Dynamical Critical Exponent Research Articles

Doping-Induced Quantum Spin Hall Insulator to Superconductor Transition.

A quantum spin Hall insulating state that arises from spontaneous symmetry breaking has remarkable properties: skyrmion textures of the SO(3) order parameter carry charge 2e. Doping this state of matter opens a new route to superconductivity via the condensation of skyrmions. We define a model amenable to large-scale negative sign free quantum MonteCarlo simulations that allows us to study this transition. Our results support a direct and continuous doping-induced transition between the quantum spin Hall insulator and an s-wave superconductor. We can resolve dopings away from half-filling down to δ=0.0017. Such routes to superconductivity have been put forward in the realm of twisted bilayer graphene.

Towards holographic flat bands

Motivated by the phenomenology in the condensed-matter flat-band Dirac systems, we here construct a holographic model that imprints the symmetry breaking pattern of a rather simple Dirac fermion model at zero chemical potential. In the bulk we explicitly include the backreaction to the corresponding Lifshitz geometry and compute the dynamical critical exponent. Most importantly, we find that such a geometry is unstable towards a nematic phase, exhibiting an anomalous Hall effect and featuring a Drude-like shift of its spectral weight. Our findings should motivate further studies of the quantum phases emerging from such holographic models.

Universal scaling of work statistics in conformal field theory models

In this paper, we systematically study the work statistics for quantum phase transition. For a quantum system approached by an anisotropic conformal field theory near the critical point, the driving protocols is divided into three different regimes for different quench rates, which reflects the competition between the frozen time and the quench time scale. In each regime, we find universal scaling behaviors in work statistics (after renormalization). It is shown that the critical exponents are determined by the space-time dimension $d$, the dynamical critical exponent $z$, the correlation-length exponent $\nu$, and the power-law protocols. These universal scalings in nonequilibrium process may be found in quantum phase transition by measuring the Loschmidt echo or the Ramsey interferometry.

Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder

This study investigates the dynamical critical exponent of disordered Ising chains under transverse fields to examine the effect of a correlated disorder on quantum phase transitions. The correlated disorder, where the on-site transverse field depends on the nearest-neighbor coupling strengths connecting the site, gives a qualitatively different result from the uncorrelated disorder. In the uncorrelated disorder cases where the transverse field is either homogeneous over sites or random independently of the nearest-neighbor coupling strengths, the dynamical critical exponent is infinite. In contrast, in the presence of the correlated disorder, we analytically show that the dynamical critical exponent is finite. We also show that the dynamical critical exponent depends on the tuning process of the transverse field strengths.

Informational properties of holographic Lifshitz field theory * *Supported by the Natural Science Foundation of China (11775036, 11905083, 11847055, 11705161) and Fok Ying Tung Education Foundation (171006). Guoyang Fu is supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX20_2973). Top Talent Support Program from Yangzhou University

In this paper, we explore the properties of holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP) in holographic Lifshitz theory. These informational quantities exhibit some universal properties of holographic dual field theory. For most configuration parameters and temperatures, these informational quantities change monotonically with the Lifshitz dynamical critical exponent z. However, we also observe some non-monotonic behaviors for these informational quantities in some specific spaces of configuration parameters and temperatures. A particularly interesting phenomenon is that a dome-shaped diagram emerges in the behavior of MI vs z, and correspondingly a trapezoid-shaped profile appears in that of EoP vs z. This means that for some specific configuration parameters and temperatures, the system measured in terms of MI and EoP is entangled only in a certain intermediate range of z.

Neural Systems Under Change of Scale.

We derive a theoretical construct that allows for the characterisation of both scalable and scale free systems within the dynamic causal modelling (DCM) framework. We define a dynamical system to be “scalable” if the same equation of motion continues to apply as the system changes in size. As an example of such a system, we simulate planetary orbits varying in size and show that our proposed methodology can be used to recover Kepler’s third law from the timeseries. In contrast, a “scale free” system is one in which there is no characteristic length scale, meaning that images of such a system are statistically unchanged at different levels of magnification. As an example of such a system, we use calcium imaging collected in murine cortex and show that the dynamical critical exponent, as defined in renormalization group theory, can be estimated in an empirical biological setting. We find that a task-relevant region of the cortex is associated with higher dynamical critical exponents in task vs. spontaneous states and vice versa for a task-irrelevant region.

