arXiv subjects

Hai-Qing Zhang

Publications and source records attributed to Hai-Qing Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2024

A universal approach to Renyi entropy of multiple disjoint intervals

We develop a general theory for computing the Renyi entropy with general multiple disjoint intervals from the swapping operations. Our theory is proposed based on the fact that we have observed the resemblance between the replica trick in quantum field theory and the swapping operation. Consequently, the Renyi entropy can be obtained by evaluating the expectation values of the swapping operator. As an application, we study the Renyi entropy of a one-dimensional transverse-field Ising model for two, three and four disjoint intervals. As the system is at the critical point, our computations of the Renyi entropy are consistent with the analytical results from the conformal field theory. Moreover, our methods can go beyond the critical regime of the Ising model.

cond-mat.stat-mech↗

arXiv2024

Probing Krylov Complexity in Scalar Field Theory with General Temperatures

Krylov complexity characterizes the operator growth in the quantum many-body systems or quantum field theories. The existing literatures have studied the Krylov complexity in the low temperature limit in the quantum field theories. In this paper, we extend and systematically study the Krylov complexity and Krylov entropy in a scalar field theory with general temperatures. To this end, we propose a new method to calculate the Wightman power spectrum which allows us to compute the Lanczos coefficients and subsequently to study the Krylov complexity (entropy) in general temperatures. We find that the Lanczos coefficients and Krylov complexity (entropy) in the high temperature limit will behave somewhat differently from those studies in the low temperature limit. We give an explanation of why the Krylov complexity does not oscillate in the high-temperature region. Moreover, we uncover the transition temperature that separates the oscillating and monotonic increasing behavior of Krylov complexity.

hep-th↗

arXiv2024

Effective Action and Gravitational Pair Production in (A)dS Spacetime

We compute the effective action for a massive scalar field in (A)dS spacetime using the Euclidean heat kernel method. We highlight that in even-dimensional dS spacetimes, the effective action exhibits a non-trivial imaginary part, reminiscent of the Schwinger effect in quantum electrodynamics. We find consistency between the results obtained from the Euclidean heat kernel method with those from the Green's function approach in Lorentzian signature. Additionally, we compare our results with the perturbative calculations and find that the perturbation theory almost fails to capture the correct non-perturbative imaginary part of the effective action. This discrepancy presents a challenge to computing the gravitational pair production using the perturbation theory.

gr-qc↗

arXiv2024

Holographic Timelike Entanglement Entropy from Rindler Method

For a Lorentzian invariant theory, the entanglement entropy should be a function of the domain of dependence of the subregion under consideration. More precisely, it should be a function of the domain of dependence and the appropriate cut-off. In this paper, we refine the concept of cut-off to make it applicable to timelike regions and assume that the usual entanglement entropy formula also applies to timelike intervals. Using the Rindler method, the timelike entanglement entropy can be regarded as the thermal entropy of the CFT after the Rindler transformation plus a constant $icπ/6$ with $c$ the central charge. The gravitational dual of the `covariant' timelike entanglement entropy is finally presented following this method.

hep-th↗

arXiv2024

Universal Critical Holography and Domain Wall Formation

Using holography, we study the universal scaling laws governing the coarsening dynamics of strongly coupled domain walls. Specifically, we studied the universal dependence of the length of the domain wall interfaces on the quench rate. The relation satisfies the Kibble-Zurek scaling shortly after the critical point. However, as time goes by, the coarsening dynamics suppresses the Kibble-Zurek scaling in favor of a universal dynamical scaling of the characteristic length and the adiabatic growth of the system. Theoretical predictions of the universal scaling laws are consistent with numerical findings in both regimes for both weak and strongly coupled systems.

cond-mat.stat-mech↗

arXiv2024

Asymmetric Symmetry Breaking: Unequal Probabilities of Vacuum Selection

Spontaneous symmetry breaking is a fundamental notion in modern physics, ranging from high energy to condensed matter. However, the usual spontaneous symmetry breaking only considers the equal probability to select the vacua. In this work, we conceive a model to realize the unequal probability of the symmetry breaking, leading to an unbalanced number of ground states. Specifically, we study the probabilities of a scalar field to roll down from the top of a potential, where the top is only $C^1$ continuous. As the whole system is subject to random perturbations, we find that the probability for the field to roll down to the left or right side depends the square root of the second derivative of the potential at the top. We solve this problem theoretically by using the Fokker-Planck equations in stochastic process and verify our findings numerically. This study may potentially be a new mechanism to explain the origins of asymmetries in the Universe.

hep-th↗

arXiv2024

Is a photon ring invariably a closed structure?

