doping.
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