Zero-temperature Phase Transition Research Articles

External Control of a Metal-Insulator Transition in GaMnAs Wires

Quantum transport in disordered ferromagnetic (III,Mn)V semiconductors is studied theoretically. Mesoscopic wires exhibit an Anderson disorder-induced metal-insulator transition that can be controlled by a weak external magnetic field. This metal-insulator transition should also occur in other materials with large anisotropic magnetoresistance effects. The transition can be useful for studies of zero-temperature quantum critical phase transitions and fundamental material properties.

Interplay between spin-glass-like and non-Fermi-liquid behavior inCeNi1−xRhxSn

The effect of doping in CeNiSn has been studied by measurements of electrical resistivity, magnetic susceptibility, and specific heat for polycrystalline samples of ${\text{CeNi}}_{1\ensuremath{-}x}{\text{Rh}}_{x}\text{Sn}$. It was observed that the semimetallic compound CeNiSn transforms into a Kondo semiconductor upon the substitution of 2% of Rh for Ni. We show that the narrow Kondo-insulator gap formation can be associated with disorder-induced $f$-electron localization. The magnetic properties of the system gradually evolve from magnetic glassy state, observed for $0<x<0.08$, to non-Fermi-liquid (NFL) behavior, when the Rh doping increases. The series of ${\text{CeNi}}_{1\ensuremath{-}x}{\text{Rh}}_{x}\text{Sn}$ exhibits NFL behavior in the vicinity of a zero-temperature magnetic phase transition, which is associated with spin-glass-like ordering due to chemical substitution. The detailed investigations of magnetic properties with decreasing Rh concentration suggest an interplay between the spin-glass-like (glassy state) and NFL ground states for the concentration region $x<0.08$. On the basis of the experimental results, we propose a schematic phase diagram on the $T\ensuremath{-}x$ plane and demonstrate the rationale for the existence of a quantum critical point at ${x}_{c}\ensuremath{\approx}0.08$.

Quantum phase transition in a single-molecule quantum dot

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, is believed to govern many of the fascinating properties of strongly correlated systems such as heavy-fermion compounds or high-temperature superconductors. In contrast to bulk materials with very complex electronic structures, artificial nanoscale devices could offer a new and simpler means of understanding quantum phase transitions. Here we demonstrate this possibility in a single-molecule quantum dot, where a gate voltage induces a crossing of two different types of electron spin state (singlet and triplet) at zero magnetic field. The quantum dot is operated in the Kondo regime, where the electron spin on the quantum dot is partially screened by metallic electrodes. This strong electronic coupling between the quantum dot and the metallic contacts provides the strong electron correlations necessary to observe quantum critical behaviour. The quantum magnetic phase transition between two different Kondo regimes is achieved by tuning gate voltages and is fundamentally different from previously observed Kondo transitions in semiconductor and nanotube quantum dots. Our work may offer new directions in terms of control and tunability for molecular spintronics.

Phase glass and zero-temperature phase transition in a randomly frustrated two-dimensionalquantum rotor model

The ground state of the quantum rotor model in two dimensions with random phase frustrationis investigated. Extensive Monte Carlo simulations are performed on the corresponding(2+1)-dimensional classical model under the entropic sampling scheme. For weak quantumfluctuation, the system is found to be in a phase glass phase characterized by a finitecompressibility and a finite value for the Edwards–Anderson order parameter, signifyinglong-range phase rigidity in both spatial and imaginary time directions. The scalingproperties of the model near the transition to the gapped, Mott insulator state withvanishing compressibility are analyzed. At the quantum critical point, the dynamicexponent is greater than one. Correlation length exponents in the spatial and imaginary timedirections are given by and , respectively; both assume values greater than 0.6723 of the pure case. We speculate thatthe phase glass phase is superconducting rather than metallic in the zero-currentlimit.

Quantum criticality in heavy-fermion metals

Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy-fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, that use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including the extent to which the quantum criticality in heavy-fermion metals goes beyond the standard theory of order-parameter fluctuations, the nature of the Kondo effect in the quantum-critical regime, the non-Fermi-liquid phenomena that accompany quantum criticality and the interplay between quantum criticality and unconventional superconductivity. At a zero-temperature phase transition from one ordered state to another, fluctuations between the two states lead to quantum critical behaviour that can lead to unexpected physics. Metals with ‘heavy’ electrons often harbour such weird states.

