Equal-time Correlation Functions Research Articles

Massless Lifshitz field theory for arbitrary z

By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index z. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary z using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the c-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a z-dependent radius scale for the Lifshitz background. This relation is consistent with the z-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.

Fourier-Matsubara series expansion for imaginary-time correlation functions.

A Fourier-Matsubara series expansion is derived for imaginary-time correlation functions that constitutes the imaginary-time generalization of the infinite Matsubara series for equal-time correlation functions. The expansion is consistent with all known exact properties of imaginary-time correlation functions and opens up new avenues for the utilization of quantum Monte Carlo simulation data. Moreover, the expansion drastically simplifies the computation of imaginary-time density-density correlation functions with the finite temperature version of the self-consistent dielectric formalism. Its existence underscores the utility of imaginary-time as a complementary domain for many-body physics.

Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-T c Superconductivity in La3Ni2O7 under High Pressure

High-T c superconductivity with possible T c ≈ 80 K has been reported in the single crystal of La3Ni2O7 under high pressure. Based on the electronic structure given by the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both 3d z 2 and 3d x 2–y 2 orbital electrons of the nickel cations. The main feature of the model is that the 3d z 2 electrons form inter-layer σ-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the 3d x 2–y 2 electrons hybridize with the 3d z 2 electrons within each NiO2 plane. The chemical potential difference of these two orbital electrons ensures that the 3d z 2 orbitals are close to half-filling and the 3d x 2–y 2 orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the 3d z 2 orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange J. Applying pressure can self dope holes on the 3d z 2 orbitals with the same amount of electrons doped on the 3d x 2–y 2 orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large J and small doping of 3d z 2 orbitals, we find the superconducting instability on both the 3d z 2 and 3d x 2–y 2 orbitals by calculating the equal-time spin singlet pair–pair correlation function. Our numerical results may provide useful insights in the high-T c superconductivity in single crystal La3Ni2O7 under high pressure.

Nonequilibrium mixture dynamics: A model for mobilities and its consequences.

Extending the famous model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples different mixture components. This approach is based on a single component fluid with particles that are artificially grouped into separate species labeled by "colors." The resulting mobility matrix depends on a single dimensionless parameter, which can be determined efficiently from experimental data or numerical simulations, and includes existing standard forms as special cases. We identify two distinct mobility regimes, corresponding to collective motion and interdiffusion, respectively, and show how they emerge from the microscopic properties of the fluid. As a test scenario, we study the dynamics after a thermal quench, providing a number of general relations and analytical insights from a Gaussian theory. Specifically, for systems with two or three components, analytical results for the time evolution of the equal time correlation function compare well to results of Monte Carlo simulations of a lattice gas. A rich behavior is observed, including the possibility of transient fractionation.

Correlation function analysis of electrodeposition kinetics and evolving microstructure

We model electrodeposition using a formalism developed to describe nucleation and growth processes. In particular, we calculate non-equilibrium, equal-time correlation functions that capture the kinetics of electrodeposition (with particular application to elemental metals) and highlight the evolving correlation lengths and associated roughness in a growing electrodeposited film. These results are interpreted for the case of diffusion-limited growth at late times and, via a phase-field model, for the case of interface-controlled growth. Finally, we discuss the analysis of experimental deposition data using the formalism outlined here and demonstrate that important kinetic information may be readily extracted.

Full view on the dynamics of an impurity coupled to two one-dimensional baths

We consider a model for the motion of an impurity interacting with two parallel, one-dimensional baths, described as two Tomonaga-Luttinger liquid systems. The impurity is able to move along the baths, and to jump from one to the other. We provide a perturbative expression for the evolution of the system when the impurity is injected in one of the baths, with a given wave packet. We obtain an approximation formally of infinite order in the impurity-bath coupling, which allows us to reproduce the orthogonality catastrophe. We monitor and discuss the dynamics of the impurity and its effect on the baths, in particular for a Gaussian wave packet. Besides the motion of the impurity, we also analyze the dynamics of the bath density and momentum density (i.e., the particle current), and show that it fits an intuitive semiclassical interpretation. We also quantify the correlation that is established between the baths by calculating the interbath, equal-time spatial correlation functions of both bath density and momentum, finding a complex pattern. We show that this pattern contains information on both the impurity motion and on the baths, and that these can be unveiled by taking appropriate ``slices'' of the time evolution.

Multiple-photon bundle emission in the n-photon Jaynes-Cummings model.

