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arXiv:2511.04101 · Physical review. B./Physical review. B

Phase diagrams of S = 1 2 bilayer models of SU(2) symmetric antiferromagnets

Fan Zhang, Nisheeta Desai, Wenan Guo, Ribhu K. Kaul

Published Feb 17, 2026• 0 citations
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Abstract

We study the $T=0$ phase diagrams of models of bilayers of $S=1/2$ square lattices antiferromagnets with SU(2) Heisenberg symmetry that have 2, 4, and 6 spin exchanges. We study two families of bilayer models with distinct internal symmetries and, hence, different phase diagram topologies. A traditional bilayer model in which the interlayer interaction is Heisenberg so that the two layers can exchange spin (and energy) with each other, making it possible to achieve a simple dimerized valence bond liquid-like state. The resulting phase diagram is rich with Néel, valence bond solid and simple dimer phases, and both first-order and continuous transitions, which we demonstrate are consistent with the conventional Landau theory of order parameters. In the second family of models in which the layers can exchange only energy but no spin (reminiscent of the Ashkin-Teller coupling), the simple dimer state cannot occur. The phase diagrams reveal a number of phase transitions that are accessed for the first time. We find that the phase transition between Néel and VBS is first order in both the spin-spin and energy-energy coupled models, although they have strikingly distinct finite-size scaling behavior and that the transition from VBS to dimer in the spin-spin coupling model deviates from the expected scenario of an XY model with dangerously irrelevant four-fold anisotropy.

DOI
10.1103/y58l-pcy1

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We present a detailed study of the destruction of SU(NNN) magnetic order in square lattice bilayer antiferromagnets using unbiased quantum Monte Carlo numerical simulations and field theoretic techniques. We study phase transitions from an SU(NNN) N\'eel state into two distinct quantum disordered ``valence-bond'' phases: a valence-bond liquid (VBL) with no broken symmetries and a lattice-symmetry-breaking valence-bond solid (VBS) state. For finite interlayer coupling, the cancellation of Berry phases between the layers has dramatic consequences on the two phase transitions: the N\'eel-VBS transition is first order for all $N\ensuremath{\ge}5$ accesible in our model, whereas the N\'eel-VBL transition is continuous for N=2N=2N=2 and first order for $N\ensuremath{\ge}4$; for N=3N=3N=3 the N\'eel-VBL transition show no signs of first-order behavior.
We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5<J(2)/J(1)<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J(2)/J(1)<0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.
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Phase diagram of the SU(NNN) antiferromagnet of spin SSS on a square lattice
We investigate the ground state phase diagram of an SU(NNN)-symmetric antiferromagnetic spin model on a square lattice where each site hosts an irreducible representation of SU(NNN) described by a square Young tableau of N/2N/2N/2 rows and 2S2S2S columns. We show that negative sign free fermion Monte Carlo simulations can be carried out for this class of quantum magnets at any SSS and even values of NNN. In the large-NNN limit, the saddle point approximation favors a four-fold degenerate valence bond solid phase. In the large SSS-limit, the semi-classical approximation points to Néel state. On a line set by N=8S+2N=8S + 2N=8S+2 in the SSS versus NNN phase diagram, we observe a variety of phases proximate to the Néel state. At S=1/2S = 1/2S=1/2 and 3/23/23/2 we observe the aforementioned four fold degenerate valence bond solid state. At S=1S=1S=1 a two fold degenerate spin nematic state in which the C4_44​ lattice symmetry is broken down to C2_22​ emerges. Finally at S=2S=2S=2 we observe a unique ground state that pertains to a two-dimensional version of the Affleck-Kennedy-Lieb-Tasaki state. For our specific realization, this symmetry protected topological state is characterized by an SU(18), S=1/2S=1/2S=1/2 boundary state, that has a dimerized ground state. These phases that are proximate to the Néel state are consistent with the notion of monopole condensation of the antiferromagnetic order parameter. In particular one expects spin disordered states with degeneracy set by mod(4,2S)\text{mod}(4,2S)mod(4,2S).
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