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We study 't Hooft lines in four-dimensional holomorphic-topological Chern-Simons theory. We relate them to Q-operators in the theory of integrable systems. We give a physical interpretation of the fundamental TQ and QQ relations satisfied by Q-operators and conventional transfer matrices. [ABSTRACT FROM AUTHOR]

The minimization of the action of a QFT with a constraint dictated by the block averaging procedure is an important part of Bałaban’s approach to renormalization. It is particularly interesting for QFTs with non-trivial target spaces, such as gauge theories or non-linear sigma models on a lattice. We analyze this step for the O(4) non-linear sigma model in two dimensions and demonstrate, in this case, how various ingredients of Bałaban’s approach play together. First, using variational calculus on Lie groups, the equation for the critical point is derived. Then, this non-linear equation is solved by the Banach contraction mapping theorem. This step requires detailed control of lattice Green functions and their integral kernels via random walk expansions. [ABSTRACT FROM AUTHOR]

We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical critical exponent. This model is different from the one introduced in [Hartmann et al., SciPost Phys.11 (2021) 031] due to a proper treatment of the square Laplace operator. Dirac fermion Lifshitz theory is local as opposed to its scalar counterpart which strongly affects its entanglement structure. We show that there is quantum entanglement across arbitrary subregions in various pure (including the vacuum) and mixed states of this theory for arbitrary integer values of the dynamical critical exponent. Our numerical investigations show that quantum entanglement in this theory is tightly bounded from above. Such a bound and other physical properties of quantum entanglement are carefully explained from the correlation structure in these theories. A generalization to (2+1)-dimensions where the entanglement structure is seriously different is addressed. [ABSTRACT FROM AUTHOR]

We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed. [ABSTRACT FROM AUTHOR]

A well-known difficulty of perturbative approaches to quantum field theory at finite temperature is the necessity to address theoretical constraints that are not present in the vacuum theory. In this work, we use lattice simulations of scalar correlation functions in massive ϕ4 theory to analyse the extent to which these constraints affect the perturbative predictions. We find that the standard perturbative predictions deteriorate even in the absence of infrared divergences at relatively low temperatures, and that this is directly connected to the analytic structure of the propagators used in the expansion. This suggests that the incorporation of non-perturbative thermal effects in the propagators is essential for a consistent perturbative formulation of scalar quantum field theories at finite temperature. By utilising the spectral constraints imposed on finite-temperature correlation functions, we explore how these effects manifest themselves in the lattice data, and discuss why the presence of distinct thermoparticle excitations provides a potential resolution to these issues. [ABSTRACT FROM AUTHOR]

We study the ℤ2 and U(1) Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ Lmax to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. We answer this question by bootstrapping the 2D U(1) lattice gauge theory. We show that with sufficiently large Lmax = 60, the two-sided bounds provide estimates for the plaquette averages with precision near 10−8 or even higher, suggesting the bootstrap constraints are sufficient to numerically pin down this theory. We compute the bootstrap bounds on the plaquette averages in the 3D ℤ2 and U(1) lattice gauge theories with Lmax = 16. In the regions with weak or strong coupling, the two-sided bootstrap bounds converge quickly and coincide with the perturbative results to high precision. The bootstrap bounds are well consistent with the Monte Carlo results in the nonperturbative region. We observe interesting connections between the bounds generated by the bootstrap computations and the Griffiths' inequalities. We present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories. [ABSTRACT FROM AUTHOR]

We consider conformal transitions arising from the merging of IR and UV fixed points, expected to occur in QCD with a large enough number of flavors. We study the smoothness of physical quantities across this transition, being mostly determined by the logarithmic breaking of conformal invariance. We investigate this explicitly using holography where approaching the conformal transition either from outside or inside the conformal window (perturbed by a mass term) is characterized by the same dynamics. The mass of spin-1 mesons and Fπ are shown to be continuous across the transition, as well as the dilaton mass. This implies that the lightness of the dilaton cannot be a consequence of the spontaneous breaking of scale invariance when leaving the conformal window. Our analysis suggests that the light scalar observed in QCD lattice simulations is a q q ¯ meson that becomes light since the q q ¯ -operator dimension reaches its minimal value. [ABSTRACT FROM AUTHOR]

Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories. [ABSTRACT FROM AUTHOR]

Brain–computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex. [ABSTRACT FROM AUTHOR]