We study the multiple-photon bundle emission in the n-photon Jaynes-Cummings model composed of a two-level system coupled to a single-mode optical field via the n-photon exciting process. Here, the two-level system is strongly driven by a near-resonant monochromatic field, and hence the system can work in the Mollow regime, in which a super-Rabi oscillation between the zero-photon state and the n-photon state can take place under proper resonant conditions. We calculate the photon number populations and the standard equal-time high-order correlation functions, and find that the multiple-photon bundle emission can occur in this system. The multiple-photon bundle emission is also confirmed by investigating the quantum trajectories of the state populations and both the standard and generalized time-delay second-order correlation functions for multiple-photon bundle. Our work paves the way towards the study of multiple-photon quantum coherent devices, with potential application in quantum information sciences and technologies.

Prethermal Fragmentation in a Periodically Driven Fermionic Chain.

We study a fermionic chain with nearest-neighbor hopping and density-density interactions, where the nearest-neighbor interaction term is driven periodically. We show that such a driven chain exhibits prethermal strong Hilbert space fragmentation (HSF) in the high drive amplitude regime at specific drive frequencies ω_{m}^{*}. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of ω_{m}^{*} using a Floquet perturbation theory and provide exact numerical computation of entanglement entropy, equal-time correlation functions, and the density autocorrelation of fermions for finite chains. All of these quantities indicate clear signatures of strong HSF. We study the fate of the HSF as one tunes away from ω_{m}^{*} and discuss the extent of the prethermal regime as a function of the drive amplitude.

Ternary Unitary Quantum Lattice Models and Circuits in 2+1 Dimensions.

We extend the concept of dual unitary quantum gates introduced in Phys. Rev. Lett. 123, 210601 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.210601 to quantum lattice models in 2+1 dimensions, by introducing and studying ternary unitary four-particle gates, which are unitary in time and both spatial dimensions. When used as building blocks of lattice models with periodic boundary conditions in time and space (corresponding to infinite temperature states), dynamical correlation functions exhibit a light ray structure. We also generalize solvable matrix product states introduced in Phys. Rev. B 101, 094304 (2020)PRBMDO2469-995010.1103/PhysRevB.101.094304 to two spatial dimensions with cylindrical boundary conditions, by showing that the analogous solvable projected entangled pair states can be identified with matrix product unitaries. In the resulting tensor network for evaluating equal-time correlation functions, the bulk ternary unitary gates cancel out. We delineate and implement a numerical algorithm for computing such correlations by contracting the remaining tensors.

Steady state quantum statistics of a hybrid optomechanical-ferromagnet system: photon and magnon blockade

Magnon and photon blockade implementation and manipulation have significant practical applications in quantum information processing and quantum metrology due to their tight relations to single-photon and -magnon source devices. In this paper, we propose an experimentally feasible hybrid scheme for the dynamical description of the tripartite interacting system consisting of magnon and phonon modes with photons in an optomechanical system, from which we aim to explore the quantum statistics, as well as the magnon and photon blockade phenomenon. To achieve the purpose, the dissipative solution of the system is obtained with the help of the Lindblad master equation. Via employing the equal-time second-order correlation function and using the steady state solution of the system, the statistics and blockade effects of magnon and photon are analyzed and also their dependence on the parameters involved in the system are discussed. Utilizing feasible parameters, our simulations illustrate that, sub-Poissonian behavior and therefore, blockade of magnon and photon are simultaneously achieved. More importantly, the mentioned blockade effects can be obtained in a range of parameters (and not with specific) which makes our proposal easy to access, experimentally. Considering the above realizations, the introduced scheme opens up a pathway to design single-magnon and -photon generators, which are of crucial importance in advanced quantum science and technologies.

Nonlinear dissipation-induced photon blockade

We propose a theoretical scheme for photon blockade in a cavity quantum electrodynamic system consisting of an $N$-type atomic medium interacting with a single-mode Fabry-P\'erot cavity. In contrast to inefficient nonlinear-dispersion-induced photon blockade suppressed by a large detuning of atomic transitions, the photon blockade in our scheme is induced by a large nonlinear dissipation of the cavity created by the near-resonant $N$-type atomic system. A deep photon blockade is manifested by a vanishing equal-time second-order correlation function within the cavity linewidth. We also provide an explanation for this dissipation-induced photon blockade. This work provides an efficient photon blockade because it works in the near-resonance case.

