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arXiv:cond-mat/9907178 · Physical review. B, Condensed matter

Nature of the transition from the spontaneously dimerized to the Néel phase in the two-dimensional J1−J2 model

Valeri N. Kotov, Oleg P. Sushkov

Published May 1, 2000• 16 citations
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Abstract

We analyze the spectrum of the two-dimensional $S=1/2$ frustrated Heisenberg model near the transition from the spontaneously dimerized spin-liquid phase into the N\'eel ordered phase. Two excitation branches, the triplet magnon and the collective singlet mode, both become gapless at the transition point. However, we find that the length scales associated with these modes are well separated at the quantum transition. While in the quantum disordered phase the singlet excitation has finite spectral weight and reflects the existence of spontaneous dimer order, near the transition point the size of the singlet bound state grows exponentially with the correlation length, and hence the quasiparticle residue is exponentially small. Therefore the critical dynamics remains in the O(3) universality class in spite of the four gapless modes.

DOI
10.1103/physrevb.61.11820

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We analyze the stability of the spontaneously dimerized phase of the frustrated Heisenberg antiferromagnet---the ${J}_{1}{\ensuremath{-}J}_{2}$ model---in two dimensions. The lowest triplet excitation, corresponding to breaking of a singlet bond, is found to be stable in the region $0.38\ensuremath{\lesssim}{J}_{2}{/J}_{1}\ensuremath{\lesssim}0.62.$ In addition we find a stable low-energy collective singlet mode, which reflects the spontaneous violation of the discrete symmetry. The spontaneous dimerization vanishes at the point of second-order quantum transition into the N\'eel ordered phase $[{(J}_{2}{/J}_{1}{)}_{c1}\ensuremath{\approx}0.38].$ We argue that the disappearance of dimer order is related to the vanishing of the singlet energy gap at the transition point.
We overview some recent work and present new results on the ground-state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyse the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation in the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.
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We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the ${J}_{1}{\ensuremath{-}J}_{2}$ model, in two dimensions. Two quantum phase transitions in the model are already known: the second-order transition from the N\'eel state to the spin liquid state at ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38,$ and the first-order transition from the spin liquid state to the collinear state at ${(J}_{2}{/J}_{1}{)}_{c4}\ensuremath{\approx}0.60.$ We have found evidence for two second-order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette-type modulation at ${(J}_{2}{/J}_{1}{)}_{c3}=0.50\ifmmode\pm\else\textpm\fi{}0.02,$ and the transition from the simple N\'eel state to the N\'eel state with spin columnar dimerization at ${(J}_{2}{/J}_{1}{)}_{c1}=0.34\ifmmode\pm\else\textpm\fi{}0.04.$ We also present an independent calculation of ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38$ using another approach.