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Register a new userStark time crystals: Symmetry breaking in space and time
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The compelling original idea of a time crystal has referred to a structure that repeats in time as well as in space, an idea that has attracted significant interest recently. While obstructions to realize such structures became apparent early on, focus has shifted to seeing a symmetry breaking in time in periodically driven systems, a property of systems referred to as discrete time crystals. In this work, we introduce Stark time crystals based on a type of localization that is created in the absence of any spatial disorder. We argue that Stark time crystals constitute a phase of matter coming very close to the original idea and exhibit a symmetry breaking in space and time. Complementing a comprehensive discussion of the physics of the problem, we move on to elaborating on possible practical applications and argue that the physical demands of witnessing genuine signatures of many-body localization in large systems may be lessened in such physical systems.
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We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in the topological superconducting state is result of spontaneous breaking of time-reversal symmetry in the superconducting state. The peculiarities in the chiral gapless edge modes behavior are studied, the Chern numbers are calculated.
We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry breaking occurs via a nonequilibrium quantum phase transition. For dissipative oscillators, the main effect of the weak coupling is to make the switching rate of an oscillator between its period-2 states dependent on the states of other oscillators. This allows mapping the oscillators onto a system of coupled spins. Away from the bifurcation parameter values where the period-2 states emerge, the stationary state corresponds to having a microscopic current in the spin system, in the presence of disorder. In the vicinity of the bifurcation point or for identical oscillators, the stationary state can be mapped on that of the Ising model with an effective temperature $propto hbar$, for low temperature. Closer to the bifurcation point the coupling can not be considered weak and the system maps onto coupled overdamped Brownian particles performing quantum diffusion in a potential landscape.
The noncentrosymmetric superconductor Re$_{24}$Ti$_{5}$, a time-reversal symmetry (TRS) breaking candidate with $T_c = 6$,K, was studied by means of muon-spin rotation/relaxation ($mu$SR) and tunnel-diode oscillator (TDO) techniques. At a macroscopic level, its bulk superconductivity was investigated via electrical resistivity, magnetic susceptibility, and heat capacity measurements. The low-temperature penetration depth, superfluid density and electronic heat capacity all evidence an $s$-wave coupling with an enhanced superconducting gap. The spontaneous magnetic fields revealed by zero-field $mu$SR below $T_c$ indicate a time-reversal symmetry breaking and thus the unconventional nature of superconductivity in Re$_{24}$Ti$_{5}$. The concomitant occurrence of TRS breaking also in the isostructural Re$_6$(Zr,Hf) compounds, hints at its common origin in this superconducting family and that an enhanced spin-orbital coupling does not affect pairing symmetry.
We found that thermodynamic quantum time crystals in fermi systems, defined as quantum orders oscillating periodically in the imaginary Matsubara time with zero mean, are metastable for two general classes of solutions. Mean-field time independent solutions proved to have lower free energy manifesting true thermodynamic equilibrium with either single or multiple (competing) charge, spin and superconducting symmetry breaking orders. The no-go theorem is proven analytically for a case of long-range interactions between fermions in momentum space in electron-hole and Cooper channels.
States of matter that break time-reversal symmetry are invariably associated with magnetism or circulating currents. Recently, one of us proposed a phase, the directional scalar spin chiral order (DSSCO), as an exception: it breaks time-reversal symmetry via chiral ordering of spins along a particular direction, but is spin-rotation symmetric. In this work, we prove the existence of this state via state-of-the-art density matrix renormalization group (DMRG) analysis on a spin-1 chain with nearest-neighbor bilinear-biquadratic interactions and additional third-neighbor ferromagnetic Heisenberg exchange. Despite the large entanglement introduced by the third-neighbor coupling, we are able to access system sizes up to $L=918$ sites. We find first order phase transitions from the DSSCO into the famous Haldane phase as well as a spin-quadrupolar phase where spin nematic correlations dominate. In the Haldane phase, we propose and demonstrate a method for detecting the topological edge states using DMRG that could be useful for other topological phases too.
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