Point Of Quantum Phase Transition Research Articles

Chaos propeties of the time-dependent driven Dicke model

Now, many different approaches have been presented to study the different semi-classical models derived from the Dicke Hamiltonian, which reflect a fact that the quantum-mechanical spin possesses no direct classical analog. The Hartree-Fock-type approximation is one of the widely used approaches, with which we derive the Heisenberg equations of motion for the system and replace the operators in these equations with the corresponding expectation values. In the present paper, we investigate the role of quantum phase transition in determining the chaotic property of the time-dependent driven Dicke model. The semi-classical Hamiltonian is derived by evaluating the expectation value of the Dicke Hamiltonian in a state, which is a product state of photonic and atomic coherent states. Based on the inverse of the relations between the position-momentum representation and the Bosonic creation-annihilation operators, the Hamiltonian is rewritten in the position-momentum representation and it undergoes a spontaneous symmetry-breaking phase transition, which is directly analogous to the quantum phase transition of the quantum system. In order to depict the Poincaré sections, which are used to analyze the trajectories through the four-dimensional phase space, we give the equations of motion of system from the derivatives of the semi-classical Hamiltonian for a variety of different parameters and initial conditions. According to the Dicke quantum phase transition observed from the experimental setup , we study the effect of a monochromatic non-adiabatic modulation of the atom-field coupling in Dicke model (i.e., the driven Dicke model) on the system chaos by adjusting the pump laser intensity. The change from periodic track to chaotic figure reflects the quantum properties of the system, especially the quantum phase transition point, which is a key position for people to analyse the shift from periodic orbit to chaos. In an undriven case, the system reduces to the standard Dicke model. We discover from the Poincaré sections that the system undergoes a change from the classical periodic orbit to a number of chaotic trajectories and in the superradiant phase area, the whole phase space is completely chaotic. When the static and driving coupling both exist, the system shows rich chaotic motion. The ground state properties are mainly determined by the static coupling, while the orbit of the system is adjusted by the driving coupling. If the static coupling is greater than the critical coupling, the system displays completely chaotic images in the Poincaré sections, and the periodic orbits in the chaos can also be adjusted by the strong driving coupling. While the static coupling is less than the critical coupling, the system can also show the chaotic images by adjusting the driving coupling strength and oscillation frequency. Moreover, by tuning the oscillation frequency, the Poincaré sections may change from the classical orbits to the chaos, and back to the classical orbits in the normal phase of the system.

Gaussian phase transition and critical exponents in spin-1 bond-alternative Heisenberg chains

The quantum Gaussian phase transition is investigated for the infinite spin-1 bond-alternative Heisenberg model in one spatial dimension. By using a tensor network representation with an infinite matrix product state approach, the ground state energy, bipartite entanglement entropy, non-local string order, and fidelity per lattice site are calculated to characterize the phase transition. At the quantum phase transition point, the scaling behavior of various physical observables with respect to the finite truncation dimension are discussed for the ground state wavefunctions. In addition, the central charge is extracted from the finite entanglement entropies and the finite correlation lengths. Furthermore, the various critical exponents of the string order are calculated. The characteristic critical exponents and the central charge determine the universality class of the phase transition.

One-norm geometric quantum discord and critical point estimation in the XY spin chain

In contrast with entanglement and quantum discord (QD), we investigate the thermal quantum correlation in terms of Schatten one-norm geometric quantum discord (GQD) in the XY spin chain, and analyze their capabilities in detecting the critical point of quantum phase transition. We show that the one-norm GQD can reveal more properties about quantum correlation between two spins, especially for the long-range quantum correlation at finite temperature. Under the influences of site distance, anisotropy and temperature, one-norm GQD and its first derivative make it possible to detect the critical point efficiently for a general XY spin chain.

Coherence susceptibility as a probe of quantum phase transitions

We introduce a coherence susceptibility method, based on the fact that it signals quantum fluctuations, for identifying quantum phase transitions, which are induced by quantum fluctuations. This method requires no prior knowledge of order parameter, and there is no need for careful considerations concerning the choice of a bipartition of the system. It can identify different types of quantum phase transition points exactly. At finite temperatures, where quantum criticality is influenced by thermal fluctuations, our method can pinpoint the temperature frame of quantum criticality, which perfectly coincides with recent experiments.