Polymorphism in transition metal dichalcogenides (TMDs) allows unique physical properties to be controlled, such as artificial heavy fermion phenomena, the quantum spin Hall effect, and optimized device operations with 2D materials. Besides lattice structural and metal‐semiconductor polymorphs, intriguing charge density wave (CDW) states with different electronic and magnetic phases are demonstrated in TMDs. Typically, the "normal" state is stabilized at high temperature above the CDW energy scale, and therefore, is not relevant to many low‐temperature quantum phenomena, such as magnetic ordering and the heavy fermion Kondo state. Here, a local and robust phase manipulation of the normal (1T) and CDW (1T') states of VTe2 is reported by laser irradiation, and polymorphic Kondo effects are demonstrated with the two phases at low temperatures. The theoretical calculations show that Kondo screening of vanadium 3d electron moments is markedly enhanced in 1T'‐VTe2, which is responsible for the observed transport properties distinct from its 1T counterpart. Controlling the spin‐lattice coupling and Kondo physics via laser‐driven CDW phase patterning allows the design of correlated electronic and magnetic properties in TMDs. [ABSTRACT FROM AUTHOR]

Polymorphism in transition metal dichalcogenides (TMDs) allows unique physical properties to be controlled, such as artificial heavy fermion phenomena, the quantum spin Hall effect, and optimized device operations with 2D materials. Besides lattice structural and metal‐semiconductor polymorphs, intriguing charge density wave (CDW) states with different electronic and magnetic phases are demonstrated in TMDs. Typically, the "normal" state is stabilized at high temperature above the CDW energy scale, and therefore, is not relevant to many low‐temperature quantum phenomena, such as magnetic ordering and the heavy fermion Kondo state. Here, a local and robust phase manipulation of the normal (1T) and CDW (1T') states of VTe2 is reported by laser irradiation, and polymorphic Kondo effects are demonstrated with the two phases at low temperatures. The theoretical calculations show that Kondo screening of vanadium 3d electron moments is markedly enhanced in 1T'‐VTe2, which is responsible for the observed transport properties distinct from its 1T counterpart. Controlling the spin‐lattice coupling and Kondo physics via laser‐driven CDW phase patterning allows the design of correlated electronic and magnetic properties in TMDs. [ABSTRACT FROM AUTHOR]

The muon, a short-lived cousin of the electron, has provided a longstanding discrepancy between the standard model of particle physics and experimental measurements. This suggests that a not-yet-known particle or force perturbs the muon. The discovery of such "new physics" would have profound consequences on our understanding of Nature. In 2021, the attention of the world was drawn to this discrepancy when the announcement of the independent confirmation of the experiment by Fermilab [ 1 ] coincided with the publication of our ab-initio calculation (Nature [ 2 ]). Our result dramatically updated the theoretical prediction, bringing it significantly closer to the experimental value: it may be possible to explain the Fermilab measurement without any new physics, even with the latest Fermilab update [ 3 ]. Our result established a new standard of precision for such calculations that has yet to be challenged; with uncertainties comparable to the experimental measurement and the reference, data-driven computations. We are carrying out new simulations to reduce both the systematic and statistical uncertainties. Both improvements are required in order to match the precision of the final Fermilab measurement, to be obtained in the coming years. As such, these simulations will be critical to determine whether the muon's magnetic moment harbours new fundamental physics. [ABSTRACT FROM AUTHOR]

In this paper, we study a few versions of the uncertainty principle for the short‐time Fourier transform on the lattice Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. In particular, we establish the uncertainty principle for orthonormal sequences, Donoho–Stark's uncertainty principle, Benedicks‐type uncertainty principle, Heisenberg‐type uncertainty principle, and local uncertainty inequality for this transform on Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. Also, we obtain the Heisenberg‐type uncertainty inequality using the k$k$‐entropy of the short‐time Fourier transform on Zn×Tn$\mathbb {Z}^n \times \mathbb {T}^n$. [ABSTRACT FROM AUTHOR]

Motivated by the recently-established connection between Jarzynski's equality and the theoretical framework of Stochastic Normalizing Flows, we investigate a protocol relying on out-of-equilibrium lattice Monte Carlo simulations to mitigate the infamous computational problem of topological freezing. We test our proposal on 2d CPN−1 models and compare our results with those obtained adopting the Parallel Tempering on Boundary Conditions proposed by M. Hasenbusch, obtaining comparable performances. Our work thus sets the stage for future applications combining our Monte Carlo setup with machine learning techniques. [ABSTRACT FROM AUTHOR]