In this study, we investigate the image of a rotating compact object (CO) illuminated by a geometrically thin, optically thin disk on the equatorial plane. As the radius of the CO's surface fluctuates, the CO may partially or entirely obscure the photon region. We observe that the perceived photon ring may exhibit discontinuities, deviating from a closed structure, and may even disappear entirely. We find that the disruption and disappearance of the photon ring are dependent on the observational angle$-$a novel phenomenon not previously observed in black hole imaging studies. Our study reveals that while the factors influencing this unique photon ring phenomenon are diverse and the outcomes complex, we can provide a clear and comprehensive explanation of the physical essence and variation trends of this phenomenon. We do this by introducing and analyzing the properties and interrelationships of three characteristic functions, $\tildeη$, $η_o$, and $η_s$ related to the photon impact parameters. Additionally, our analysis of the intensity cuts and inner shadows of the images uncovers patterns that differ significantly from the shadow curve.

gr-qc↗

arXiv2024

Measuring Renyi Entropy in Neural Network Quantum States

We compute the Renyi entropy in a one-dimensional transverse-field quantum Ising model by employing a swapping operator acting on the states which are prepared from the neural network methods. In the static ground state, Renyi entropy can uncover the critical point of the quantum phase transition from paramagnetic to ferromagnetic. At the critical point, the relation between the Renyi entropy and the subsystem size satisfies the predictions from conformal field theory. In the dynamical case, we find coherent oscillations of the Renyi entropy after the end of the linear quench. These oscillations have universal frequencies which may come from the superpositions of excited states. The asymptotic form of the Renyi entropy implies a new length scale away from the critical point. This length scale is also verified by the overlap of the reduced Renyi entropy against the dimensionless subsystem size.

cond-mat.dis-nn↗

arXiv2024

Topologically Protected Metastable States in Classical Dynamics

We propose that domain walls formed in a classical Ginzburg-Landau model can exhibit topologically stable but thermodynamically metastable states. This proposal relies on Allen-Cahn's assertion that the velocity of domain wall is proportional to the mean curvature at each point. From this assertion we speculate that domain wall behaves like a rubber band that can winds the background geometry in a nontrivial way and can exist permanently. We numerically verify our proposal in two and three spatial dimensions by using various boundary conditions. It is found that there are possibilities to form topologically stable domain walls in the final equilibrium states. However, these states have higher free energies, thus are thermodynamically metastable. These metastable states that are protected by topology could potentially serve as storage media in the computer and information technology industry.

cond-mat.stat-mech↗

arXiv2023

From black hole to one-dimensional chain: parity symmetry breaking and kink formation

AdS/CFT correspondence is a "first-principle" tool to study the strongly coupled many-body systems. While it has been extensively applied to investigate the continuous symmetry breaking dynamics, the discrete symmetry breaking dynamics are rarely investigated. In this paper, the model of kink formation in a strongly coupled one-dimensional chain is realized from the AdS/CFT correspondence. In doing so, we first construct a model of real scalar fields with parity symmetries in the AdS bulk. By quenching the system across the critical point at a finite rate, kink hairs turn out in the bulk due to the spontaneous parity symmetry breaking, which accomplishes a counter-example of "no hair conjecture" of black hole. Due to the AdS/CFT correspondence, kink hairs in the bulk are dual to the kinks in the AdS boundary. The mean of the dual kink numbers are found to satisfy a universal power-law relation to the quench rate, in agreement with the celebrated Kibble-Zurek mechanism. Moreover, the higher cumulants of the kink numbers are proportional to the mean numbers, consistent with the assumption that the formation of kinks satisfy the binomial distributions which goes beyond the Kibble-Zurek mechanism.

hep-th↗

arXiv2023

Learning topological defects formation with neural networks in a quantum phase transition

Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during a quantum phase transition, pose a greater challenge for neural networks. To address this, we utilize neural networks and machine learning algorithms to investigate the time evolutions, universal statistics, and correlations of topological defects in a one-dimensional transverse-field quantum Ising model. Specifically, our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength. The excitation energies satisfy a power-law relation to the quench rate, indicating a proportional relationship between the excitation energy and the kink numbers. Moreover, we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate, indicating a binomial distribution of the kinks. Finally, the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.

