Thermodynamics’ third law and quantum phase transitions

We report on the fact that microscopically enforcing fulfillment of thermodynamics’ third law on a system of fermions automatically yields the values of the external parameter (here coupling strengths in the pertinent Hamiltonian) at which quantum phase transitions take place. Our considerations are illustrated via an exactly solvable model of Plastino and Moszkowski [Il Nuovo Cimento 47, 470 (1978)].     

Picturing quantum phase transitions

We discuss the quantum phase transitions (QPT) in N-spin chains from the point of view of collective observables. We show that the measurement space representation is a convenient tool for the analysis of phase transitions, allowing the determination of an appropriate set of macroscopic order parameters (for a given Hamiltonian). Quantum correlations in the vicinity of the critical points are analyzed both in the ground states and low temperature thermal states.     

Replacing energy by von Neumann entropy in quantum phase transitions

We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.     

Disorder effects on transport near AFM quantum phase transitions

We discuss three different scenarios recently proposed to account for the non-Fermi liquid behavior near antiferromagnetic (AFM) quantum critical points in heavy-Fermion systems: (i) scattering of Fermi liquid quasiparticles by strong spin fluctuations near the spin-density-wave instability, (ii) the breakdown of the Kondo effect due to the competition with the RKKY interaction, and (iii) the formation of magnetic regions due to rare configurations of the disorder. Here we focus on the first scenario and show that it explains in some detail the anomalous temperature dependence of the resistivity observed, e.g. in CePd₂Si₂, CeNi₂Ge₂ or CeIn₃. The interplay of strongly anisotropic scattering due to critical spin-fluctuations and weak isotropic impurity scattering leads to a regime with a resistivity

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for sufficiently large T and small ρ₀.     

Excited state quantum phase transitions in many-body systems

Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean-field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.     

Fisher information,Rényi entropy power and quantum phase transition in the Dicke model

Fisher information, Rényi entropy power and Fisher–Rényi information product are presented for the Dicke model. There is a quantum phase transition in this quantum optical model. It is pointed out that there is an abrupt change in the Fisher information, Rényi entropy power, the Fisher, Shannon and Rényi lengths at the transition point. It is found that these quantities diverge as the characteristic length: |_λc−λ|^−1/4${|{\lambda }_c-\lambda |}^{-1/4}$ around the critical value of the coupling strength _λc${\lambda }_c$ for any value of the parameter β$\beta$.     

Fermi-liquid instability at magnetic–nonmagnetic quantum phase transitions

In metals with strong electronic correlations such as heavy-fermion systems or itinerant-electron magnets it is possible to change from a magnetically ordered to a nonmagnetic groundstate by variation of an external parameter such as composition or pressure. In principle a transition between these groundstates can occur at zero temperature. In case of a continuous transition quantum fluctuations take the role of thermal fluctuations in finite-temperature transitions. The abundance of low-lying magnetic excitations leads in the vicinity of the quantum critical point to unusual behavior of thermodynamic and transport properties at low temperatures T not envisioned by the classical Fermi-liquid behavior that is observed even in strongly correlated electron systems away from the quantum phase transition. We discuss in detail a few examples of this ‘non-Fermi-liquid behavior', viz., CeCu_6−xAu_x, Ce_1−xLa_xRu₂Si₂, Ce₇Ni₃, CeCu₂Si₂ and CeCu₂Ge₂, CePd₂Si₂, and UCu_1−xPd_x. In CeCu_6−xAu_x the very unusual low-T behavior of the linear specific-heat coefficient C/T−ln(T/T₀) and of the resistivity ΔρT can be attributed to quasi-two-dimensional fluctuations as determined from inelastic neutron scattering. The systems CeCu₂Ge₂ and CePd₂Si₂ are particuarly interesting since here the magnetic order which is suppressed under hydrostatic pressure gives way to superconductivity, suggesting that spin fluctuations mediate the formation of Cooper pairs at least in the latter system.     

Genuine tripartite entanglement and quantum phase transition

A new simplified formula is presented to characterize genuine tripartite entanglement of （2 2 n）-dimensional quantum pure states. The formula turns out equivalent to that given in （Quant. Inf. Comp. 7（7） 584 （2007））, hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local （2 2）-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang （Phys. Rev. A 71 030302（R） （2005）） are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.     