A new approach is presented to compute entropy for massless scalar quantum fields. By perturbing a skewed correlation matrix composed of field operator correlation functions, the mutual information is obtained for disjoint spherical regions of size r at separation R, including an expansion to all orders in r/R. This approach also permits a perturbative expansion for the thermal field entropy difference in the small temperature limit (T ≪ 1/r). [ABSTRACT FROM AUTHOR]

The reconstruction of the porous media model is crucial for researching the mesoscopic seepage characteristics of porous concrete. Based on a self-compiled MATLAB program, a porous concrete model was modeled by controlling four parameters (distribution probability, growth probability, probability density, and porosity) with clear physical meanings using a quartet structure generation set (QSGS) along with the lattice Boltzmann method (LBM) to investigate permeability. The rationality of the numerical model was verified through Poiseuille flow theory. The results showed that the QSGS model exhibited varied pore shapes and disordered distributions, resembling real porous concrete. Seepage velocity distribution showed higher values in larger pores, with flow rates reaching up to 0.012 lattice point velocity. The permeability–porosity relationship demonstrated high linearity (the Pearson correlation coefficient is 0.92), consistent with real porous concrete behavior. The integration of QSGS-LBM represents a novel approach, and the research results can provide new ideas and new means for subsequent research on the permeability of porous concrete or similar porous medium materials. [ABSTRACT FROM AUTHOR]

We derive the primitive quantum gate sets to simulate lattice quantum chromodynamics (LQCD) in the strong-coupling limit with one flavor of massless staggered quarks. This theory is of interest for studies at non-zero density as the sign problem can be overcome using Monte Carlo methods. In this work, we use it as a testing ground for quantum simulations. The key point is that no truncation of the bosonic Hilbert space is necessary as the theory is formulated in terms of color-singlet degrees of freedom ("baryons" and "mesons"). The baryons become static in the limit of continuous time and decouple, whereas the dynamics of the mesonic theory involves two qubits per lattice site. Lending dynamics also to the "baryons" simply requires to use the derived gate set in its controlled version. [ABSTRACT FROM AUTHOR]

Topological entanglement entropy (TEE), the sub-leading term in the entanglement entropy of topological order, is the direct evidence of the long-range entanglement. While effective in characterizing topological orders on closed manifolds, TEE is model-dependent when entanglement cuts intersect with physical gapped boundaries. In this paper, we study the origin of this model-dependence by introducing a model-independent picture of partitioning the topological orders with gapped boundaries. In our picture, the entanglement boundaries (EBs), i.e. the virtual boundaries of each subsystem induced by the entanglement cuts, are assumed to be gapped boundaries with boundary defects. At this model-independent stage, there are two choices one has to make manually in defining the bi-partition: the boundary condition on the EBs, and the coherence between certain boundary states. We show that TEE appears because of a constraint on the defect configurations on the EBs, which is choice-dependent in the cases where the EBs touch gapped boundaries. This choice-dependence is known as the ambiguity in entanglement entropy. Different models intrinsically employ different choices, rendering TEE model-dependent. For D(ℤ2) topological order, the ambiguity can be fully characterized by two parameters that respectively quantifies the EB condition and the coherence. In particular, calculations compatible with the folding trick naturally choose EB conditions that respect electric-magnetic duality and set specific parameter values. [ABSTRACT FROM AUTHOR]

We explain the microscopic origin of linear confinement potential with the Casimir scaling in generic confining gauge theories. In the low-temperature regime of confining gauge theories such as QCD, Polyakov lines are slowly varying Haar random modulo exponentially small corrections with respect to the inverse temperature, as shown by one of the authors (M. H.) and Watanabe. With exact Haar randomness, computation of the two-point correlator of Polyakov loops reduces to the problem of random walk on group manifold. Linear confinement potential with approximate Casimir scaling except at short distances follows naturally from slowly varying Haar randomness. With exponentially small corrections to Haar randomness, string breaking and loss of Casimir scaling at long distance follow. Hence we obtain the Casimir scaling which is only approximate and holds only at intermediate distance, which is precisely needed to explain the results of lattice simulations. For (1 + 1)-dimensional theories, there is a simplification that admits the Casimir scaling at short distances as well. [ABSTRACT FROM AUTHOR]