Spatial spin-spin correlations of the single-impurity Anderson model with a ferromagnetic bath

We investigate the interplay between the Kondo effect and the ferromagnetism by an one dimension Anderson impurity model with a spin partially polarized bath, using the projective truncation approximation under Lacroix basis.The equal-time spatial spin-spin correlation function (SSCF) is calculated. For the case of spin-unpolarized conduction electrons, it agrees qualitatively with the results from density matrix renormalization group (DMRG). For system with partially spin-polarized conduction electrons, an oscillation in the envelope of SSCF emerges due to the beating of two Friedel oscillations associated to two spin-split Fermi surfaces of conduction electrons. The period is proportional to the inverse of magnetic field $h$. A fitting formula is proposed to perfectly fits the numerical results of SSCF in both the short- and long-range regions. For large enough bath spin polarization, a bump appears in the curve of the integrated SSCF. It marks the boundary between the suppressed Kondo cloud and the polarized bath sites.

Transverse-momentum-dependent wave functions and soft functions at one-loop in large momentum effective theory

In large-momentum effective theory (LaMET), the transverse-momentum-dependent (TMD) light-front wave functions and soft functions can be extracted from the simulation of a four-quark form factor and equal-time correlation functions. In this work, using expansion by regions we provide a one-loop proof of TMD factorization of the form factor. For the one-loop validation, we also present a detailed calculation of mathcal{O} (αs) perturbative corrections to these quantities, in which we adopt a modern technique for the calculation of TMD form factor based the integration by part and differential equation. The one-loop hard functions are then extracted. Using lattice data from Lattice Parton Collaboration on quasi-TMDWFs, we estimate the effects from the one-loop matching kernel and find that the perturbative corrections depend on the operator to define the form factor, but are less sensitive to the transverse separation. These results will be helpful to precisely extract the soft functions and TMD wave functions from the first-principle in future.

Topological Multipartite Entanglement in a Fermi Liquid

We show that the topology of the Fermi sea of a D-dimensional Fermi gas is reflected in the multipartite entanglement characterizing D+1 regions that meet at a point. For odd D we introduce the multipartite mutual information and show that it exhibits a logDL divergence as a function of system size L with a universal coefficient that is proportional to the Euler characteristic χF of the Fermi sea. This provides a generalization, for a Fermi gas, of the well-known result for D=1 that expresses the logL divergence of the bipartite entanglement entropy in terms of the central charge c characterizing a conformal field theory. For even D we introduce a charge-weighted entanglement entropy that is manifestly odd under a particle-hole transformation. We show that the corresponding charge-weighted mutual information exhibits a similar logDL divergence proportional to χF. Our analysis relates the universal behavior of the multipartite mutual information in the absence of interactions to the D+1 order equal-time density correlation function, which we show exhibits a universal behavior in the long wavelength limit proportional to χF. Our analytic results are based on the replica method. In addition, we perform a numerical study of the charge-weighted mutual information for D=2 that confirms several aspects of the analytic theory. Finally, we consider the effect of interactions perturbatively within the replica theory. We show that for D=3 the log3L divergence of the topological mutual information is not perturbed by weak short-ranged interactions, though for D=2 the charge-weighted mutual information is perturbed. Thus, for D=3 the multipartite mutual information provides a robust classification that distinguishes distinct topological Fermi liquid phases.12 MoreReceived 19 April 2022Accepted 12 July 2022DOI:https://doi.org/10.1103/PhysRevX.12.031022Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement entropyEntanglement in field theoryFermi surfaceTopological materialsCondensed Matter, Materials & Applied Physics

XY model for cascade transfer

We propose a modified XY model in which cascade transfer emerges from spatially local interactions where the spin corresponds to the “velocity” of a turbulent field. For this model, we theoretically calculate the scale-to-scale energy flux and the equal time correlation function in d dimensions. The result indicates an inverse energy cascade with the non-Kolmogorov energy spectrum proportional to k−3. We also numerically confirm the result for the cases of d=2 and d=3. We thus conclude that the cascade transfer in our model represents a different universality class from standard fluid turbulence.Received 25 June 2021Accepted 24 March 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L022015Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNonequilibrium statistical mechanicsTurbulencePhysical SystemsNonequilibrium lattice modelsTechniquesLangevin equationXY modelStatistical PhysicsFluid Dynamics

Computing light-front wave functions without light-front quantization: A large-momentum effective theory approach

