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arXiv · 2109.10042

Weakly first-order quantum phase transition between Spin Nematic and Valence Bond Crystal Order in a square lattice SU(4) fermionic model

Pranay Patil·Fabien Alet·Sylvain Capponi·Matthieu Mambrini
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Abstract

We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultracold atom experiments and existence of spin liquid ground states. Using a basis transformation, we show that part of the phase diagram is amenable to quantum Monte Carlo simulations without a sign problem. We find evidence for spin nematic and valence bond crystalline phases, which are separated by a weak first order phase transition. A U(1) symmetry is found to emerge in the valence bond crystal histograms, suggesting proximity to a deconfined quantum critical point. Our results are obtained with the help of a loop algorithm which allows large-scale simulations of bilinear-biquadratic SO(N ) models on arbitrary lattices in a certain parameter regime.

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Pranay Patil, Fabien Alet, Sylvain Capponi, Matthieu Mambrini. 2021-09-21. Weakly first-order quantum phase transition between Spin Nematic and Valence Bond Crystal Order in a square lattice SU(4) fermionic model. https://arxiv.org/abs/2109.10042

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