Massive Thirring Model Research Articles

On Bound States in Quantum Field Theory

In this paper, a new method to describe the energy spectrums of bound states in Quantum Field Theory is presented. We point out that the fundamental field and its dual soliton combine together to form bound states and the soliton corresponds to the ghost particle in our regularization scheme which takes advantage of dimensional regularization and Pauli-Villars regularization. Based on this point of view, we discuss the bound states of massive Thirring model, the positronium (e+e−) in QED and the vector meson in QCD. We also give a new way to obtain the mass of soliton (quantum soliton) from the stationary condition (gap equation). Our results agree with experimental data to high precision. We argue that the hypothetic X17 particle in decay of 8Be and 4He is a soliton. For vector meson, we find the squared masses of ρ resonances are \(m^{2}(n)\sim (an^{1/3}-b)^{2}\) (n ∈ N) which coincide well with experiments.

Approximate solutions of nonlinear fractional Kundu-Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method

In quantum field theory, the fractional Kundu-Eckhaus and massive Thirring models are nonlinear partial differential equations under fractional sense inside nonlinear Schrödinger class. In this study, approximate analytical solutions of such complex nonlinear fractional models are acquired by means of conformable residual power series method. This method presents a systematic procedure for constructing a set of periodic wave series solutions based on the generalization of conformable power series and gives the unknown coefficients in a simple pattern. By plotting the solutions behavior of the models; the convergence regions in which the solutions coincide to each other are checked for various fractional values. The approximate solutions generated by the proposed approach are compared with the exact solutions -if exist- and the approximate solutions obtained using qHATM and LADM. Numerical results show that the proposed method is easy to implement and very computationally attractive in solving several complex nonlinear fractional systems that occur in applied physics under a compatible fractional sense.

Lattice sine-Gordon model

We obtain nonperturbative results on the sine-Gordon model using the lattice field technique. In particular, we employ the Fourier accelerated hybrid Monte Carlo algorithm for our studies. We find the critical temperature of the theory based on autocorrelation time, as well as the finite size scaling of the "thickness" observable used in an earlier lattice study by Hasenbusch et al. We study the entropy, which is smooth across all temperatures, supportive of an infinite order transition. This system has a well-known duality with the massive Thirring model, which can play the role of a toy models for Montonen-Olive duality in N=4 super-Yang-Mills theory, since it relates solitons to elementary field excitations. Our research lays a groundwork for such study on the lattice.

Duality between Dirac fermions in curved spacetime and optical solitons in non-linear Schrodinger model: magic of 1+1-dimensional bosonization

Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized Sine–Gordon model, both living in 1+1-dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, in non-relativistic limit, gets identified with the soliton of non-linear Scrodinger model with Kerr form of non-linearity. We discuss one particular optical soliton in the latter model and relate it with the Thirring model fermion.

Phase structure of the (1+1)-dimensional massive Thirring model from matrix product states

Employing matrix product states as an ansatz, we study the non-thermal phase structure of the (1+1)-dimensional massive Thirring model in the sector of vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with non-zero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behaviour, and serve as an important ingredient for controlling the continuum extrapolation of the model.

Darboux transformation and soliton solutions of the semi-discrete massive Thirring model

A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and the dressing method. This transformation is used to find the exact expressions for soliton solutions on zero and nonzero backgrounds. It is shown that the discrete solitons have the same properties as their continuous counterparts.

Q-homotopy analysis transform method applied to fractional Kundu–Eckhaus equation and fractional massive Thirring model arising in quantum field theory

In this paper, [Formula: see text]-homotopy analysis transform method ([Formula: see text]-HATM) is used to solve fractional Kundu–Eckhaus equation and fractional massive Thirring model. This method is a mixture of Homotopy analysis method (HAM) and Laplace transform method (LTM) when [Formula: see text]. The approximate solutions obtained by [Formula: see text]-HATM are compared with the exact solutions. Numerical results are known through different graphs and tables. The results light the power, efficiency, simplicity, and reliability of the proposed method.

Initial boundary value problem for nonlinear Dirac equation of Gross-Neveu type in 1 + 1 dimensions

This paper studies an initial boundary value problem for a class of nonlinear Dirac equations with cubic terms, which include the equations for the massive Thirring model and the massive Gross-Neveu model. Under the assumptions that the initial data has bounded L2 norm and the boundary satisfies suitable conditions, the global existence and the uniqueness of the strong solution are proved.

The massive Thirring system in the quarter plane

AbstractThe unified transform method (UTM) or Fokas method for analyzing initial-boundary value (IBV) problems provides an important generalization of the inverse scattering transform (IST) method for analyzing initial value problems. In comparison with the IST, a major difficulty of the implementation of the UTM, in general, is the involvement of unknown boundary values. In this paper we analyze the IBV problem for the massive Thirring model in the quarter plane, assuming that the initial and boundary data belong to the Schwartz class. We show that for this integrable model, the UTM is as effective as the IST method: Riemann-Hilbert problems we formulated for such a problem have explicit (x, t)-dependence and depend only on the given initial and boundary values; they do not involve additional unknown boundary values.