What lies beneath the dome?

Numerous experiments on cuprate materials suggest that a zero-temperature phase transition is hidden beneath the superconducting dome. Is it the key to understanding high-temperature superconductivity, and can it explain the anomalous normal state properties?

Vortex Quantum Creation and Winding Number Scaling in a Quenched Spinor Bose Gas

Motivated by a recent experiment, we study nonequilibrium quantum phenomena taking place in the quench of a spinor Bose-Einstein condensate through the zero-temperature phase transition separating the polar paramagnetic and planar ferromagnetic phases. We derive the typical spin domain structure (correlations of the effective magnetization) created by the quench arising due to spin-mode quantum fluctuations, and we establish a sample-size scaling law for the creation of spin vortices, which are topological defects in the transverse magnetization.

On the nature of the phase transition in the three-dimensional random field Isingmodel

A brief survey of the theoretical, numerical and experimental studies of the random fieldIsing model (RFIM) during the last three decades is given. The nature of the phasetransition in the three-dimensional RFIM with Gaussian random fields is discussed. Usingsimple scaling arguments it is shown that if the strength of the random fields is nottoo small (bigger than a certain threshold value), the finite temperature phasetransition in this system is equivalent to the low temperature order–disordertransition which takes place with variations of the strength of the random fields.A detailed study of the zero-temperature phase transition in terms of simpleprobabilistic arguments and a modified mean field approach (which take intoaccount nearest neighbor spin–spin correlations) is given. It is shown that if allthermally activated processes are suppressed, the ferromagnetic order parameterm(h) as a functionof the strength h of the random fields becomes history dependent. In particular, the behavior of the magnetization curvesm(h) for increasingand decreasing h reveals a hysteresis loop.

Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system

The Dicke model consisting of an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realise an effective Dicke system operating in the phase transition regime. Output light from the cavity carries signatures of the critical behavior which is analyzed for the thermodynamic limit where the number of atoms is very large.

Universal crossovers and critical dynamics of quantum phase transitions: A renormalization group study of the pseudogap Kondo problem

The pseudogap Kondo problem, describing a magnetic impurity embedded in an electronic environment with a power-law density of states, displays continuous quantum phase transitions between free and screened moment phases. In this paper we employ renormalization group techniques to analytically calculate universal crossover functions, associated to these transitions, for various observables. Quantitative agreement with the results of Numerical Renormalization Group (NRG) simulations is obtained for temperature-dependent static and zero-temperature dynamic quantities, at and away from criticality. In the notoriously difficult realm of finite-temperature low-frequency dynamics, usually inaccessible to both NRG and perturbative methods, we show that progress can be made by a suitable renormalization procedure in the framework of the Callan-Symanzik equations. Our general strategy can be extended to other zero-temperature phase transitions, both in quantum impurity models and bulk systems.

Random field Ising model on networks with inhomogeneous connections

We study a zero-temperature phase transition in the random field Ising model on scale-free networks with the degree exponent gamma. Using an analytic mean-field theory, we find that the spins are always in the ordered phase for gamma<3. On the other hand, the spins undergo a phase transition from an ordered phase to a disordered phase as the dispersion of the random fields increases for gamma>3. The phase transition may be either continuous or discontinuous depending on the shape of the random field distribution. We derive the condition for the nature of the phase transition. Numerical simulations are performed to confirm the results.

Dimensional reduction at a quantum critical point

Competition between electronic ground states near a quantum critical point (QCP)--the location of a zero-temperature phase transition driven solely by quantum-mechanical fluctuations--is expected to lead to unconventional behaviour in low-dimensional systems. New electronic phases of matter have been predicted to occur in the vicinity of a QCP by two-dimensional theories, and explanations based on these ideas have been proposed for significant unsolved problems in condensed-matter physics, such as non-Fermi-liquid behaviour and high-temperature superconductivity. But the real materials to which these ideas have been applied are usually rendered three-dimensional by a finite electronic coupling between their component layers; a two-dimensional QCP has not been experimentally observed in any bulk three-dimensional system, and mechanisms for dimensional reduction have remained the subject of theoretical conjecture. Here we show evidence that the Bose-Einstein condensate of spin triplets in the three-dimensional Mott insulator BaCuSi2O6 (refs 12-16) provides an experimentally verifiable example of dimensional reduction at a QCP. The interplay of correlations on a geometrically frustrated lattice causes the individual two-dimensional layers of spin-(1/2) Cu2+ pairs (spin dimers) to become decoupled at the QCP, giving rise to a two-dimensional QCP characterized by linear power law scaling distinctly different from that of its three-dimensional counterpart. Thus the very notion of dimensionality can be said to acquire an 'emergent' nature: although the individual particles move on a three-dimensional lattice, their collective behaviour occurs in lower-dimensional space.

