arXiv subjects

Fan Zhong

Publications and source records attributed to Fan Zhong.

51 records · Page 3Linked to original sources

arXiv2014

Generalized dynamic scaling for quantum critical relaxation in imaginary time

We study the imaginary-time relaxation critical dynamics of a quantum system with a vanishing initial correlation length and an arbitrary initial order parameter $M_0$. We find that in quantum critical dynamics, the behavior of $M_0$ under scale transformations deviates from a simple power-law, which was proposed for very small $M_0$ previously. A universal characteristic function is then suggested to describe the rescaled initial magnetization, similar to classical critical dynamics. This characteristic function is shown to be able to describe the quantum critical dynamics in both short- and long-time stages of the evolution. The one-dimensional transverse-field Ising model is employed to numerically determine the specific form of the characteristic function. We demonstrate that it is applicable as long as the system is in the vicinity of the quantum critical point. The universality of the characteristic function is confirmed by numerical simulations of models belonging to the same universality class.

cond-mat.stat-mech↗

arXiv2014

Kibble-Zurek Mechanism and Finite-Time Scaling

The Kibble-Zurek (KZ) mechanism has been applied to a variety of systems ranging from low temperature Bose-Einstein condensations to grand unification scales in particle physics and cosmology and from classical phase transitions to quantum phase transitions. Here we show that finite-time scaling (FTS) provides a detailed improved understanding of the mechanism. In particular, the finite time scale, which is introduced by the external driving (or quenching) and results in FTS, is the origin of the division of the adiabatic regimes from the impulse regime in the KZ mechanism. The origin of the KZ scaling for the defect density, generated during the driving through a critical point, is not that the correlation length ceases growing in the nonadiabatic impulse regime, but rather, is that it is taken over by the effective finite length scale corresponding to the finite time scale. We also show that FTS accounts well for and improves the scaling ansatz proposed recently by Liu, Polkovnikov, and Sandvik [Phys. Rev. B {\bf 89}, 054307 (2014)]. Further, we show that their universal power-law scaling form applies only to some observables in cooling but not to heating. Even in cooling, it is invalid either when an appropriate external field is present. However, this finite-time-finite-size scaling calls for caution in application of FTS. Detailed scaling behaviors of the FTS and finite-size scaling, along with their crossover, are explicitly demonstrated, with the dynamic critical exponent $z$ being estimated for two- and three-dimensional Ising models under the usual Metropolis dynamics. These values of $z$ are found to give rise to better data collapses than the extant values do in most cases but take on different values in heating and cooling in both two- and three-dimensional spaces.

cond-mat.stat-mech↗

arXiv2014

Floquet poor man's Majorana fermions in double quantum dots

We consider a system consisting of two quantum dots connected by an s-wave superconductor in the presence of periodically varying electric or magnetic fields. The Floquet theory shows that there may be Floquet poor man's Majorana fermions (FPMMFs) in the high frequency region depending on the phase difference between the applied external fields to the two dots. Numerical results confirm this expectation and find in addition a lot of FPMMFs in the low frequency region. The FPMMFs survive for nonzero energy levels of the two dots and their interaction though the frequencies at which they emerge change and thus may be a promising candidate to be detected in experiments.

cond-mat.mes-hall↗

arXiv2014

Tunable Floquet Majorana Fermions in Driven Coupled Quantum Dots

We propose a system of coupled quantum dots in proximity to a superconductor and driven by separate ac potentials to realize and detect Floquet Majorana fermions. We show that the appearance of Floquet Majorana fermions can be finely controlled in the expanded parameter space of the drive frequency, amplitude, and phase difference across the two dots. While these Majorana fermions are not topologically protected, the highly tunable setup provides a realistic system for observing the exotic physics associated with Majorana fermions as well as their dynamical generation and manipulation.

cond-mat.mes-hall↗

arXiv2014

Universal short-time quantum critical dynamics in imaginary time

We propose a scaling theory for the universal imaginary-time quantum critical dynamics for both short times and long times. We discover that there exists a universal critical initial slip related to a small initial order parameter $M_0$. In this stage, the order parameter $M$ increases with the imaginary time $τ$ as $M\propto M_0τ^θ$ with a universal initial slip exponent $θ$. For the one-dimensional transverse-field Ising model, we estimate $θ$ to be $0.373$, which is markedly distinct from its classical counterpart. Apart from the local order parameter, we also show that the entanglement entropy exhibits universal behavior in the short-time region. As the critical exponents in the early stage and in equilibrium are identical, we apply the short-time dynamics method to determine quantum critical properties. The method is generally applicable in both the Landau-Ginzburg-Wilson paradigm and topological phase transitions.

cond-mat.stat-mech↗

arXiv2013

Nonequilibrium quantum criticality in open systems: The dissipation rate as an additional indispensable scaling variable

We propose that nonequilibrium quantum criticality in open systems at both zero and finite temperatures can be described by a master equation of the Lindblad form. We derive this equation from a system coupling microscopic to a heat bath. It is suggested to be valid generally for studying dynamical quantum criticality and is thus designated as Model Q upon generalizing Hohenberg and Halperin's classification of classical critical dynamics. We find that the dissipation rate in the equation must be included in the scaling forms as an indispensable additional scaling variable in order to correctly describe the nonequilibrium quantum critical behavior. Yet, the equilibrium fixed point determines the nonequilibrium critical behavior in the weak coupling limit. Through numerically solving the Lindblad equation for the quantum Ising chain, we attest these propositions by finite-time scaling forms with the dissipation rate. Nonequilibrium dynamic critical behavior of spontaneous emissions in dissipative open systems at zero temperature near their quantum critical points is found and is also described well by the scaling forms. Model Q thus provides a general approach to study quantum critical behavior of a system itself through its weak coupling to the environment.

