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Register a new userSpin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model
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Kai Schmidt Phillip
Publication date
2016
fields
Physics
and research's language is
English
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We show that the highly frustrated transverse-field Ising model on the three-dimensional pyrochlore lattice realizes a first-order phase transition without symmetry breaking between the low-field Coulomb quantum spin liquid and the high-field polarized phase. The quantum phase transition is located quantitively by comparing low- and high-field series expansions. Furthermore, the intriguing properties of the elementary excitations in the polarized phase are investigated. We argue that this model can be achieved experimentally by applying mechanical strain to a classical spin ice material comprised of non-Kramers spins such as Ho_2Ti_2O_7. Taken together with our results, this provides a new experimental platform to study quantum spin liquid physics.
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We present numerical evidence for the presence of a finite-temperature ($T$) phase transition separating paramagnet and quantum spin liquid in a three-dimensional variant of the Kitaev model defined on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from quantum spin liquid to paramagnet at a finite critical temperature $T_c$. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above $T_c$, while it obeys the Curie law at high $T$ and approaches a nonzero Van Vleck-type constant at low $T$. Although the susceptibility changes continuously at $T_c$, its $T$ derivative shows critical divergence at $T_c$. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to the discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables as well as the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition is interpreted as the one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. A correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently-discovered hyperhoneycomb compound, $beta$-Li$_2$IrO$_3$, is mentioned.
Neutron scattering is used to study magnetic field induced ordering in the quasi-1D quantum spin-tube compound Sul--Cu$_2$Cl$_4$ that in zero field has a non-magnetic spin-liquid ground state. The experiments reveal an incommensurate chiral high-field phase stabilized by a geometric frustration of the magnetic interactions. The measured critical exponents $betaapprox0.235$ and $ uapprox0.34$ at $H_capprox3.7$ T point to an unusual sub-critical scaling regime and may reflect the chiral nature of the quantum critical point.
A quantum magnet, LiCuSbO4, with chains of edge-sharing S = 1/2 CuO6 octahedra is reported. While the Curie-Weiss constant is ferromagnetic, theta = 30 K, no phase transition or spin freezing occurs down to 100 mK. Specific heat indicates a distinct high field phase near the 12 T saturation field. Neutron scattering shows incommensurate spin correlations with q = 0.47pm0.01{pi}/a and places an upper limit of 70 mueV on a potential spin gap. Exact diagonalization of easy plane S = 1/2 chains with competing ferro- and antiferromagnetic interactions (J1 = - 75 K, J2 = 34 K) accounts for the T > 2 K data.
The one-dimensional (1D) model system Au/Ge(001), consisting of linear chains of single atoms on a surface, is scrutinized for lattice instabilities predicted in the Peierls paradigm. By scanning tunneling microscopy and electron diffraction we reveal a second-order phase transition at 585 K. It leads to charge ordering with transversal and vertical displacements and complex interchain correlations. However, the structural phase transition is not accompanied by the electronic signatures of a charge density wave, thus precluding a Peierls instability as origin. Instead, this symmetry-breaking transition exhibits three-dimensional critical behavior. This reflects a dichotomy between the decoupled 1D electron system and the structural elements that interact via the substrate. Such substrate-mediated coupling between the wires thus appears to have been underestimated also in related chain systems.
The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions. More exotic symmetry-preserving boundary conditions, like cylindrical antiperiodic, are less frequently used for special tasks, such as the study of phase coexistence or the roughening of an interface. Here we show, instead, that when the thermodynamic limit is taken with these boundary conditions, a novel type of transition takes place below $T_c$ (the usual Ising transition temperature) without breaking neither ergodicity nor symmetry. Then, the low temperature phase is characterized by a regime (condensation) of strong magnetizations fluctuations which replaces the usual ferromagnetic ordering. This is due to critical correlations perduring for all T below Tc. The argument is developed exactly in the $d=1$ case and numerically in the d=2 case.
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