Black hole based quantum computing in labs and in the sky

Analyzing some well established facts, we give a model‐independent parameterization of black hole quantum computing in terms of a set of macro and micro quantities and their relations. These include the relations between the extraordinarily‐small energy gap of black hole qubits and important time‐scales of information‐processing, such as, scrambling time and Page's time. We then show, confirming and extending previous results, that other systems of nature with identical quantum informatics features are attractive Bose‐Einstein systems at the critical point of quantum phase transition. Here we establish a complete isomorphy between the quantum computational properties of these two systems. In particular, we show that the quantum hair of a critical condensate is strikingly similar to the quantum hair of a black hole. Irrespectively whether one takes the similarity between the two systems as a remarkable coincidence or as a sign of a deeper underlying connection, the following is evident. Black holes are not unique in their way of quantum information processing and we can manufacture black hole based quantum computers in labs by taking advantage of quantum criticality.

Exact asymptotic correlation functions of bilinear spin operators of the Heisenberg antiferromagnetic spin-12chain

Exact asymptotic expressions of the uniform parts of the two-point correlation functions of bilinear spin operators in the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain are obtained. Apart from the algebraic decay, the logarithmic contribution is identified, and the numerical prefactor is determined. We also confirm numerically the multiplicative logarithmic correction of the staggered part of the bilinear spin operators $\langle\langle S^{a}_0S^{a}_{1}S^{b}_{r}S^{b}_{r+1} \rangle\rangle=(-1)^rd/(r \ln^{\frac{3}{2}}r) +(3\delta_{a,b}-1) \ln^2r /(12 \pi^4 r^4)$, and estimate the numerical prefactor as $d\simeq 0.067$. The relevance of our results for ground state fidelity susceptibility at the Berezinskii-Kosterlitz-Thouless quantum phase transition points in one-dimensional systems is discussed at the end of our work.

Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach

The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.

Magnetic quantum phase transitions and entropy in Van Vleck magnet

Field-induced magnetic quantum phase transitions in the Van Vleck paramagnet with easy-plane single-ion anisotropy and competing Ising exchange between ions with the spin S=1 have been studied theoretically. The description was made by minimizing the Lagrange function at zero temperature (Т=0) and the free energy at T≠0. Stable and unstable solutions of equations corresponding to the case ψ0=|0〉 asymptotically transform into those following from the Lagrange function at Т=0. First-order phase transitions from the Van Vleck paramagnet state into the ferromagnet one were found to take place at a sufficiently high single-ion anisotropy. The entropy of such a magnet was shown to grow with its magnetization, as it occurs for antiferromagnets. At the point of quantum phase transition, the entropy has a jump, which magnitude depends on the ratio between the Ising exchange and anisotropy constants, as well as on the temperature. The described magnetic phase transition was supposed to be accompanied by the magnetocaloric effect. In the case when the Ising exchange dominates over the single-ion anisotropy, the magnetization reversal of ferromagnetic state by an external field was shown to be a phase transition of the first kind, which does not belong to orientational ones and which should be regarded as a quantum order-order phase transition.

Survival of time-evolved quantum correlations depending on whether quenching is across a critical point in anXYspin chain

The time-dynamics of quantum correlations in the quantum transverse anisotropic XY spin chain of infinite length is studied at zero as well as finite temperatures. The evolution occurs due to the instantaneous quenching of the coupling constant between the nearest-neighbor spins of the model, which is either performed within the same phase or across the quantum phase transition point connecting the order-disorder phases of the model. We characterize the time-evolved quantum correlations, entanglement and quantum discord, which exhibit varying behavior depending on the initial state and the quenching scheme. We show that the system is endowed with enhanced bipartite quantum correlations compared to that of the initial state, when quenched from ordered to the deep disordered phase. However, bipartite quantum correlations are almost washed out when the system is quenched from disordered to the ordered phase with the initial state being at the zero-temperature. Moreover, we identify the condition for the occurrence of enhanced bipartite correlations when the system is quenched within the same phase. Finally, we investigate the bipartite quantum correlations when the initial state is a thermal equilibrium state with finite temperature which reveals the effects of thermal fluctuation on the phenomena observed at zero-temperature.