We investigate the entanglement and Rényi entropies for the (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method. The central charge is determined from the asymptotic scaling properties of both entropies. We also examine the consistency between the entanglement entropy and the nth-order Rényi entropy with n → 1. [ABSTRACT FROM AUTHOR]

One of the ultimate missions of lattice quantum chromodynamics (QCD) is to simulate atomic nuclei from the first principles of the strong interaction. This is an extremely hard task for current computational technology, but might be reachable in the coming quantum computing era. In this paper, we discuss the computational complexities of classical and quantum simulations of lattice QCD. It is shown that the quantum simulation scales better as a function of nucleon number and thus will outperform classical simulation for large nuclei. [ABSTRACT FROM AUTHOR]

In the present work, we employ a nonlocal Nambu–Jona–Lasinio (NJL) model with a Gaussian form factor that is dependent on the spatial components of the momentum (3D‐FF). Focusing on the temperature‐baryon chemical potential plane, we investigate some aspects of the phase diagram. Initially, we propose an assumption that the range of interactions in momentum space may be modified by temperature, allowing us to obtain the critical temperature values based on lattice QCD (LQCD) predictions. Subsequently, we consider this model within a hybrid framework to examine the effects of temperature, together with neutrino trapping, in compact object configurations. [ABSTRACT FROM AUTHOR]

Formal concept analysis is an effective tool for data analysis and visualization by means of concept lattice. Many concept lattice models have been studied in various settings. Variable threshold concept lattice is a fuzzy concept lattice constructed from fuzzy data. However, variable threshold concept lattice is not robust to noise because it employs a single threshold, instead of an interval to derive formal concepts. Thus, the paper introduces the tolerance threshold to variable threshold concept lattice, and forms the ROBust variable threshold fuzzy Concept Lattice (RobCL). By analyzing the properties of RobCL, we show that RobCL has some incremental characteristics and is able to model the incremental cognitive process, which makes RobCL distinctive from other concept lattice models. A comparative study shows that variable threshold concept lattice is just a special case of RobCL; in other words, when two thresholds coincide with each other, RobCL degenerates to variable threshold concept lattice and the incremental characteristics vanish. In addition, the proposed model is also applied to medical diagnosis and shows its superiority over the previous model. [ABSTRACT FROM AUTHOR]

We explore the relationship between lattice field theory and graph theory, placing special emphasis on the interplay between Dirac and scalar lattice operators and matrices within the realm of spectral graph theory. Beyond delving into fundamental concepts of spectral graph theory, such as adjacency and Laplacian matrices, we introduce a novel matrix called an "antisymmetrized adjacency matrix", specifically tailored for cycle digraphs (T 1 lattice) and simple directed paths (B 1 lattice). The nontrivial relationship between graph theory matrices and lattice operators shows that the graph Laplacian matrix mirrors the lattice scalar operator and the Wilson term in lattice fermions, while the antisymmetrized adjacency matrix, along with its extensions to higher dimensions, is equivalent to naive lattice Dirac operators. Building upon these connections, we provide rigorous proofs for two key assertions: (i) The count of zero-modes in a free lattice scalar operator coincides with the zeroth Betti number of the underlying graph (lattice). (ii) The maximum count of Dirac zero-modes in a free lattice fermion operator is equivalent to the cumulative sum of all Betti numbers when the D -dimensional graph results from a Cartesian product of cycle digraphs (T 1 lattice) and simple directed paths (B 1 lattice). [ABSTRACT FROM AUTHOR]

This paper presents a study on the dielectric characteristics of the Bi-MXene lattice using Monte Carlo simulations through the Metropolis algorithm. The study utilizes the Blume–Capel Ising model to analyze the dielectric characteristics under the effects of temperature, ferrielectric parameter, and external electric longitudinal and crystalline fields. Also, it examines the impact of the ferrielectric parameter J A B , the external electric field ( E Z) , and the crystalline field on the behavior of the blocking temperature ( T B). The results suggest a significant influence of the physical parameters on the blocking temperature analyzed in this study. Additionally, these findings hold implications on ferrielectric materials. [ABSTRACT FROM AUTHOR]

This paper first establishes the lattice model for nonlocal stochastic genetic regulatory networks with reaction diffusions by employing a mix of the finite difference and Mittag–Leffler time Euler difference techniques. Second, the existence of a unique bounded almost automorphic sequence in distribution and global mean-square exponential convergence to the achieved difference model are investigated. An illustrative example is used to show the feasible of the works of the current paper. [ABSTRACT FROM AUTHOR]

