Optimal non-linear passage through a quantum critical point

We analyze the problem of optimal adiabatic passage through a quantum critical point. We show that to minimize the number of defects the tuning parameter should be changed as a power-law in time. The optimal power is proportional to the logarithm of the total passage time multiplied by universal critical exponents characterizing the phase transition. We support our results by the general scaling analysis and by explicit calculations for the transverse field Ising model.Comment: 4+ pages, 2 figure

Universal adiabatic dynamics across a quantum critical point

We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated near the critical point, the number of created excitations still goes to zero in the limit of infinitesimally slow variation of the tuning parameter. It scales with the adiabaticity parameter as a power related to the critical exponents $z$ and $\nu$ characterizing the phase transition. We support general arguments by direct calculations for the Boson Hubbard and the transverse field Ising models.Comment: Final versio

Superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors

We study the quantum phase transition between the superfluid and the Mott insulator in the one-dimensional (1D) Bose-Hubbard model. Using the time-evolving block decimation method, we numerically calculate the tunneling splitting of two macroscopically distinct states with different winding numbers. From the scaling of the tunneling splitting with respect to the system size, we determine the critical point of the superfluid to Mott insulator transition for arbitrary integer filling factors. We find that the critical values versus the filling factor in 1D, 2D, and 3D are well approximated by a simple analytical function. We also discuss the condition for determining the transition point from a perspective of the instanton method.Comment: 6 pages, 6 figures, 2 table

Geometric phase contribution to quantum non-equilibrium many-body dynamics

We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum non-equilibrium dynamics revealed by the geometrical structure of the quantum space of states. As a primary example we use the anisotropic XY ring in a transverse magnetic field with an additional time-dependent flux. In particular, if the flux insertion is slow, non-adiabatic transitions in the dynamics are dominated by the dynamical phase. In the opposite limit geometric phase strongly affects transition probabilities. We show that this interplay can lead to a non-equilibrium phase transition between these two regimes. We also analyze the effect of geometric phase on defect generation during crossing a quantum critical point.Comment: 4 pages, 3 figures. Added an appendix with supplementary informatio

Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous $1/f$-noise at strong disorder.Comment: 9 pages, 9 figure

Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics

We study the problem of rapid change of the interaction parameter (quench) in many-body low-dimensional system. It is shown that, measuring correlation functions after the quench the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for non-integrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring power spectrum in dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as experimental test of our predictions.Comment: 4 pages, 2 figures; replaced with revised versio

Breakdown of the adiabatic limit in low dimensional gapless systems

It is generally believed that a generic system can be reversibly transformed from one state into another by sufficiently slow change of parameters. A standard argument favoring this assertion is based on a possibility to expand the energy or the entropy of the system into the Taylor series in the ramp speed. Here we show that this argumentation is only valid in high enough dimensions and can break down in low-dimensional gapless systems. We identify three generic regimes of a system response to a slow ramp: (A) mean-field, (B) non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp speed going to zero and the system size going to infinity do not commute and the adiabatic process does not exist in the thermodynamic limit. We support our results by numerical simulations. Our findings can be relevant to condensed-matter, atomic physics, quantum computing, quantum optics, cosmology and others.Comment: 11 pages, 5 figures, to appear in Nature Physics (originally submitted version

Oscillating fidelity susceptibility near a quantum multicritical point

We study scaling behavior of the geometric tensor $\chi_{\alpha,\beta}(\lambda_1,\lambda_2)$ and the fidelity susceptibility $(\chi_{\rm F})$ in the vicinity of a quantum multicritical point (MCP) using the example of a transverse XY model. We show that the behavior of the geometric tensor (and thus of $\chi_{\rm F}$) is drastically different from that seen near a critical point. In particular, we find that is highly non-monotonic function of $\lambda$ along the generic direction $\lambda_1\sim\lambda_2 = \lambda$ when the system size $L$ is bounded between the shorter and longer correlation lengths characterizing the MCP: $1/|\lambda|^{\nu_1}\ll L\ll 1/|\lambda|^{\nu_2}$, where $\nu_1<\nu_2$ are the two correlation length exponents characterizing the system. We find that the scaling of the maxima of the components of $\chi_{\alpha\beta}$ is associated with emergence of quasi-critical points at $\lambda\sim 1/L^{1/\nu_1}$, related to the proximity to the critical line of finite momentum anisotropic transition. This scaling is different from that in the thermodynamic limit $L\gg 1/|\lambda|^{\nu_2}$, which is determined by the conventional critical exponents. We use our results to calculate the defect density following a rapid quench starting from the MCP and show that it exerts a step-like behavior for small quench amplitudes. Study of heat density and diagonal entropy density also show signatures of quasi-critical points.Comment: 12 pages, 9 figure

Vortex pinning by a columnar defect in planar superconductors with point disorder

We study the effect of a single columnar pin on a $(1+1)$ dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, the pinning is most effective right at the temperature of the vortex glass transition. In particular, there is a pronounced maximum in the number of vortices which are prevented from tilting by the columnar defect in a weak transverse magnetic field. Using renormalization group techniques we show that the columnar pin is irrelevant at long length scales both above and below the transition, but due to very different mechanisms. This behavior differs from the disorder-free case, where the pin is relevant in the low temperature phase. Solutions of the renormalization equations in the different regimes allow a discussion of the crossover between the pure and disordered cases. We also compute density oscillations around the columnar pin and the response of these oscillations to a weak transverse magnetic field.Comment: 12 pages, 5 figures, minor typos corrected, a new reference adde