Quantum phase transition in the generalized single-mode superradiant model

In this paper we reveal a zero-temperature quantum phase transition for the single-mode superradiant model with the form A2 from the normal to superradiant phase by mean of the Holstein-Primakoff transformation. In the thermodynamic limit, in which the numbers of atoms becomes infinite, the ground state energy and corresponding wavefunctions of both the normal and superradiant phases are obtained and therefore the scaling behavior near the critical transition point is derived.

Rare region effects at classical, quantum and nonequilibrium phase transitions

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate

A central goal in condensed matter and modern atomic physics is the exploration of quantum phases of matter--in particular, how the universal characteristics of zero-temperature quantum phase transitions differ from those established for thermal phase transitions at non-zero temperature. Compared to conventional condensed matter systems, atomic gases provide a unique opportunity to explore quantum dynamics far from equilibrium. For example, gaseous spinor Bose-Einstein condensates (whose atoms have non-zero internal angular momentum) are quantum fluids that simultaneously realize superfluidity and magnetism, both of which are associated with symmetry breaking. Here we explore spontaneous symmetry breaking in 87Rb spinor condensates, rapidly quenched across a quantum phase transition to a ferromagnetic state. We observe the formation of spin textures, ferromagnetic domains and domain walls, and demonstrate phase-sensitive in situ detection of spin vortices. The latter are topological defects resulting from the symmetry breaking, containing non-zero spin current but no net mass current.

Chiral phase structure of QCD with many flavors

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(Nc) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an Nf window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is Nf cr=10.0±0.29 (fermion)+1.55 -0.63 (gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively.

Non-Fermi liquid behavior and quantum criticality in [formula omitted] and [formula omitted

The compounds Sc 1 - x U x Pd 3 and URu 2 - x Re x Si 2 exhibit non-Fermi liquid behavior in the vicinity of zero-temperature magnetic phase transitions accessed by chemical substitution. Notably, the quantum phase transitions in these pseudobinary systems are associated with spin glass and ferromagnetic ordering, respectively. Recent studies have uncovered new details of the unconventional physical phenomena occurring in these materials.

Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: From superfluidity to density waves

For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the {\it lattice attenuation factor}. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on site occupation numbers. In mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is in principle possible, but completely suppressed at lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.

Numerical renormalization group for impurity quantum phase transitions: structure ofcritical fixed points

The numerical renormalization group method is used to investigate zero-temperature phasetransitions in quantum impurity systems, in particular in the particle–hole symmetricsoft-gap Anderson model. The model displays two stable phases whose fixed points can bebuilt up of non-interacting single-particle states. In contrast, the quantum phase transitionsturn out to be described by interacting fixed points, and their excitations cannot bedescribed in terms of free particles. We show that the structure of the many-bodyspectrum of these critical fixed points can be understood using renormalizedperturbation theory close to certain values of the bath exponents which play the role ofcritical dimensions. Contact is made with perturbative renormalization groupcalculations for the soft-gap Anderson and Kondo models. A complete description ofthe quantum critical many-particle spectra is achieved using suitable marginaloperators; technically this can be understood as epsilon-expansion for full many-bodyspectra.

Dynamical Zero-Temperature Phase Transitions and Cosmic Inflation or Deflation

For a rather general class of scenarios, sweeping through a zero-temperature phase transition by means of a time-dependent external parameter entails universal behavior: In the vicinity of the critical point, excitations behave as quantum fields in an expanding or contracting universe. The resulting effects such as the amplification or suppression of quantum fluctuations (due to horizon crossing, freezing, and squeezing) including the induced spectrum can be derived using the curved space-time analogy. The observed similarity entices the question of whether cosmic inflation itself might perhaps have been such a phase transition.