Algebraic hyperstructures are the classical generalizations of algebraic structures which has several applications in uncertainity theory [6], rough set theory [7], lattice based probability theories, analysis etc. Davvaz et.al.[5] extensively studied the chemical and biological applications of hyperstructures by exploring several inheritance examples of algebraic hyperstructures. This paper focusses on the occurences of twin zeros and triple zeros in Hyperlattices with respect to hyperideals. A lattice is a partially ordered set in which every pair of elements has a least upper bound (supremum or join) and a greatest lower bound (infimum or meet). Multilattice is a generalization of a lattice introduced by Benado [3]. They extended the concept of supremum and infimum to"multi" versions, allowing for the consideration of suprema and infima over multiple elements instead of just pairs. This provides a more flexible framework for dealing with larger collections of elements. A lattice can also be viewed as an algebraic structure with two binary operations: join (supremum) and meet (infimum). These operations are used to define the least upper bound and greatest lower bound of elements in the lattice, respectively. Konstantinidou [12], further generalized lattices by replacing the binary operations of join and meet with hyperoperations. However, with these generalizations some properties are not retained. Later, Konstantinidou [11] discussed the concept of distributivity of hyperlattices, particularly of P-hyperlattices. Rasouli and Davvaz [17] considered special relations on hyperlattices, called regular relations and showed that the quotient structure with respect to regular relations form a lattice. Rasouli and Davvaz [16] defined a topology on the spectrum of join hyperlattices and showed that it forms a T0-space. Ameri [2] and others have explored the distributivity and dual distributivity of elements in a hyperlattice. [ABSTRACT FROM AUTHOR]

We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral subspaces, and it is known as the fermion doubling. In oder to overcome this difficulty, two methods were proposed. The first one is to introduce a new term, called the Wilson term, and the second one is the KS-fermion model or the staggered fermion model. We discuss mathematical formulations of these, and study their continuum limits. [ABSTRACT FROM AUTHOR]

We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by (×Z3)3 ≡ Z3 × Z3 × Z3 symmetry and smaller Z3 symmetry. We derive microscopic models for the gapless edge, uncover their symmetries and analyze the conformal properties. We study the properties of the gapless edge by employing the numerical density-matrix renormalization group (DMRG) simulation and exact diagonalization. We discuss the corresponding conformal field theory, its central charge, and the scaling dimension of the corresponding primary field. We argue, that the low energy limit of our edge modes defined by the SUk(3)/SUk(2) coset conformal field theory with the level k = 2. The discussed two-dimensional models realize a variety of symmetry-protected topological phases, opening a window for studies of the unconventional quantum criticalities between them. [ABSTRACT FROM AUTHOR]

We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems. [ABSTRACT FROM AUTHOR]

A construction of a gravity dual to a physical gauge theory requires confronting data. We establish a proof-of-concept for precision holography, i.e., the explicit reconstruction of the dual background metric functions directly from the entanglement entropy (EE) of strip subregions that we extract from pure glue Yang-Mills theory discretized on a lattice. Our main focus is on a three-dimensional Euclidean SU2 theory in the deconfining phase. Holographic EE suggests, and we find evidence for, that the scaling of the thermal entropy with temperature is to power 7/3 and that it approaches smoothly the critical point, consistent with black hole thermodynamics. In addition, we provide frugal results on the potential between quenched quarks by the computation of the Polyakov loop correlators on the lattice. Holographic arguments pique curiosity in the substratum of Debye screening at strong coupling. [ABSTRACT FROM AUTHOR]

Monte Carlo study of the Schwinger model (quantum electrodynamics in one spatial dimension) with a topological θ term is very difficult due to the sign problem in the conventional lattice formulation. In this paper, we point out that this problem can be circumvented by utilizing the lattice formulation of the bosonized Schwinger model, initially invented by Bender et al. in 1985. After conducting a detailed review of their lattice formulation, we explicitly validate its correctness through detailed comparisons with analytical and previous numerical results at θ = 0. We also obtain the θ dependence of the chiral condensate and successfully reproduce the mass perturbation result for small fermion masses m/g ≲ 0.125. As an application, we perform a precise calculation of the string tension and quantitatively reveal the confining properties in the Schwigner model at finite temperature and θ region for the first time. In particular, we find that the string tension is negative for noninteger probe charges around θ = π at low temperatures. [ABSTRACT FROM AUTHOR]