Light-front wave functions play a fundamental role in the light-front quantization approach to QCD and hadron structure. However, a naive implementation of the light-front quantization suffers from various subtleties including the well-known zero-mode problem, the associated rapidity divergences which mixes ultraviolet divergences with infrared physics, as well as breaking of spatial rotational symmetry. We advocate that the light-front quantization should be viewed as an effective theory in which small ${k}^{+}$ modes have been effectively ``integrated out,'' with an infinite number of renormalization constants. Instead of solving light-front quantized field theories directly, we make the large momentum expansion of the equal-time Euclidean correlation functions in instant quantization as an effective way to systematically calculate light-front correlations, including the light-front wave function amplitudes. This large-momentum effective theory accomplishes an effective light-front quantization through lattice QCD calculations. We demonstrate our approach using an example of a pseudoscalar meson wave function.

Dissipation-induced nonreciprocal magnon blockade in a magnon-based hybrid system

We propose an experimentally realizable nonreciprocal magnonic device at the single-magnon level by exploiting magnon blockade in a magnon-based hybrid system. The coherent qubit-magnon coupling, mediated by virtual photons in a microwave cavity, leads to the energy-level anharmonicity of the composite modes. In contrast, the corresponding dissipative counterpart, induced by traveling microwaves in a waveguide, yields inhomogeneous broadenings of the energy levels. As a result, the cooperative effects of these two kinds of interactions give rise to the emergence of the direction-dependent magnon blockade. We show that this can be demonstrated by studying the equal-time second-order correlation function of the magnon mode. Our study opens an avenue to engineer nonreciprocal magnonic devices in the quantum regime involving only a small number of magnons.

Quantum correlations across the horizon in acoustic and gravitational black holes

We investigate, within the framework of quantum field theory in curved space, the correlations across the horizon of a black hole in order to highlight the particle-partner pair creation mechanism at the origin of Hawking radiation. The analysis concerns both acoustic black holes, formed by Bose-Einstein condensates, and gravitational black holes. More precisely, we have considered a typical acoustic black hole metric with two asymptotic homogeneous regions and the Schwarzschild metric as describing a gravitational black hole. By considering equal-time correlation functions, we find a striking disagreement between the two cases: the expected characteristic peak centered along the trajectories of the Hawking particles and their partners seems to appear only for the acoustic black hole and not for the gravitational Schwarzschild one. The reason for that is the existence of a quantum atmosphere displaced from the horizon as the locus of origin of Hawking radiation together, and this is the crucial aspect, with the presence of a central singularity in the gravitational case swallowing everything is trapped inside the horizon. Correlations, however, are not absent in the gravitational case; to see them, one simply has to consider correlation functions at unequal times, which indeed display the expected peak.

Retrieval of photon blockade effect in the dispersive Jaynes-Cummings model

We propose a reliable scheme to recover the conventional photon blockade effect in the dispersive Jaynes-Cummings model, which describes a two-level atom coupled to a single-mode cavity field in the large-detuning regime. This is achieved by introducing a transversal driving to the atom and then photonic nonlinearity is obtained. The eigenenergy spectrum of the system is derived analytically and the photon blockade effect is confirmed by numerically calculating the photon-number distributions and equal-time second-order correlation function of the cavity field in the presence of system dissipations. We find that the conventional photon blockade effect can be recovered at proper atomic and cavity-field drivings. This work will provide a method to generate the conventional photon blockade effect in the dispersively coupled quantum optical systems.

Giant nonreciprocal unconventional photon blockade with a single atom in an asymmetric cavity

Inspired by the advantage of unconventional photon blockade (UCPB), we propose a simple cavity-driven quantum electrodynamics model composed of a single two-level atom embedded in an asymmetrical Fabry-Perot cavity. We derive the necessary matching conditions of frequency and intensity required for unconventional photon blockade. In the asymmetric cavity, the optimal atom-cavity coupling strength to get UCPB is related to the driving direction, which causes the equal-time second-order correlation function ${g}^{(2)}(0)$ of the cavity field depending on the driving direction, too. Due to the direction dependent effect, the output photons can be bunched in one direction incident while they are antibunched in the opposite direction incident, which is the so-called nonreciprocal UCPB (NUCPB). A giant NUCPB can be obtained under the appropriate parameter regime, where the output photons are fully antibunching in the opposite driving case. Our findings show a prospective path to producing giant quantum nonreciprocity.