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arXiv:0704.0114 · Physical Review B

Quantum phase transition in the four-spin exchange antiferromagnet

Valeri N. Kotov, Dao‐Xin Yao, A. H. Castro Neto, David K Campbell

Published Nov 10, 2009• 17 citations
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Abstract

We study the $S=1/2$ Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N\'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.

DOI
10.1103/physrevb.80.174403

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We study the S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges [introduced by A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).] This model undergoes a quantum phase transition from a spontaneously dimerized phase to N'eel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.
We study a Heisenberg S=1/2 ring-exchange antiferromagnet which exhibits a quantum phase transition from a spontaneously dimerized (valence bond solid) phase to a magnetically ordered (Neel) phase. We argue that the quantum transition is of unconventional nature; both singlet and triplet modes of high density condense as the transition is approached from the dimer side, signaling restoration of lattice symmetry. These features are consistent with "deconfined quantum criticality", of which the present model is believed to be the only example so far.
Quantum phase transition from the N\'eel to the dimer states in an antiferromagnetic (AF) Heisenberg model on square lattice is studied. We introduce a control parameter $\ensuremath{\alpha}$ for the exchange coupling that connects the N\'eel $(\ensuremath{\alpha}=0)$ and the dimer $(\ensuremath{\alpha}=1)$ states. We employ the CP1{\mathit{CP}}^{1}CP1 representation of the s=12s=\frac{1}{2}s=21​ spin operator and integrate out the half of the CP1{\mathit{CP}}^{1}CP1 variables at odd sites to obtain a CP1{\mathit{CP}}^{1}CP1 nonlinear $\ensuremath{\sigma}$ model. The effective coupling constant is a function of $\ensuremath{\alpha}$, and at $\ensuremath{\alpha}=0$, the CP1{\mathit{CP}}^{1}CP1 model is in the ordered phase that corresponds to the N\'eel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of ${\ensuremath{\alpha}}_{C}$ as $\ensuremath{\alpha}$ increases. In the N\'eel state, the dynamical composite U(1) gauge field in the CP1{\mathit{CP}}^{1}CP1 model is in a Higgs phase, and low-energy excitations are gapless spin waves. In the dimer phase, a confinement phase of the gauge theory with s=1s=1s=1 excitations is realized. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in three spatial dimensions, is realized and s=12s=\frac{1}{2}s=21​ spinons appear as low-energy excitations.
Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin- 12\frac{1}{2}21​ Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J 1 and J 2. It is well known that a nonmagnetic phase arises in this model for 0.4 ≲ J 2/J 1 ≲ 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J 2 ≈ 0.64 J 1 from the non-magnetic phase to the Néel one. A large gap (≳ 0.4J 1) is found in the singlet spectrum for J 2 < 0.64J 1, which excludes a gapless spin-liquid state for 0.4 ≲ J 2/J 1 ≲ 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J 2 ≈ 0.55J 1, presumably between two nonmagnetic phases.
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.
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.
Based on a special variant of plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of spin-12\frac1221​ Heisenberg antiferromagnet on square lattice with nearest- and frustrating next-nearest-neighbor exchange couplings J1J_1J1​ and J2J_2J2​. It is well known that a non-magnetic phase arises in this model at 0.4≲J2/J1≲0.60.4\lesssim J_2/J_1\lesssim 0.60.4≲J2​/J1​≲0.6 sandwiched by two Neel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J2≈0.64J1J_2\approx 0.64J_1J2​≈0.64J1​ from the non-magnetic phase to the Neel one. Large gap (≳0.4J1\gtrsim0.4J_1≳0.4J1​) is found in the singlet spectrum at J2<0.64J1J_2<0.64J_1J2​<0.64J1​ that excludes a gapless spin-liquid state at 0.4≲J2/J1≲0.60.4\lesssim J_2/J_1\lesssim 0.60.4≲J2​/J1​≲0.6 and the deconfined quantum criticality scenario for the QPT to another Neel phase. We observe a first-order QPT at J2≈0.55J1J_2\approx 0.55J_1J2​≈0.55J1​ presumably between two non-magnetic phases.