Given a lattice L, we denote by Res(L) the lattice of all residuated maps on L. The main objective of the paper is to study the atoms of Res(L) where L is a complete lattice. Note that the description of dual atoms of Res(L) easily follows from earlier results of Shmuely (1974). We first consider lattices L for which all atoms of Res(L) are mappings with 2-element range and give a sufficient condition for this. Extending this result, we characterize these atoms of Res(L) which are weakly regular residuated maps in the sense of Blyth and Janowitz (Residuation Theory, 1972). In the rest of the paper we investigate the atoms of Res(M) where M is the lattice of a finite projective plane, in particular, we describe the atoms of Res(F), where F is the lattice of the Fano plane. [ABSTRACT FROM AUTHOR]

We establish in this paper the logarithmic Bramson correction for Fisher-KPP equations on the lattice \mathbb {Z}. The level sets of solutions with step-like initial conditions are located at position c_*t-\frac {3}{2\lambda _*}\ln t+O(1) as t\rightarrow +\infty for some explicit positive constants c_* and \lambda _*. This extends a well-known result of Bramson in the continuous setting to the discrete case using only PDE arguments. A by-product of our analysis also gives that the solutions approach the family of logarithmically shifted traveling front solutions with minimal wave speed c_* uniformly on the positive integers, and that the solutions converge along their level sets to the minimal traveling front for large times. [ABSTRACT FROM AUTHOR]

The article explores the concept of qubit lattice algorithms (QLA) and their potential applications in physics. QLA is a computational method that utilizes quantum computers to solve physics problems more efficiently than traditional computational codes. It has been successfully applied to solve the Schrodinger equation, model electromagnetic wave propagation in plasmas, and study nonlinear equations. The article also discusses the application of QLA in different types of media, such as dispersive and dissipative media. The authors propose using QLAs to simulate the behavior of plasma systems by directly simulating the nonlinear two-fluid plasma equations. The authors have expertise in plasma physics and quantum computing. [Extracted from the article]

Off-central heavy-ion collisions are known to feature magnetic fields with magnitudes and characteristic gradients corresponding to the scale of the strong interactions. In this work, we employ equilibrium lattice simulations of the underlying theory, QCD, involving similar inhomogeneous magnetic field profiles to achieve a better understanding of this system. We simulate three flavors of dynamical staggered quarks with physical masses at a range of magnetic fields and temperatures, and extrapolate the results to the continuum limit. Analyzing the impact of the field on the quark condensate and the Polyakov loop, we find non-trivial spatial features that render the QCD medium qualitatively different as in the homogeneous setup, especially at temperatures around the transition. In addition, we construct leading-order chiral perturbation theory for the inhomogeneous background and compare its prediction to our lattice results at low temperature. Our findings will be useful to benchmark effective theories and low-energy models of QCD for a better description of peripheral heavy-ion collisions. [ABSTRACT FROM AUTHOR]

The dynamics of zero modes in gauge theory is highly nontrivial due to its nonperturbative nature even in the case where the other modes can be treated perturbatively. One of the related issues concerns the possible instability of the trivial vacuum Aμ(x) = 0 due to the existence of nontrivial degenerate vacua known as "torons". Here we investigate this issue for the 4D SU(2) and SU(3) pure Yang-Mills theories on the lattice by explicit Monte Carlo calculation of the Wilson loops and the Polyakov line at large β. While we confirm the leading 1/β predictions obtained around the trivial vacuum in both SU(2) and SU(3) cases, we find that the subleading term vanishes only logarithmically in the SU(2) case unlike the power-law decay in the SU(3) case. In fact, the 4D SU(2) case is marginal according to the criterion by Coste et al. Here we show that the trivial vacuum dominates in this case due to large fluctuations of the zero modes around it, thereby providing a clear understanding of the observed behaviors. [ABSTRACT FROM AUTHOR]

Because of the mass gap, lattice QCD simulations exhibit stochastic locality: distant regions of the lattice fluctuate independently. There is a long history of exploiting this to increase statistics by obtaining multiple spatially-separated samples from each gauge field; in the extreme case, we arrive at the master-field approach in which a single gauge field is used. Here we develop techniques for studying hadronic observables using position-space correlators, which are more localized, and compare with the standard time-momentum representation. We also adapt methods for estimating the variance of an observable from autocorrelated Monte Carlo samples to the case of correlated spatially-separated samples. [ABSTRACT FROM AUTHOR]