Crossover in the dynamical critical exponent of a quenched two-dimensional Bose gas

We study the phase ordering dynamics of a uniform Bose gas in two dimensions following a quench into the ordered phase. We explore the crossover between dissipative and conservative evolution by performing numerical simulations within the classical field methodology. Regardless of the dissipation strength, we find clear evidence for universal scaling, with dynamical critical exponent $z$ characterising the growth of the correlation length. In the dissipative limit we find growth consistent with the logarithmically corrected law $[t/\log(t/t_0)]^{1/z}$, and exponent $z=2$, in agreement with previous studies. Decreasing the dissipation towards the conservative limit, we find strong numerical evidence for the expected growth law $t^{1/z}$. However, we observe a smooth crossover in $z$ that converges to an anomalous value distinctly lower than $2$ at a small finite dissipation strength. We show that this lower exponent may be attributable to a power-law vortex mobility arising from vortex--sound interactions.

Equilibrium to off-equilibrium crossover in homogeneous active matter

We study the crossover between equilibrium and off-equilibrium dynamical universality classes in the Vicsek model near its ordering transition. Starting from the incompressible hydrodynamic theory of Chen et al \cite{chen2015critical}, we show that increasing the activity leads to a renormalization group (RG) crossover between the equilibrium ferromagnetic fixed point, with dynamical critical exponent $z = 2$, and the off-equilibrium active fixed point, with $z = 1.7$ (in $d=3$). We run simulations of the classic Vicsek model in the near-ordering regime and find that critical slowing down indeed changes with activity, displaying two exponents that are in remarkable agreement with the RG prediction. The equilibrium-to-off-equilibrium crossover is ruled by a characteristic length scale beyond which active dynamics takes over. Such length scale is smaller the larger the activity, suggesting the existence of a general trade-off between activity and system's size in determining the dynamical universality class of active matter.

Quantum critical diffusion and thermodynamics in Lifshitz holography

We present the full charge and energy diffusion constants for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. Therein we compute the fully renormalized static thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking entropy and Smarr-like relationship. All thermodynamics are based on a direct computation of the free energy. Our exact computation demonstrates a modification to the Lifshitz-Ward identity for the EMD theory. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. While our exact results corroborate anticipated bounds, we are able to demonstrate that the diffusivities are governed by the engineering dimension of the diffusion coefficient, $[D]=2\ensuremath{-}z$. Consequently, a $\ensuremath{\beta}$ function defined as the derivative of the trace of the diffusion matrix with respect to the effective lattice spacing changes sign precisely at $z=2$. At $z=2$, the diffusion equation exhibits perfect scale invariance and the corresponding diffusion constant is the pure number $1/{d}_{s}$ for both the charge and energy sectors, where ${d}_{s}$ is the number of spatial dimensions. Further, we find that as $z\ensuremath{\rightarrow}\ensuremath{\infty}$, the charge diffusion constant vanishes, indicating charge localization. Deviation from universal decoupled transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions.

Geometric allocation approach to accelerating directed worm algorithm.

The worm algorithm is a versatile technique in the Markov chain Monte Carlo method for both classical and quantum systems. The algorithm substantially alleviates critical slowing down and reduces the dynamic critical exponents of various classical systems. It is crucial to improve the algorithm and push the boundary of the Monte Carlo method for physical systems. We here propose a directed worm algorithm that significantly improves computational efficiency. We use the geometric allocation approach to optimize the worm scattering process: worm backscattering is averted, and forward scattering is favored. Our approach successfully enhances the diffusivity of the worm head (kink), which is evident in the probability distribution of the relative position of the two kinks. Performance improvement is demonstrated for the Ising model at the critical temperature by measurement of exponential autocorrelation times and asymptotic variances. The present worm update is approximately 25 times as efficient as the conventional worm update for the simple cubic lattice model. Surprisingly, our algorithm is even more efficient than the Wolff cluster algorithm, which is one of the best update algorithms. We estimate the dynamic critical exponent of the simple cubic lattice Ising model to be z≈0.27 in the worm update. The worm and the Wolff algorithms produce different exponents of the integrated autocorrelation time of the magnetic susceptibility estimator but the same exponent of the asymptotic variance. We also discuss how to quantify the computational efficiency of the Markov chain Monte Carlo method. Our approach can be applied to a wide range of physical systems, such as the |ϕ|^{4} model, the Potts model, the O(n) loop model, and lattice QCD.