Few-Body Precursor of the Higgs Mode in a Fermi Gas.

We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalization, the lowest monopole mode frequency is shown to depend nonmonotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the few-body analogue of a many-body Higgs mode in the superfluid phase, which has a vanishing frequency at the quantum phase transition point to the normal phase. We show that this mode mainly consists of coherent excitations of time-reversed pairs, and that it can be selectively excited by modulating the interaction strength, using, for instance, a Feshbach resonance in cold atomic gases.

Interplay of charge density wave and multiband superconductivity in 2H-PdxTaSe2.

2H-TaSe2 has been one of unique transition metal dichalcogenides exhibiting several phase transitions due to a delicate balance among competing electronic ground states. An unusual metallic state at high-T is sequentially followed by an incommensurate charge density wave (ICDW) state at ≈122 K and a commensurate charge density wave (CCDW) state at ≈90 K, and superconductivity at TC ~ 0.14 K. Upon systematic intercalation of Pd ions into TaSe2, we find that CCDW order is destabilized more rapidly than ICDW to indicate a hidden quantum phase transition point at x ~ 0.09–0.10. Moreover, TC shows a dramatic enhancement up to 3.3 K at x = 0.08, ~24 times of TC in 2H-TaSe2, in proportional to the density of states N(EF). Investigations of upper critical fields Hc2 in single crystals reveal evidences of multiband superconductivity as temperature-dependent anisotropy factor γH = , quasi-linear increase of , and an upward, positive-curvature in near TC. Furthermore, analysis of temperature-dependent electronic specific heat corroborates the presence of multiple superconducting gaps. Based on above findings and electronic phase diagram vs x, we propose that the increase of N(EF) and effective electron-phonon coupling in the vicinity of CDW quantum phase transition should be a key to the large enhancement of TC in PdxTaSe2.

Effect of Disorder in a Three-Dimensional Layered Chern Insulator.

We studied the effects of disorder in a three-dimensional layered Chern insulator, which, in the clean limit, is either a Chern insulator or a Weyl semimetal depending on an interlayer coupling strength. By calculating the localization length by the transfer matrix method, we found two distinct types of metallic phases between the Anderson insulator and the Chern insulator: one is a diffusive metallic phase and the other is a renormalized Weyl semimetal phase. By calculating the conductance and density of states, we characterize these two metallic phases and reveal a critical nature of a quantum critical line between these two metallic phases.

Hierarchy, factorization law of two measurement-induced nonlocalities and their performances in quantum phase transition

There are two measurement-induced nonlocalities, which are, respectively, defined via the trace norm (MIN-1) and Hilbert---Schmidt norm (MIN-2). We investigate the hierarchy relation and factorization law of them. Their performances in quantum phase transition have also been explored. For X-shape states, a rigorous hierarchy relation is established between two MINs. When two qubits, which are initially prepared in an X-shape state, interact independently with the corresponding multimode vacuum reservoirs, the evolutions of two MINs satisfy the factorization law. With quantum renormalization group method, it is found that two MINs can signify the criticality of the spin system while the position where the derivative of MIN-1 takes the minimum value is always larger than that where the derivative of MIN-2 takes the minimum value. Therefore, MIN-1 is more suitable to identify the critical point of quantum phase transition.

Quantum speed limit for a central system in Lipkin-Meshkov-Glick bath

We investigate the physical feature of quantum phase transition (QPT) in a Lipkin-Meshkov-Glick (LMG) model by calculating the quantum speed limit (QSL) time for a central qubit coupled to a LMG bath. We propose that with a suitable choice of the number of spins in bath and the coupling strength between central system and environment, the transition from no speed-up to speed-up of the open system evolution can be achieved at the QPT point, so the QSL is a potential candidate for witnessing QPT of a LMG model. By considering the physical reason for the acceleration, we study the non-Markovianity of the open system and verify that the non-Markovian property can induce the decrease of evolution time, which is also an indication that the phase transition of the system from Markovian to non-Markovian could occur at the QPT point.

