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We study the coupled-top model with three large spins located on a triangle. Depending on the coupling strength, there exist three phases: disordered paramagnetic phase, ferromagnetic phase, and frustrated antiferromagnetic phase, which can be distinguished by the mean-field approach. The paramagnetic-ferromagnetic phase transition is accompanied by the breaking of the global $Z_2$ symmetry, whereas the paramagnetic-antiferromagnetic phase transition is accompanied by the breaking of both the global $Z_2$ symmetry and the translational symmetry. Exact analytical results of higher-order quantum effects beyond the mean-field contribution, such as the excitation energy, quantum fluctuation, and von Neumann entropy, can be achieved by the Holstein-Primakoff transformation and symplectic transformation in the thermodynamic limit. Near the quantum critical point, the energy gap closes, along with the divergence of the quantum fluctuation in certain quadrature and von Neumann entropy. Particular attention should be paid to the antiferromagnetic phase, where geometric frustration takes effect. The critical behaviors in the antiferromagnetic phase are quite different from those in the paramagnetic and ferromagnetic phases, which highlight the importance of geometric frustration. The triangular coupled-top model provides a simple and feasible platform to study the quantum phase transition and the novel critical behaviors induced by geometric frustration., Comment: 10 pages, 6 figures

We study the anisotropic spin-boson model (SBM) with the subohmic bath by a numerically exact method based on variational matrix product states. A rich phase diagram is found in the anisotropy-coupling strength plane by calculating several observables. There are three distinct quantum phases: a delocalized phase with even parity (phase I), a delocalized phase with odd parity (phase II), and a localized phase with broken $Z_2$ symmetry (phase III), which intersect at a quantum tricritical point. The competition between those phases would give overall picture of the phase diagram. For small power of the spectral function of the bosonic bath, the quantum phase transition (QPT) from phase I to III with mean-field critical behavior is present, similar to the isotropic SBM. The novel phase diagram full with three different phases can be found at large power of the spectral function: For highly anisotropic case, the system experiences the QPTs from phase I to II via 1st-order, and then to the phase III via 2nd-order with the increase of the coupling strength. For low anisotropic case, the system only experiences the continuous QPT from phase I to phase III with the non-mean-field critical exponents. Very interestingly, at the moderate anisotropy, the system would display the continuous QPTs for several times but with the same critical exponents. This unusual reentrance to the same localized phase is discovered in the light-matter interacting systems. The present study on the anisotropic SBM could open an avenue to the rich quantum criticality., Comment: 9 pages, 6 figures

We present a pressure study of the electrical resistivity, ac magnetic susceptibility, and powder x-ray diffraction (XRD) of the recently discovered ${\text{BiS}}_{2}$-based superconductor ${\text{EuBiS}}_{2}\text{F}$. At ambient pressure, ${\text{EuBiS}}_{2}\text{F}$ shows an anomaly in the resistivity at around ${T}_{0}\ensuremath{\approx}280$ K and a superconducting transition at ${T}_{c}\ensuremath{\approx}0.3$ K. Upon applying hydrostatic pressure, there is little change in ${T}_{0}$ but the amplitude of the resistive anomaly is suppressed, whereas there is a dramatic enhancement of ${T}_{c}$ from 0.3 K to about 8.6 K at a critical pressure of ${p}_{c}\ensuremath{\approx}1.4$ GPa. XRD measurements confirm that this enhancement of ${T}_{c}$ coincides with a structural phase transition from a tetragonal phase ($P4/nmm$) to a monoclinic phase ($P{2}_{1}/m$), which is similar to that observed in isostructural ${\text{LaO}}_{0.5}{\text{F}}_{0.5}{\text{BiS}}_{2}$. Our results suggest the presence of two different superconducting phases with distinct crystal structures in ${\text{EuBiS}}_{2}\text{F}$, which may be a general property of this family of ${\text{BiS}}_{2}$-based superconductors.

The recent discovery of superconductivity in the quasi-one-dimensional compound ${\mathrm{K}}_{2}{\mathrm{Cr}}_{3}{\mathrm{As}}_{3}$, which consists of double-walled tubes of ${[{({\mathrm{Cr}}_{3}{\mathrm{As}}_{3})}^{2\ensuremath{-}}]}^{\ensuremath{\infty}}$ that run along the $c$ axis, has attracted immediate attention as a potential system for studying superconductors with reduced dimensionality. Here we report clear experimental evidence for the unconventional nature of the superconducting order parameter in ${\mathrm{K}}_{2}{\mathrm{Cr}}_{3}{\mathrm{As}}_{3}$, by precisely measuring the temperature dependence of the change in the penetration depth $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}(T)$ using a tunnel-diode oscillator. Linear behavior of $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}(T)$ is observed for $T\ensuremath{\ll}{T}_{c}$, instead of the exponential behavior of conventional superconductors, indicating that there are line nodes in the superconducting gap. This is strong evidence for unconventional behavior and may provide key information for identifying the pairing state of this super-conductor.