Renormalization group study of quantum fluctuations near classical critical points of Hamiltonian systems

A general framework is considered for treating quantum corrections to the classical limit in the Wigner function formalism. We discuss the quantal effect on the classical phenomena such as period doubling and the breakup of KAM tori. By using an exact renormalization group method, the scaling factor for Planck's constant is derived as an eigenvalue of the linearized renormalization transformation.     

Topological order and conformal quantum critical points

We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary two-dimensional free boson, the two-dimensional Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously varying critical exponents separating phases with long-range order from a deconfined topologically ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-Abelian symmetry, the strong-coupling limit of 2+1-dimensional Yang–Mills gauge theory with a Chern–Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.     

Clusters and fluctuations at mean-field critical points and spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different from the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.     

Excitation and entanglement transfer near quantum critical points

Recently, there has been growing interest in employing condensed matter systems such as quantum spin or harmonic chains as quantum channels for short distance communication. Many properties of such chains are determined by the spectral gap between their ground and excited states. In particular this gap vanishes at critical points of quantum phase transitions. In this article we study the relation between the transfer speed and quality of such a system and the size of its spectral gap. We find that the transfer is almost perfect but slow for large spectral gaps and fast but rather inefficient for small gaps. The text was submitted by the authors in English.     

Random field effects in field-driven quantum critical points

We investigate the role of disorder for field-driven quantum phase transitions of metallic antiferromagnets. For systems with sufficiently low symmetry, the combination of a uniform external field and non-magnetic impurities leads effectively to a random magnetic field which strongly modifies the behavior close to the critical point. Using perturbative renormalization group, we investigate in which regime of the phase diagram the disorder affects critical properties. In heavy fermion systems where even weak disorder can lead to strong fluctuations of the local Kondo temperature, the random field effects are especially pronounced. We study possible manifestation of random field effects in experiments and discuss in this light neutron scattering results for the field driven quantum phase transition in CeCu_5.8Au_0.2.     

The partition function zeroes of quantum critical points

The Lee–Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e^hΔτ, and the Euclidean-time lattice spacing Δτ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as Parity. We now present a first numerical analysis for this new zeroes approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.     

Electron self-trapping at quantum and classical critical points

Using Feynman path integral technique estimations of the ground state energy have been found for a conduction electron interacting with order parameter fluctuations near quantum critical points. In some cases only singular perturbation theory in the coupling constant emerges for the electron ground state energy. It is shown that an autolocalized state (quantum fluctuon) can be formed and its characteristics have been calculated depending on critical exponents for both weak and strong coupling regimes. The concept of fluctuon is considered also for the classical critical point (at finite temperatures) and the difference between quantum and classical cases has been investigated. It is shown that, whereas the quantum fluctuon energy is connected with a true boundary of the energy spectrum, for classical fluctuon it is just a saddle-point solution for the chemical potential in the exponential density of states fluctuation tail.     

Theory of the quantum critical fluctuations in cuprate superconductors

The statistical mechanics of the time-reversal and inversion symmetry breaking order parameter, possibly observed in the pseudogap region of the phase diagram of the cuprates, can be represented by the Ashkin-Teller model. We add kinetic energy and dissipation to the model for a quantum generalization and show that the spectrum of the quantum-critical fluctuations is of the form postulated in 1989 to give the marginal Fermi-liquid properties. The model solved and the methods devised are likely to be of interest also to other quantum phase transitions.     

Large-alphabet quantum key distribution using energy-time entangled bipartite States

We present a protocol for large-alphabet quantum key distribution (QKD) using energy-time entangled biphotons. Binned, high-resolution timing measurements are used to generate a large-alphabet key with over 10 bits of information per photon pair, albeit with large noise. QKD with 5% bit error rate is demonstrated with 4 bits of information per photon pair, where the security of the quantum channel is determined by the visibility of Franson interference fringes. The protocol is easily generalizable to even larger alphabets, and utilizes energy-time entanglement which is robust to transmission over large distances in fiber.     

Detection of quantum critical points by a probe qubit

Quantum phase transitions occur when the ground state of a quantum system undergoes a qualitative change when an external control parameter reaches a critical value. Here, we demonstrate a technique for studying quantum systems undergoing a phase transition by coupling the system to a probe qubit. It uses directly the increased sensibility of the quantum system to perturbations when it is close to a critical point. Using an NMR quantum simulator, we demonstrate this measurement technique for two different types of quantum phase transitions in an Ising spin chain.     