Quantum speed limit and a signal of quantum criticality.

We study the quantum speed limit time (QSLT) of a coupled system consisting of a central spin and its surrounding environment, and the environment is described by a general XY spin-chain model. For initial pure state, we find that the local anomalous enhancement of the QSLT occurs near the critical point. In addition, we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point. These anomalous behaviors in the critical vicinity of XY spin-chain environment can be used to indicate the quantum phase transition point. Especially for the XX spin-chain environment, we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point. In this case, the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field, while the QSLT can still witness the quantum phase transition. So, the QSLT provides a further insight and sharper identification of quantum criticality.

Effect of Dzyaloshinskii-Moriya Interaction on Thermal Quantum Correlation in a Two-Qubit Heisenberg XXZ Model with an Inhomogeneous External Magnetic Field

By using the two-qubit Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction and an inhomogeneous external magnetic field, we investigate the similarities and differences of negativity (N), quantum discord (QD), and measurement-induced disturbance (MID) and the behaviors of quantum phase transition (QPT) at finite temperature. The results indicate that DM interaction D can enhance the N, QD, and MID, while the uniform magnetic field B suppresses them, and the role played by the inhomogeneity b of magnetic field in N is obviously different from those in QD and MID for the smaller D region. Moreover, compared with N, we notice the QD and MID are more general measures of the thermal quantum correlation (TQC). And that the MID cannot completely replace the QD has been discovered. It is also observed that the DM interaction is a more optimal parameter than the inhomogeneous external magnetic field in the process of improving the TQC measured by QD and MID at the higher temperature. In addition, we note that the DM interaction and an inhomogeneous external magnetic field present remarkable different effects on the behavior of the QPT point at finite temperature.

Spin crossover and Mott—Hubbard transition under high pressure and high temperature in the low mantle of the Earth

Effect of high pressure induced spin crossover on the magnetic, electronic and structural properties of the minerals forming the Earth's low mantle is discussed. The low temperature P, T phase diagram of ferropericlase has the quantum phase transition point Pc = 56 GPa at T = 0 confirmed recently by the synchrotron Mössbauer spectroscopy. The LDA+GTB calculated phase diagram describes the experimental data. Its extension to the high temperature resulted earlier in prediction of the metallic properties of the Earth's mantle at the depth 1400 km < h < 1800 km. Estimation of the electrical conductivity based on the percolation theory is given. We discuss also the thermodynamic properties and structural anomalies resulting from the spin crossover and metal-insulator transition and compare them with the experimental seismic and geomagnetic field data.

Winding numbers of phase transition points for one-dimensional topological systems

We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and to the extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.

Generalized Moment Method for Gap Estimation and Quantum MonteCarlo Level Spectroscopy.

We formulate a convergent sequence for the energy gap estimation in the worldline quantum MonteCarlo method. The ambiguity left in the conventional gap calculation for quantum systems is eliminated. Our estimation will be unbiased in the low-temperature limit, and also the error bar is reliably estimated. The level spectroscopy from quantum MonteCarlo data is developed as an application of the unbiased gap estimation. From the spectral analysis, we precisely determine the Kosterlitz-Thouless quantum phase-transition point of the spin-Peierls model. It is established that the quantum phonon with a finite frequency is essential to the critical theory governed by the antiadiabatic limit, i.e., the k=1 SU(2) Wess-Zumino-Witten model.

Characterization of topological phase transitions via topological properties of transition points

We study topological properties of phase transition points of topological quantum phase transitions by assigning a topological invariant defined on a closed circle or surface surrounding the phase transition point in the parameter space of momentum and transition driving parameter. By applying our scheme to the Su-Schrieffer-Heeger model and Haldane model, we demonstrate that the topological phase transition can be well characterized by the defined topological invariant of the transition point, which reflects the change of topological invariants of topologically different phases across the phase transition point.