Integrable quantum spin chains with free fermionic and parafermionic spectrum

We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in \cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density operators defining the quantum chains. The Hamiltonians are characterized by a parameter $p=1,2,\dots$ related to the number of interacting spins in the multispin interaction. In the general case the quantum spins are of infinite dimension. In special cases, characterized by the parameter $N=2,3,\ldots$, the quantum chains describe the dynamics of $Z(N)$ quantum spin chains. The simplest case $p=1$ corresponds to the free fermionic quantum Ising chain ($N=2$) or the $Z(N)$ free parafermionic quantum chain. The eigenenergies of the quantum chains are given in terms of the roots of special polynomials, and for general values of $p$ the quantum chains are characterized by a free fermionic ($N=2$) or free parafermionic ($N>2$) eigenspectrum. The models have a special critical point when all coupling constants are equal. At this point the ground-state energy is exactly calculated in the bulk limit, and our analytical and numerical analyses indicate that the models belong to universality classes of critical behavior with dynamical critical exponent $z = (p+1)/N$ and specific-heat exponent $\alpha = \max\{0,1-(p+1)/N\}$.

Ground-state energy density, susceptibility, and Wilson ratio of a two-dimensional disordered quantum spin system

A two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model with a specific kind of quenched disorder is investigated, using the first principles nonperturbative quantum Monte Carlo calculations (QMC). The employed disorder distribution has a tunable parameter $p$ which can be considered as a measure of the corresponding randomness. In particular, when $p=0$ the disordered system becomes the clean one. Through a large scale QMC, the dynamic critical exponents $z$, the ground state energy densities $E_0$, as well as the Wilson ratios $W$ of various $p$ are determined with high precision. Interestingly, we find that the $p$ dependence of $z$ and $W$ are likely to be complementary to each other. For instance, while the $z$ of $0.4 \le p \le 0.9$ match well among themselves and are statistically different from $z=1$ which corresponds to the clean system, the $W$ for $p < 0.7$ are in reasonable good agreement with that of $p=0$. The technical subtlety of calculating these physical quantities for a disordered system is demonstrated as well. The results presented here are not only interesting from a theoretical perspective, but also can serve as benchmarks for future related studies.

Far-away-from-equilibrium quantum-critical conformal dynamics: Reversibility, thermalization, and hydrodynamics

Generic far-away-from-equilibrium many-body dynamics involve entropy production, and hence are thermodynamically irreversible. Near quantum critical points, an emergent conformal symmetry can impose strong constraints on entropy production rates, and in some cases completely forbid entropy production, which usually occurs for systems that deviate from quantum critical points. In this article, we illustrate how the vanishing entropy production near a quantum critical point results in reversible far-away-from-equilibrium dynamics at finite temperatures that are otherwise irreversible. Away from the quantum critical point, the quantum dynamics are damped, and our analysis directly relates the thermalization time scale to the hydrodynamic viscosity near quantum critical points with dynamical critical exponent $z=2$. We demonstrate how both controllable reversible and irreversible dynamics can be potentially studied in cold gas experiments using Feshbach resonances.

Critical dynamics of anisotropic antiferromagnets in an external field.

We numerically investigate the nonequilibrium critical dynamics in three-dimensional anisotropic antiferromagnets in the presence of an external magnetic field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. The nonconserved components of the staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field. Employing a hybrid computational algorithm that combines reversible spin precession with relaxational Monte Carlo updates, we study the aging scaling dynamics for the model C critical line, identifying the critical initial slip, autocorrelation, and aging exponents for both the order parameter and the conserved field, thus also verifying the dynamic critical exponent. We further probe the model F critical line by investigating the system size dependence of the characteristic spin wave frequencies near criticality and measure the dynamic critical exponents for the order parameter including its aging scaling at the bicritical point.

Superspin glass behavior and giant exchange bias effect in hexagonal (Mn0.7Cu0.3)66Ga34 ferrimagnet

A hexagonal Ni2In-type single phase is obtained in the (Mn0.7Cu0.3)66Ga34 sample. The superspin glass (SSG) behavior and exchange bias effect are investigated in depth. The DC thermomagnetic M(T) measurements show a remarkable bifurcation between the zero-field cooling and field-cooling patterns below 100 K, suggesting a SSG behavior, which is verified by the simulation of de Almeida–Thouless relation from M(T) curves under different fields. Furthermore, the SSG behavior is justified by the AC susceptibility, temporal magnetic relaxation, and memory effect measurements. The asymmetric response of memory effect clearly indicates that it supports the hierarchical model. More importantly, the fitted parameters including Mydosh parameter Φ = 0.0255, dynamical critical exponent zv = 10.02, and τ0 ~ 5.5 × 10−9 s give the convincing evidences for the SSG behavior at low temperatures for (Mn0.7Cu0.3)66Ga34. Above all, a giant exchange bias field of μ0HEB = 308.4 mT is obtained at T = 2 K under the cooling field μ0HCF = 0.5 T and maximum applied magnetic field |μ0Hmax| = | +μ0H | = | −μ0H | = 8 T. The origin for giant exchange bias effect is discussed.