Duality Between 3D Massive Thirring and Maxwell-Chern-Simons Models from 2D Bosonization.

Bosonization techniques are important nonperturbative tools in quantum field theory. In three dimensions they possess interesting connections to topologically ordered systems and ultimately have driven the observation of an impressive web of dualities. In this work, we use the quantum wires formalism to show how the fermion-boson mapping relating the low-energy regime of the massive Thirring model in three spacetime dimensions with the Maxwell-Chern-Simons model can be obtained from the exact bosonization in two dimensions.

Norm of Bethe-wave functions in the continuum limit

The 6-vertex model with appropriately chosen alternating inhomogeneities gives the so-called light-cone lattice regularization of the sine-Gordon (Massive-Thirring) model. In this integrable lattice model we consider pure hole states above the antiferromagnetic vacuum and express the norm of Bethe-wave functions in terms of the hole's positions and the counting-function of the state under consideration. In the light-cone regularized picture pure hole states correspond to pure soliton (fermion) states of the sine-Gordon (massive Thirring) model. Hence, we analyze the continuum limit of our new formula for the norm of the Bethe-wave functions. We show, that the physically most relevant determinant part of our formula can be expanded in the large volume limit and turns out to be proportional to the Gaudin-determinant of pure soliton states in the sine-Gordon model defined in finite volume.

Exact finite volume expectation values of overline{varPsi}varPsi in the massive Thirring model from light-cone lattice correlators

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator overline{varPsi}varPsi between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator overline{varPsi}varPsi is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

Tensor Network study of the (1+1)-dimensional Thirring Model

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the massive Thirring model. We also show the possibility of studying soliton dynamics and topological phase transition via the Thirring model.

Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.

Parallel tempering algorithm for integration over Lefschetz thimbles

The algorithm based on integration over Lefschetz thimbles is a promising method to resolve the sign problem for complex actions. However, this algorithm often meets a difficulty in actual Monte Carlo calculations because the configuration space is not easily explored due to the infinitely high potential barriers between different thimbles. In this paper, we propose to use the flow time of the antiholomorphic gradient flow as an auxiliary variable for the highly multimodal distribution. To illustrate this, we implement the parallel tempering method by taking the flow time as a tempering parameter. In this algorithm, we can take the maximum flow time to be sufficiently large such that the sign problem disappears there, and two separate modes are connected through configurations at small flow times. To exemplify that this algorithm does work, we investigate the (0+1)-dimensional massive Thirring model at finite density and show that our algorithm correctly reproduces the analytic results for large flow times such as T=2.

High-order rogue wave solutions of the classical massive Thirring model equations

The nth-order solutions of the classical massive Thirring model (MTM) equations are derived by using the n-fold Darboux transformation. These solutions are expressed by the ratios of the two determinants consisted of 2n eigenfunctions under the reduction conditions. Using this method, rogue waves are constructed explicitly up to the third-order. Three patterns, i.e., fundamental, triangular and circular patterns, of the rogue waves are discussed. The parameter μ in the MTM model plays the role of the mass in the relativistic field theory while in optics it is related to the medium periodic constant, which also results in a significant rotation and a remarkable lengthening of the first-order rogue wave. These results provide new opportunities to observe rouge waves by using a combination of electromagnetically induced transparency and the Bragg scattering four-wave mixing because of large amplitudes.

Fermion bag approach for the massive Thirring model at finite density

We consider the 2+1 dimensional massive Thirring model with one flavor at finite density. Two numerical methods, fermion bag approach and complex Langevin dynamics, are used to calculate the chiral condensate and fermion density of this model. The numerical results obtained by fermion bag approach are compared with those obtained by complex Langevin dynamics. They are also compared with those obtained under phase quenched approximation. We show that in some range of fermion coupling strength and chemical potential the sign problem in fermion bag approach is mild, while it becomes severe for the complex Langevin dynamics.

Erratum to: Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling $\beta$ and/or large lattice size $L$, while they are in good agreement at the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit keeping the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model's thimble structure. And these results imply that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.

Finite field-dependent symmetry in the Thirring model

In this paper, we consider a $D$-dimensional massive Thirring model with ($2<D<4$). We derive an extended BRST symmetry of the theory with finite field-dependent parameter. Further we compute the Jacobian of functional measure under such an extended transformation. Remarkably, we find that such Jacobian extends the BRST exact part of the action which leads to a mapping between different gauges. We illustrate this with the help of Lorentz and $R_\xi$ gauges. We also discuss the results in Batalin-Vilkovisky framework.

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling β and/or large lattice size L, while they are in good agreement in the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit to keep the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model and implies that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.