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Paper IPM / P / 15025  


Abstract:  
We investigate the groundstate nature of the transverse field Ising model on the J1J2 square lattice at the highly frustrated point J2/J1=0.5. At zero field, the model has an exponentially large degenerate classical ground state, which can be affected by quantum fluctuations for nonzero field toward a unique quantum ground state. We consider two types of quantum fluctuations, harmonic ones by using linear spinwave theory (LSWT) with singlespinflip excitations above a longrange magnetically ordered background and anharmonic fluctuations, by employing a clusteroperator approach (COA) with multispin clustertype fluctuations above a nonmagnetic clusterordered background. Our findings reveal that the harmonic fluctuations of LSWT fail to lift the extensive degeneracy as well as signaling a violation of the HellmannFeynman theorem. However, the stringtype anharmonic fluctuations of COA are able to lift the degeneracy toward a string valencebondsolid (VBS) state, which is obtained from an effective theory consistent with the HellmannFeynman theorem as well. Our results are further confirmed by implementing numerical tree tensor network simulation. The emergent nonmagnetic string VBS phase is gapped and breaks lattice rotational symmetry with only twofold degeneracy, which bears a continuous quantum phase transition at ï¿½?/J1ï¿½??0.50 to the quantum paramagnet phase of high fields. The critical behavior is characterized by Î½ï¿½??1.0 and Î³ï¿½??0.33 exponents.
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