cond-mat.dis-nn↗

arXiv2023

Revisit the entanglement entropy with gravitational anomaly

In this paper we study the entanglement entropy in the CFT$_2$, whose gravity dual is AdS$_3$ spacetime with a Chern-Simons term. Using the generalized Rindler method, we obtain the Rindler transformation in the two-dimensional planar CFT and compute the entanglement entropy of the CFT with gravitational anomalies. The conditions under which the entanglement entropy may have anomalous contributions is also discussed. In addition, we present a relatively general form of the Rindler AdS metric and compute its thermal entropy, which agrees with the entanglement entropy in the field theory. Moreover, we utilize the conformal transformation, which maps a cylinder to a plane, to compute the entanglement entropy of the CFT residing on a cylinder, as well as the entanglement entropy of the CFT at finite temperature on a plane. The corresponding contribution of the Chern-Simons term in gravity to the black hole thermal entropy is also obtained from this approach. These results are important for further understandings of the two-dimensional CFT with gravitational anomalies.

hep-th↗

arXiv2022

Locality of Spontaneous Symmetry Breaking and Universal Spacing Distribution of Topological Defects Formed Across a Phase Transition

The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density. Numerical simulations in a one-dimensional $ϕ^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly-coupled superconductor indicating the suppression of defect-defect spatial correlations.

cond-mat.stat-mech↗

arXiv2022

Periodicities in a multiply connected geometry from quenched dynamics

Exploring the lowest energy configurations of a quantum system is consistent with the counting statistics of the frequently appeared states from quenching dynamics. By studying the Little-Parks periodicities in a multiply-connected ring-shaped geometry from the holographic technique, it is found that the frequently appeared states from dynamics incline to have lower free energies. In particular, the resulting winding numbers from quenched dynamics are constrained in a normal distribution for a fixed magnetic flux threading the ring. Varying the magnetic fluxes, Little-Parks periodicities will take place with periods identical to the flux quantum $Φ_0$. Favorable solutions with lowest free energies perform first order phase transitions which transform between distinct winding numbers as the magnetic flux equals half-integers multiplying $Φ_0$.

hep-th↗

arXiv2022

Holographic topological defects in a ring: role of diverse boundary conditions

We investigate the formation of topological defects in the course of a dynamical phase transition with different boundary conditions in a ring from AdS/CFT correspondence. According to the Kibble-Zurek mechanism, quenching the system across the critical point to symmetry-breaking phase will result in topological defects -- winding numbers -- in a compact ring. By setting two different boundary conditions, i.e., Dirichlet and Neumann boundary conditions for the spatial component of the gauge fields in the AdS boundary, we achieve the holographic superfluid and holographic superconductor models, respectively. In the final equilibrium state, different configurations of the order parameter phases for these two models indicate a persistent superflow in the holographic superfluid, however, the holographic superconductor lacks this superflow due to the existence of local gauge fields. The two-point correlation functions of the order parameter also behave differently. In particular, for holographic superfluid the correlation function is a cosine function depending on the winding number. The correlation function for the holographic superconductor, however, decays rapidly at short distances and vanishes at long distance, due to the random localities of the gauge fields. These results are consistent with our theoretical analysis.

hep-th↗

arXiv2021

Holographic topological defects and local gauge symmetry: clusters of strongly coupled equal-sign vortices

Gauge invariance plays an important role in forming topological defects. In this work, from the AdS/CFT correspondence, we realize the clusters of equal-sign vortices during the course of critical dynamics of a strongly coupled superconductor. This is the first time to achieve the equal-sign vortex clusters in strongly coupled systems, considering that vortices with equal sign repel. The appearance of clusters of equal-sign vortices is a typical character of flux trapping mechanism, distinct from Kibble-Zurek mechanism which merely presents vortex-antivortex pair distributions resulting from global symmetry breaking. Numerical results of spatial correlations and net fluxes of the equal-sign vortex clusters quantitatively support the positive correlations between vortices. The linear dependence between the vortex number and the amplitude of magnetic field at the `trapping' time demonstrates the flux trapping mechanism very well.

hep-th↗

arXiv2021

Universal Statistics of Vortices in a Newborn Holographic Superconductor: Beyond the Kibble-Zurek Mechanism

Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quench time. Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates.

cond-mat.stat-mech↗

arXiv2021

Topological Defects Formation with Momentum Dissipation

We employ holographic techniques to explore the effects of momentum dissipation on the formation of topological defects during the critical dynamics of a strongly coupled superconductor after a linear quench of temperature. The gravity dual is the dRGT massive gravity in which the conservation of momentum in the boundary field theory is broken by the presence of a bulk graviton mass. From the scaling relations of defects number and "freeze-out" time to the quench rate for various graviton masses, we demonstrate that the momentum dissipation induced by graviton mass has little effect on the scaling laws compared to the Kibble-Zurek mechanism. Inspired from Pippard's formula in condensed matter, we propose an analytic relation between the coherence length and the graviton mass, which agrees well with the numerical results from the quasi-normal modes analysis. As a result, the coherence length decreases with respect to the graviton mass, which indicates that the momentum dissipation will augment the number of topological defects.

hep-th↗