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.     

Ground-state properties and quantum entanglement in rung-dimerized spin-1/2 antiferromagnetic ladder

The ground-state properties and quantum entanglement of the two-leg rung-dimerized spin-1/2 Heisenberg antiferromagnetic ladders are investigated based on the Green? function combined with the Bond mean-field theory. Numerical results show that the ground-state energies do not change with the rung dimerization, and the ground-state gaps are almost proportionate to the rung dimerization coefficient δ and coupling strength α  . Magnetization curves and entanglement measurements demonstrate that there are five magnetic phases, which are identified in the h–δ$h\text{–}\delta$ phase diagram. Entanglement measurements in different phases exhibit distinct behaviors, implying the fundamental differences of the five magnetic phases.     

Entanglement entropy, decoherence, and quantum phase transitions of a dissipative two-level system

The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. The entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy.     

Characterizing quantum phase transition by teleportation

In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence at the quantum critical point. The implications of this phenomenon and possible applications are also briefly discussed.     

磁性量子相变

量子相变广泛存在于关联电子材料体系中,与非常规超导和奇异金属行为有着紧密的联系。近年来,人们对量子相变的认识正在不断深入,不同类型的量子相变相继被发现。揭示量子相变的普适分类,发展和完善量子相变理论,探索量子临界点附近的呈展量子态及其产生机理是当前量子相变研究的热点。文章简要介绍磁性量子相变的一些最新研究进展以及面临的挑战。     

Coherent control of quantum entropy via quantum interference in a four-level N-type atomic system

The time evaluation of quantum entropy in a four-level N-type atomic system is theoretically investigated. Quantum entanglement of the atom and its spontaneous emission fields is then discussed via quantum entropy. It is found that the degree of entanglement can be increased by the quantum interference induced by spontaneous emission. The phase dependence of the atom-field entanglement is also presented.     

Global quantum discord and quantum phase transition in XY model

We study the relationship between the behavior of global quantum correlations and quantum phase transitions in XY model. We find that the two kinds of phase transitions in the studied model can be characterized by the features of global quantum discord (GQD) and the corresponding quantum correlations. We demonstrate that the maximum of the sum of all the nearest neighbor bipartite GQDs is effective and accurate for signaling the Ising quantum phase transition, in contrast, the sudden change of GQD is very suitable for characterizing another phase transition in the XY model. This may shed lights on the study of properties of quantum correlations in different quantum phases.     

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic "Landau" potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.     

Frustration and quantum phase transitions in an anisotropic antiferromagnet on a square lattice

We study the effect of frustration between nearest and next-nearest neighbors of the quantum S=1 anisotropic Heisenberg model on a square lattice using the bond operator technique. A single-site anisotropy term induces a quantum phase transition in the system. We calculate the effect of zero-temperature quantum fluctuations on the magnetization for the Néel and collinear antiferromagnetic phases.     

Superconducting and excitonic quantum phase transitions in doped Dirac electronic systems

We investigate the effect of superconducting and excitonic interactions, as well as their competition, on Dirac electrons on a bipartite planar lattice. It is shown that, at half-filling, Cooper pairs and excitons coexist if the superconducting and excitonic coupling parameters are equal and above a threshold corresponding to a quantum critical point. In the case where only the excitonic interaction is present, we obtain a critical chemical potential, as a function of the interaction strength. Conversely, if only the superconducting interaction is considered, we show that the superconducting gap displays a characteristic dome as charge carriers are doped into the system. We also show that, as the chemical potential increases, superconductivity tends to suppress the excitonic order parameter.     

Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

We study the ground-state and thermal entanglement in the mixed-spin (S,s)=(1,1/2) Heisenberg chain with single-ion anisotropy D using exact diagonalization of small clusters. In this system, a quantum phase transition is revealed to occur at the value D=0, which is the bifurcation point for the global ground state; that is, when the single-ion anisotropy energy is positive, the ground state is unique, whereas when it is negative, the ground state becomes doubly degenerate and the system has the ferrimagnetic long-range order. Using the negativity as a measure of entanglement, we find that a pronounced dip in this quantity, taking place just at the bifurcation point, serves to signal the quantum phase transition. Moreover, we show that the single-ion anisotropy helps to improve the characteristic temperatures above which the quantum behavior disappears.