Superconductor-Metal Quantum Transition at the EuO/KTaO3 Interface* *Supported by the National Key R&D Program of China (Grant Nos. 2019YFA0308401 and 2017YFA0303301), the National Natural Science Foundation of China (Grant Nos. 11974025, 11674009, and 11934016), the Beijing Natural Science Foundation (Grant No. 1192009), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000).

We report the experimental investigation of the superconductor-metal quantum phase transition of the EuO/KTaO3 interface. Around the transition, a divergence of the dynamical critical exponent is observed, which supports the quantum Griffiths singularity in the EuO/KTaO3 interface. The quantum Griffiths singularity could be attributed to large rare superconducting regions and quenched disorders at the interface. Our results could pave the way for studying the exotic superconducting properties at the EuO/KTaO3 interface.

Measurement-induced entanglement transitions in many-body localized systems

The resilience of quantum entanglement to a classicality-inducing environment is tied to fundamental aspects of quantum many-body systems. The dynamics of entanglement has recently been studied in the context of measurement-induced entanglement transitions, where the steady-state entanglement collapses from a volume-law to an area-law at a critical measurement probability $p_{c}$. Interestingly, there is a distinction in the value of $p_{c}$ depending on how well the underlying unitary dynamics scramble quantum information. For strongly chaotic systems, $p_{c} > 0$, whereas for weakly chaotic systems, such as integrable models, $p_{c} = 0$. In this work, we investigate these measurement-induced entanglement transitions in a system where the underlying unitary dynamics are many-body localized (MBL). We demonstrate that the emergent integrability in an MBL system implies a qualitative difference in the nature of the measurement-induced transition depending on the measurement basis, with $p_{c} > 0$ when the measurement basis is scrambled and $p_{c} = 0$ when it is not. This feature is not found in Haar-random circuit models, where all local operators are scrambled in time. When the transition occurs at $p_{c} > 0$, we use finite-size scaling to obtain the critical exponent $\nu = 1.3(2)$, close to the value for 2+0D percolation. We also find a dynamical critical exponent of $z = 0.98(4)$ and logarithmic scaling of the R\'{e}nyi entropies at criticality, suggesting an underlying conformal symmetry at the critical point. This work further demonstrates how the nature of the measurement-induced entanglement transition depends on the scrambling nature of the underlying unitary dynamics. This leads to further questions on the control and simulation of entangled quantum states by measurements in open quantum systems.

Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model.

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this paper, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents including the dynamical exponent. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely nonequilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that captures the system's long-time memory as well as its nonequilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

Disorder-Induced Quantum Griffiths Singularity Revealed in an Artificial 2D Superconducting System.

Disorder‐induced Griffiths singularity of quantum phase transition (QPT) is a crucial issue in 2D superconductors (2DSC). In a superconducting system, the strength of disorder is found to be associated with the vortex pinning energy, which is closely related to the quantum Griffiths singularity; however, a direct study to elucidate the role of vortex pinning energy on the quantum Griffiths singularity in 2DSC remains to be undertaken. Here, an artificial 2DSC system is designed by randomly depositing superconducting nanoislands on 2Delectron gas (2DEG). Quantum Griffiths singularity is present in a graphene/Pb‐islands‐array hybrid, where the superconducting behavior transits to weakly localized metallic behavior induced by the vertical magnetic field and exhibits critical behavior with a diverging dynamical critical exponent approaching zero temperature. Compared to the study of graphene/Sn‐islands‐array hybrid where the sharp QPT is observed, the vortex pinning energy acquired from the Arrhenius plot analysis is greater in graphene/Pb‐islands‐array hybrid, which may contribute to the presence of the quantum Griffiths singularity. This work may provide a comprehensive interpretation of the QPT in 2DSC.

Bilocal quantum criticality

We consider 2+1 dimensional conformal gauge theories coupled to additional degrees of freedom which induce a spatially local but long-range in time $1/(\tau-\tau')^2$ interaction between gauge-neutral local operators. Such theories have been argued to describe the hole-doped cuprates near optimal doping. We focus on a SU(2) gauge theory with $N_h$ flavors of adjoint Higgs fields undergoing a quantum transition between Higgs and confining phases: the $1/(\tau-\tau')^2$ interaction arises from a spectator large Fermi surface of electrons. The large $N_h$ expansion leads to an effective action containing fields which are bilocal in time but local in space. We find a strongly-coupled fixed point at order $1/N_h$, with dynamic critical exponent $z > 1$. We show that the entropy preserves hyperscaling, but nevertheless leads to a linear in temperature specific heat with a co-efficient which has a finite enhancement near the quantum critical point.