cond-mat.stat-mech↗

arXiv2013

Finite-time scaling of dynamic quantum criticality

We develop a theory of finite-time scaling for dynamic quantum criticality by considering the competition among an external time scale, an intrinsic reaction time scale and an imaginary time scale arising respectively from an external driving field, the fluctuations of the competing orders and thermal fluctuations. Through a successful application in determining the critical properties at zero temperature and the solution of real-time Lindblad master equation near a quantum critical point at nonzero temperatures, we show that finite-time scaling offers not only an amenable and systematic approach to detect the dynamic critical properties, but also a unified framework to understand and explore nonequilibrium dynamics of quantum criticality, which shows specificities for open systems.

cond-mat.stat-mech↗

arXiv2012

Is an imaginary fixed point physical or unphysical?

It has been proposed that a first-order phase transition driven to happen in the metastable region exhibits scaling and universality near an instability point controlled by an instability fixed point of a $φ^3$ theory. However, this fixed point has an imaginary value and the renormalization-group flow of the $φ^3$ coupling diverges at a finite scale. Here combining a momentum-space RG analysis and a nucleation theory near the spinodal point, we show that imaginary rather than real values are physical counter-intuitively and thus the imaginary fixed point does control the scaling.

cond-mat.stat-mech↗

arXiv2012

Renormalization-group theory of dynamics of first-order phase transitions in a field-driven scalar model

We show by a detailed study of the mean-field approximation, the Gaussian approximation, the perturbation expansion, and the field-theoretic renormalization-group analysis of a $φ^{3}$ theory that its instability fixed points with their associated instability exponents are quite probably relevant to the scaling and universality behavior exhibited by the first-order phase transitions in a field-driven scalar $ϕ^4$ model below its critical temperature near their instability points. Finite-time scaling and leading corrections to scaling are considered. We also show that the instability exponents of the first-order phase transitions equal those of the Yang--Lee edge singularity and employ the latter to improve our estimates of the former. The outcomes agree well with existent numerical results.

cond-mat.stat-mech↗

arXiv2011

Functional renormalization group approach to the dynamics of first-order phase transitions

We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic flow equation which is decoupled from the static flow equation. We find the expected instability fixed points; and their associated exponents agree remarkably with the existent theoretical and numerical results. The complex renormalization group flows are found and their properties are shown. Both the exponents and the complex flows show that the spinodal decomposition possesses singularity with consequent scaling and universality.

cond-mat.stat-mech↗

arXiv2000

Symmetry Does Not Allow Canting of Spins in La_{1.4}Sr_{1.6}Mn_2O_7

We analyze the symmetry of all possible magnetic structures of bilayered manganites La_{2-2x}Sr_{1+2x}Mn_2O_7 with doping 0.3 <= x < 0.5 and formulate a corresponding Landau theory of the phase transitions involved. It is shown that canting of spins is not allowed at x=0.3 though is at x=0.4. The observed magnetic reflections from the sample with x=0.3 may be described as arising from two spatially distributed phases with close transition temperatures but different easy axes and ranges of stability. Experimental results are revisited on the basis of the theoretical findings.

cond-mat.str-el↗

arXiv1999

Dynamical Mean-Field Solution for a Model of Metal-Insulator Transitions in Moderately Doped Manganites

We propose that a specific spatial configuration of lattice sites that energetically favor {\it 3+} or {\it 4+} Mn ions in moderately doped manganites constitutes approximately a spatially random two-energy-level system. Such an effect results in a mechanism of metal-insulator transitions that appears to be different from both the Anderson transition and the Mott-Hubbard transition. Correspondingly, a disordered Kondo lattice model is put forward, whose dynamical mean-field solution agrees reasonably with experiments.

cond-mat.str-el↗

arXiv1999

Symmetry Origin of the Phase Transitions and Phase Separation in Manganites at Low Doping

We analyze the symmetry changes of the paramagnetic to the A-type antiferromagnetic and to the ferromagnetic phase transitions in undoped and moderately doped LaMnO$_3$, respectively. We show that in the orthorhombic-distorted perovskite manganites the phase separation at low doping is associated with the noncollinear nature of the magnetic orders permitted by symmetry. A simple model for the competition between the two phase transitions is put forward within the framework of Landau theory of phase transitions.

cond-mat.str-el↗

arXiv1999

Landau Theory of the Phase Transitions in Half Doped Manganites: Interplay of Magnetic, Charge and Structural Orders

The order parameters of the magnetic, charge and structural orders at half-doped manganites are identified. A corresponding Landau theory of the phase transitions is formulated. Many structural and thermodynamical behaviors are accounted for and clarified within the framework. In particular, the theory provides a unified picture for the scenario of the phase transitions and their nature with respect to the variation of the tolerance factor of the manganites. It also accounts for the origin of the incommensurate nature of the orbital order and its subsequently accompanying antiferromagnetic order.

cond-mat.str-el↗

arXiv1998

Theory of Coupled Phase Transitions: Phase Separation and Variation of Order Parameter

A simplified Ginzburg-Landau theory is presented to study generally a coupling of a first-order phase transition (FOPT) to a second-order phase transition (SOPT). We show analytically that, due to the coupling between the two phase transitions, the SOPT may exhibit a FOPT-like phase separation in which an ordered phase is separated from a disordered one. This phase separation results in a distinct behavior in the variation of the order parameter of the SOPT, namely, it is primarily the proportion of the ordered phase that contributes to the total order of the whole system during the FOPT. This growth mode may turn a mean-field critical exponent from 1/2 to 1 or even bigger.

cond-mat↗