This work investigates the gapped interfaces of 3+1d fracton phases of matter using foliated gauge theories and lattice models. We analyze the gapped boundaries and gapped interfaces in X cube model, and the gapped interfaces between the X-cube model and the toric code. The gapped interfaces are either "undecorated" or "decorated", where the "decorated" interfaces have additional Chern-Simons like actions for foliated gauge fields. We discover many new gapped boundaries and interfaces, such as (1) a gapped boundary for X-cube model where the electric lineons orthogonal to the interface become the magnetic lineons, the latter are the composite of magnetic planons; (2) a Kramers-Wannier-duality type gapped interface between the X-cube model and the toric code model from gauging planar subsystem one-form symmetry; and (3) an electromagnetic duality interface in the X-cube model that exchanges the electric and magnetic lineons. [ABSTRACT FROM AUTHOR]

Bootstrap is an idea that imposing consistency conditions on a physical system may lead to rigorous and nontrivial statements about its physical observables. In this work, we discuss the bootstrap problem for the invariant measure of the stochastic Ising model defined as a Markov chain where probability bounds and invariance equations are imposed. It is described by a linear programming (LP) hierarchy whose asymptotic convergence is shown by explicitly constructing the invariant measure from the convergent sequence of moments. We also discuss the relation between the LP hierarchy for the invariant measure and a recently introduced semidefinite programming (SDP) hierarchy for the Gibbs measure of the statistical Ising model based on reflection positivity and spin-flip equations. [ABSTRACT FROM AUTHOR]

Recently, considerable attention has been given to (2+1)-dimensional Kadomtsev-Petviashvili equations due to their extensive applications in solitons that widely exist in nonlinear science. Therefore, developing a reliable numerical algorithm for the Kadomtsev-Petviashvili equations is crucial. The lattice Boltzmann method, which has been an efficient simulation method in the last three decades, is a promising technique for solving Kadomtsev-Petviashvili equations. However, the traditional higher-order moment lattice Boltzmann model for the Kadomtsev-Petviashvili equations suffers from low accuracy because of error accumulation. To overcome this shortcoming, a splitting lattice Boltzmann scheme for (2+1)-dimensional Kadomtsev-Petviashvili-I type equations is proposed in this paper. The variable substitution method is applied to transform the Kadomtsev-Petviashvili-I type equation into two macroscopic equations. Two sets of distribution functions are employed to construct these two macroscopic equations. Moreover, three types of soliton solutions are numerically simulated by this algorithm. The numerical results imply that the splitting lattice Boltzmann schemes have an advantage over the traditional high-order moment lattice Boltzmann model in simulating the Kadomtsev-Petviashvili-I type equations. [ABSTRACT FROM AUTHOR]

The kagome-lattice materials promise emergence of Dirac fermions thanks to the special lattice geometry, which potentially realizes intriguing quantum topological states through various many-body interactions. The low-energy electromagnetic phenomena arising from such the Dirac fermions are expected to show the remarkable enhancement and, in certain conditions, to approach the universal responses, which, however, have remained elusive experimentally. Here, we show the resonantly enhanced magneto-optical response of massive Dirac fermions in kagome-lattice magnet TbMn6Sn6. The infrared magneto-optical spectroscopy reveals that the interband transition on massive Dirac bands significantly contributes to the observed resonance in the optical Hall conductivity. The analytical model expressed by a few band parameters reproduces the spectral characteristics of the resonance, which robustly produces almost 20 % of the quantized Hall conductance per one kagome layer even at room temperature. Our findings establish the general optical response of massive Dirac fermions, which is closely related to the universal electrodynamics in quantum anomalous Hall state. [ABSTRACT FROM AUTHOR]

We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation category Rep(H) of a semisimple weak Hopf algebra H, the fermionized TQFT has a superfusion category symmetry SRep(H u), which is the supercategory of super representations of a weak Hopf superalgebra H u. The weak Hopf superalgebra H u depends not only on H but also on a choice of a non-anomalous ℤ2 subgroup of Rep(H) that is used for the fermionization. We derive a general formula for H u by explicitly constructing fermionic TQFTs with SRep(H u) symmetry. We also construct lattice Hamiltonians of fermionic gapped phases when the symmetry is non-anomalous. As concrete examples, we compute the fermionization of finite group symmetries, the symmetries of finite gauge theories, and duality symmetries. We find that the fermionization of duality symmetries depends crucially on F-symbols of the original fusion categories. The computation of the above concrete examples suggests that our fermionization formula of fusion category symmetries can also be applied to non-topological QFTs. [ABSTRACT FROM AUTHOR]

