We consider two one-dimensional quantum XX magnets linked by a periodically driven quantum point contact. If magnets are initially polarized in opposite directions, one expects that a spin current through the quantum point contact will establish. It has been shown recently [Phys. Rev. B 103, L041405 (2021)] that, in fact, when the driving frequency exceeds a critical value, the current halts completely, the quantum point contact being effectively insulating. Here we enquire how this picture is affected by quantum dephasing. Our findings reveal that any nonzero dephasing restores the current.
We consider two one-dimensional quantum XX magnets linked by a periodically driven quantum point contact. If magnets are initially polarized in opposite directions, one expects that a spin current through the quantum point contact will establish. It has been shown recently [Phys. Rev. B 103, L041405 (2021)] that, in fact, when the driving frequency exceeds a critical value, the current halts completely, the quantum point contact being effectively insulating. Here we enquire how this picture is affected by quantum dephasing. Our findings reveal that any nonzero dephasing restores the current.
We study a quantum system that consists of two fermionic chains coupled by a driven quantum point contact (QPC). The QPC contains a bond with a periodically varying tunneling amplitude. Initially, the left chain is packed with fermions, while the right one is empty. We numerically track the evolution of the system and demonstrate that, at frequencies above a certain threshold, the current through the QPC halts, and the particle imbalance between the chains remains forever. This implies a spectacular breakdown of the Floquet version of the eigenstate thermalization hypothesis that predicts a homogeneous particle density profile at large times. We confirm the effect for various driving protocols and interparticle interactions.
We study the transport of noninteracting fermions through a periodically driven quantum point contact (QPC) connecting two tight-binding chains. Initially, each chain is prepared in its own equilibrium state, generally with a bias in chemical potentials and temperatures. We examine the heating rate (or, alternatively, energy increase per cycle) in the nonequilibrium time-periodic steady state established after initial transient dynamics. We find that the heating rate vanishes identically when the driving frequency exceeds the bandwidth of the chain. We first establish this fact for a particular type of QPCs where the heating rate can be calculated analytically. Then we verify numerically that this nonequilibrium phase transition is present for a generic QPC. Finally, we derive this effect perturbatively in leading order for cases when the QPC Hamiltonian can be considered a small perturbation. Strikingly, we discover that for certain QPCs the current averaged over the driving cycle also vanishes above the critical frequency, despite a persistent bias. This shows that a driven QPC can act as a frequency-controlled quantum switch.
We experimentally demonstrate the phenomenon of dynamical many-body freezing in a periodically driven Ising chain. Theoretically [A. Das, Phys. Rev. B 82, 172402 (2010)], for certain values of the drive parameters all fundamental degrees of freedom contributing to the response dynamics freeze for all time and for arbitrary initial state. Also, since the condition of freezing involves only the drive parameters and not the quantization of the momentum (i.e., the system size), our simulation with a small (3-spin) chain captures all salient features of the freezing phenomenon predicted for the infinite chain. Using optimal control techniques, we realize high-fidelity cosine-modulated drive, and observe nonmonotonic freezing of magnetization at specific frequencies of modulation. Time evolution of the excitations in momentum space has been tracked directly through magnetization measurements.
In order to reveal mechanisms to control and manipulate spin currents, we perform a detailed investigation of the dephasing effects in the open XX model with a Lindblad dynamics involving global dissipators and thermal baths. Specifically, we consider dephasing noise modeled by current-preserving Lindblad dissipators acting on graded versions of these spin systems, that is, systems in which the magnetic field and/or the spin interaction are growing (decreasing) along the chain. In our analysis, we study the nonequilibrium steady state via the covariance matrix using the Jordan-Wigner approach to compute the spin currents. We find that the interplay between dephasing and graded systems gives rise to a nontrivial behavior: When we have homogeneous magnetic field and graded interactions we have rectification enhancement mechanisms, and when we have fully graded systems we can control the spin current in order to keep the direction of the particle and/or spin flow even with inverted baths. We describe our result in detailed numerical analysis and we see that rectification in this simple model indicates that the phenomenon may generally occur in quantum spin systems.
We study a quantum point contact in a quantum spin Hall insulator. It has recently been shown that the Luttinger liquid theory of such a structure maps to the theory of a weak link in a Luttinger liquid with spin with Luttinger liquid parameters ${g}_{\ensuremath{\rho}}=1/{g}_{\ensuremath{\sigma}}=g<1$. We show that for weak interactions, 1/2<g<1, the pinch-off of the point contact as a function of gate voltage is controlled by a novel quantum critical point, which is a realization of a nontrivial intermediate fixed point found previously in the Luttinger liquid model with spin. We predict that the dependence of the conductance on gate voltage near the pinch-off transition for different temperatures collapses onto a universal curve described by a crossover scaling function associated with that fixed point. We compute the conductance and critical exponents of the critical point as well as the universal scaling function in solvable limits, which include $g=1\ensuremath{-}ϵ$, g=1/2+ϵ, and g=1/3. These results, along with a general scaling analysis, provide an overall picture of the critical behavior as a function of g. In addition, we analyze the structure of the four-terminal conductance of the point contact in the weak tunneling and weak backscattering limits. We find that different components of the conductance can have different temperature dependences. In particular, we identify a skew conductance GXY, which we predict vanishes as ${T}^{\ensuremath{\gamma}}$ with $\ensuremath{\gamma}\ensuremath{\ge}2$. This behavior is a direct consequence of the unique edge state structure of the quantum spin Hall insulator. Finally, we show that for strong interactions, g<1/2, the presence of spin nonconserving spin-orbit interactions leads to a novel time-reversal-symmetry breaking insulating phase. In this phase, the transport is carried by spinless chargons and chargeless spinons. These lead to nontrivial correlations in the low frequency shot noise. Implications for experiments on HgCdTe quantum well structures will be discussed.
We study the role played by extensive degeneracy in shaping the nature of the quantum dynamics of a one-dimensional spin model for both ramp and periodic drive protocols. The model displays an extensive degenerate manifold of states for a specific value of one of the parameters of its Hamiltonian. We study a linear ramp which takes the spin model through this degenerate point and show that it leads to a deviation from the usual Kibble-Zurek behavior. We also study the Stückelberg oscillations in such a model for a ramp which passes twice through the degenerate point. Our study indicates that such oscillations are strongly suppressed leading to a distinct behavior compared to those arising from double passage through a quantum critical point. Finally, we study the periodic dynamics of the model and show, for a large drive amplitude, the existence of special drive frequencies at which the system exhibits an approximate emergent U(1) symmetry. We study the effect of this emergent symmetry on the correlators of the driven system and demonstrate the existence of dynamic symmetry restoration at these frequencies. We study the fate of the emergent symmetry when the drive amplitude is decreased and discuss possible experiments to test our theory.