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Condensed Matter > Strongly Correlated Electrons
Title: Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
(Submitted on 24 Sep 2023 (v1), last revised 7 Apr 2024 (this version, v3))
Abstract: We perform an in-depth investigation of the phase diagram of the $J_1-J_2$ Heisenberg model on the square lattice. We take advantage of Density Matrix Renormalization Group and Fully-Augmented Matrix Product States methods and reach unprecedented accuracy with large bond dimensions. We utilize excited-level crossing analysis to pinpoint the phase transition points. It was believed before that there exists a narrow spin liquid phase sandwiched by the N\'eel antiferromagnetic (AFM) and valence bond solid (VBS) phases. Through careful finite size scaling of the level crossing points, we find a direct phase transition between the N\'eel AFM and VBS phases at $J_2/J_1 = 0.535(3)$, suggesting the absence of an intermediate spin liquid phase. We also provide accurate results for ground state energies for a variety of sizes, from which we find that the transition between the N\'eel AFM and VBS phases is continuous. These results indicate the existence of a deconfined quantum critical point at $J_2/J_1 = 0.535(3)$ in the model. From the crossing of the first derivative of the energies with $J_2$ for different sizes, we also determine the precise location of the first order phase transition between the VBS and stripe AFM phases at $J_2/J_1=0.610(5)$.
Submission history
From: Mingpu Qin [view email][v1] Sun, 24 Sep 2023 13:11:30 GMT (1514kb,D)
[v2] Thu, 14 Mar 2024 09:30:56 GMT (3568kb,D)
[v3] Sun, 7 Apr 2024 11:15:16 GMT (3433kb,D)
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