The critical endpoint of the (3+1)-dimensional ℤ3 gauge-Higgs model at finite density is determined by the tensor renormalization group method. This work is an extension of the previous one on the ℤ2 model. The vital difference between them is that the ℤ3 model suffers from the sign problem, while the ℤ2 model does not. We show that the tensor renormalization group method allows us to locate the critical endpoint for the ℤ3 gauge-Higgs model at finite density, regardless of the sign problem. [ABSTRACT FROM AUTHOR]

The entanglement entropy of a free scalar field in its ground state is dominated by an area law term. It is noteworthy, however, that the study of entanglement in scalar field theory has not advanced far beyond the ground state. In this paper, we extend the study of entanglement of harmonic systems, which include free scalar field theory as a continuum limit, to the case of the most general Gaussian states, namely the squeezed states. We find the eigenstates and the spectrum of the reduced density matrix and we calculate the entanglement entropy. We show that our method is equivalent to the correlation matrix method. Finally, we apply our method to free scalar field theory in 1+1 dimensions and show that, for very squeezed states, the entanglement entropy is dominated by a volume term, unlike the ground-state case. Even though the state of the system is time-dependent in a non-trivial manner, this volume term is time-independent. We expect this behaviour to hold in higher dimensions as well, as it emerges in a large-squeezing expansion of the entanglement entropy for a general harmonic system. [ABSTRACT FROM AUTHOR]

A correlation between the spin-polarized carrier transfer and spin relaxation processes of a two-dimensional electron gas (2DEG) in an InGaN/GaN quantum well (QW) is investigated by time-resolved Kerr rotation spectroscopy at low temperature. Upon resonant excitation with the GaN barrier band edge energy, the spin polarization of the 2DEG in the QW is acquired from the transfer of spin-polarized photoexcited carriers. Significantly, the spin relaxation time of the 2DEG is enhanced to be as long as 1 ns along with the carrier transfer. It is demonstrated that by tailoring the Rashba and Dresselhaus spin–orbit couplings to approach a spin-degenerate surface, the screening effect of the polarization field leads to a longer spin relaxation time and effective manipulation of the spin relaxation. The polarization field screening induced enhancement of the spin relaxation time is significant in the way for the development of GaN-based spintronic devices. [ABSTRACT FROM AUTHOR]

[Display omitted] We perform a lattice QCD calculation of the η c → 2 γ decay width using a model-independent method that requires no momentum extrapolation of the off-shell form factors. This method also provides a straightforward and simple way to examine the finite-volume effects. The calculation is accomplished using N f = 2 twisted mass fermion ensembles. The statistically significant excited-state effects are observed and eliminated using a multi-state fit. The impact of fine-tuning the charm quark mass is also examined and confirmed to be well-controlled. Finally, using three lattice spacings for the continuum extrapolation, we obtain the decay width Γ η c γ γ = 6.67 (16) stat (6) syst keV, which differs significantly from the Particle Data Group's reported value of Γ η c γ γ = 5.4 (4) keV (2.9 σ tension). We provide insight into the comparison between our findings, previous theoretical predictions, and experimental measurements. [ABSTRACT FROM AUTHOR]

In this paper, we investigate phase-field interface capturing equations for two-fluid systems to probe their accuracy and computational cost. Two different schemes are considered: In the first scheme, one of the two order parameters is numerically solved based on a phase-field equation, while the other order parameter is determined through the summation relation; the summation of order parameters equals unity. In the second scheme, the two order parameters are both obtained numerically by solving their respective phase-field equations. A phase-field model based on the color-gradient (CG) method is chosen, and available lattice Boltzmann models are employed for solving the interface-capturing equations together with the hydrodynamic equation. It is shown that for the first scheme, which includes the summation relation, numerical results become asymmetrical. Also, in some cases, it results in nonphysical interfaces. In terms of computational resources, this first scheme is about 11% faster with 25% less computational memory usage than the second scheme. It is shown that only for a zero velocity domain do the two schemes lead to equal results. Also, a theoretical analysis is conducted to highlight the differences between the two approaches. [ABSTRACT FROM AUTHOR]