Magnetic-field control of quantum critical points of valence transition

We study the mechanism of how critical end points of first-order valence transitions are controlled by a magnetic field. We show that the critical temperature is suppressed to be a quantum critical point (QCP) by a magnetic field, and unexpectedly, the QCP exhibits nonmonotonic field dependence in the ground-state phase diagram, giving rise to the emergence of metamagnetism even in the intermediate valence-crossover regime. The driving force of the field-induced QCP is clarified to be cooperative phenomena of the Zeeman and Kondo effects, which create a distinct energy scale from the Kondo temperature. This mechanism explains the peculiar magnetic response in CeIrIn(5) and the metamagnetic transition in YbXCu(4) for X=In as well as the sharp contrast between X=Ag and Cd.     

On non-Fermi liquid quantum critical points in heavy fermion metals

Heavy electron metals on the verge of a quantum phase transition to magnetism show a number of unusual non-Fermi liquid properties which are poorly understood. This article discusses in a general way various theoretical aspects of this phase transition with an eye toward understanding the non-Fermi liquid phenomena. We suggest that the non-Fermi liquid quantum critical state may have a sharp Fermi surface with power law quasiparticles but with a volume not set by the usual Luttinger rule. We also discuss the possibility that the electronic structure change associated with the possible Fermi surface reconstruction may diverge at a different time/length scale from that associated with magnetic phenomena.     

Partial dynamical symmetry at critical points of quantum phase transitions

We show that partial dynamical symmetries can occur at critical points of quantum phase transitions, in which case underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several types of partial dynamical symmetries are demonstrated with the example of critical-point Hamiltonians for first- and second-order transitions in the framework of the interacting boson model, whose dynamical symmetries correspond to different shape phases in nuclei.     

Nonperturbative microscopic theory of superconducting fluctuations near a quantum critical point

We consider an anisotropic gap superconductor in the vicinity of the disorder-driven quantum critical point. Starting with the BCS Hamiltonian, we derive the Ginzburg-Landau action, which is a critical theory with the dynamic critical exponent, z=2. This allows us to use the parquet method to calculate the nonperturbative effect of quantum superconducting fluctuations on thermodynamics. We derive a general expression for the fluctuation magnetic susceptibility, which exhibits a crossover from the logarithmic dependence, chi proportional, variantlndeltan, valid beyond the Ginzburg region to chi proportional, variantln(1/5)deltan valid in the immediate vicinity of the transition (where deltan is the deviation from the critical disorder concentration). These nonperturbative results may describe the quantum critical behavior of overdoped high-temperature cuprates, disordered p-wave superconductors, and conventional superconducting films with magnetic impurities.     

Detecting switching points using asymmetric detrended fluctuation analysis

This work uses the concept of Asymmetric Detrended Fluctuation Analysis (A-DFA) to investigate and characterize the occurrence of trend switching in financial series. A-DFA introduces two new roughness exponents, $H^{+}$ and $H^{?}$, which differ from the usual one $H$ by separately taking into account contributions to the fluctuations according to whether the local trend is, respectively, upward or downward. The developed methodology requires the evaluation of local values of $H\left(t\right),H^{+}\left(t\right)$, and $H^{?}\left(t\right)$, by restricting the size of the largest window around the value $t$. We show that $H^{+}\left(t\right)$ and $H^{?}\left(t\right)$ behave differently in the neighborhoods of switching points (SPs) where trends change sign. Properly taken differences between shifted local values of $H\left(t\right),H^{+}\left(t\right)$, and $H^{?}\left(t\right)$ allow to identify and characterize SP’s. Tests with Weiertrasse functions, isolated peaks, and actual financial series are presented, supporting the validity of the proposed method.     

Asymmetry of bipartite quantum discord

It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmor frequencies at both T = 0 (the ground state) and T > 0 has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with a decrease in the temperature.     

Rounding by disorder of first-order quantum phase transitions: emergence of quantum critical points

We give a heuristic argument for disorder rounding of a first-order quantum phase transition into a continuous phase transition. From both weak and strong disorder analysis of the N-color quantum Ashkin-Teller model in one spatial dimension, we find that, for N > or =3, the first-order transition is rounded to a continuous transition and the physical picture is the same as the random transverse field Ising model for a limited parameter regime. The results are strikingly different from the corresponding classical problem in two dimensions where the fate of the renormalization group flows is a fixed point corresponding to N-decoupled pure Ising models.     

Breakdown of the perturbative renormalization group at certain quantum critical points

It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from finite-order perturbative renormalization-group treatments may not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a nonrenormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.     

Observable measure of bipartite quantum correlations

We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.