Thirring Model Research Articles

Functional integrals and energy density fluctuations on black hole background

The propagator and effective action in quantum Thirring model are derived by using variational functional integrals method. The energy density fluctuations of weak and strong coupling Fermi matter are calculated in two-dimensional black hole model, scalar field fluctuations are calculated in the same physics background. The relative ratios of density fluctuations for Fermi and scalar matter are also estimated.

Fermion bag approach to lattice field theories

We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons, and there is no fermion permutation sign to worry about. We argue that as $U$ becomes finite, fermions are liberated but are naturally confined to regions which we refer to as fermion bags. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the ``silver blaze problem'' also emerges. Using the three-dimensional massless lattice Thirring model as an example, we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find $\ensuremath{\nu}=0.87(2)$ and $\ensuremath{\eta}=0.62(2)$.

Study of quasi-elastic Bragg soliton collisions in uniform fiber Bragg gratings by using the solution of the massive Thirring model

Bragg soliton is a solution of the nonlinear coupled mode equations (NLCMEs) that are a non-integrable system. Nevertheless, we show that for a broad region of soliton parameters the interaction between two Bragg solitons in a uniform fiber Bragg grating can be accurately described by using a trial function based on the known solution for two-soliton interaction in the massive Thirring model (MTM). In this region the similar behavior of Bragg solitons and solitons of the Thirring model enables one to calculate explicitly the approximate asymptotic properties of the interaction between two Bragg solitons such as the shifts in locations and phases of the solitons as a result of the interaction. We have validated that the similar behavior of Bragg solitons and solitons of the MTM is obtained for a broad range of parameters of the interacting solitons that can also be realized experimentally. Since the NLCMEs are not an integrable system, there is a parameter regime in which the interaction between Bragg solitons does not resemble the elastic interaction between MTM solitons. We describe an interaction between two co-propagating Bragg solitons that causes the inversion of the propagation direction of one of the solitons.

New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems

We propose a new type of reduction for integrable systems of coupled matrix partial differential equations; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative modified KdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semidiscretizations of the obtained systems and present new soliton solutions to both continuous and semidiscrete systems. As a by-product, a new integrable semidiscretization of the Manakov model (self-focusing vector nonlinear Schrödinger equation) is obtained.

Chiral Confinement in Quasirelativistic Bose-Einstein Condensates

In the presence of a laser-induced spin-orbit coupling an interacting ultracold spinor Bose-Einstein condensate may acquire a quasirelativistic character described by a nonlinear Dirac-like equation. We show that as a result of the spin-orbit coupling and the nonlinearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the interparticle interactions. We further show that multidimensional chiral confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case.

Physical vacuum of the Thirring and derivative coupling models

Simple two-dimensional models with massless and massive fermions are studied in the Hamiltonian framework. While the ultimate purpose of this study is a comparison between correlation functions constructed from known operator solutions in both space-like and light-front forms of the theory, the main goal at the present stage is to find physical vacuum states of the space-like models as the lowest energy eigenstates of H 0 + H int . This can be accomplished, using Klaiber's bosonization of the vector current, by means of a Bogoliubov transformation of the Hamiltonian which is quadratic in effective boson operators composed of fermion bilinears. The massless Thirring model is studied in this way and recent claims about its broken phase are critically examined. A brief discussion of the physical content of the models with derivative coupling is also included.

Calculation of energy density fluctuations for Fermi matter on black hole background

In this paper, the propagator and the effective potential in quantum Thirring model are derived by using the functional integral method, and the energy density fluctuations for coupled Fermi matter are calculated in two-dimensional point matter black hole and dilaton black hole models separately. We find that energy density fluctuation outside dilaton black hole is stronger under the same physical conditions.

Functional Integrals and Quantum Fluctuations on Two-Dimensional Noncommutative Space-Time

The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutative space-time, a modified propagator and free energy are derived by means of functional integrals method. Moreover, quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.

Anomalous discrete chiral symmetry in the Gross–Neveu model and loop gas simulations

We investigate the discrete chiral transformation of a Majorana fermion on a torus. Depending on the boundary conditions the integration measure can change sign. Taking this anomalous behavior into account we define a chiral order parameter as a ratio of partition functions with differing boundary conditions. Then the lattice realization of the Gross–Neveu model with Wilson fermions is simulated using the recent ‘worm’ technique on the loop gas or all-order hopping representation of the fermions. An algorithm is formulated that includes the Gross–Neveu interaction for N fermion species. The critical line m c ( g ) is constructed for a range of couplings at N = 6 and for N = 2 , the Thirring model, as examples.

Quantum Brownian motion on a triangular lattice and Fermi-Bose equivalence: an application of boundary state formulation

We discuss the Bose-Fermi equivalence in the quantum Brownian motion (QBM) on a triangular lattice, mapping the action for the QBM into a string theory action with a periodic boundary tachyon potential. We construct new Klein factors which are more appropriate than the conventional ones to deal with the quantum field theories defined on a two dimensioanl space-time with boundaries. Using the Fermi-Bose equivalence with the new Klein factors, we show that the model for the quantum Bownian motion on a triangular lattice is equivalent to the Thirring model with boundary terms, which are quadratic in fermion field operators, in the off-critical regions and to a SU(3) × SU(3) free fermion theory with quadratic boundary terms at the critical point.

Introduction to integrable many-body systems I

Introduction to integrable many-body systems IThis is the first volume of a three-volume introductory course about integrable (exactly solvable) systems of interacting bodies. The aim of the course is to derive and analyze, on an elementary mathematical and physical level, the Bethe ansatz solutions, ground-state properties and the thermodynamics of integrable many-body systems in many domains of physics: Nonrelativistic one-dimensional continuum Fermi and Bose gases; One-dimensional quantum models of condensed matter physics like the Heisenberg, Hubbard and Kondo models; Relativistic models of the (1+1)-dimensional Quantum Field Theory like the Luttinger model, the sine-Gordon model and its fermionic analog the Thirring model; Two-dimensional classical models, especially the symmetric Coulomb gas. In the first part of this volume, we deal with nonrelativistic one-dimensional continuum Fermi and Bose quantum gases of spinless (identical) particles with specific types of pairwise interactions like the short-range δ-function and hard-core interactions, and the long-range 1/

Massless Sine-Gordon and Massive Thirring Models: Proof of Coleman’s Equivalence

We prove the Coleman's conjecture on the equivalence between the massless Sine-Gordon model with finite volume interaction and the Thirring model with a finite volume mass term.

Dynamical Lorentz andCPTsymmetry breaking in a 4D four-fermion model

In a 4D chiral Thirring model we analyze the possibility that radiative corrections may produce spontaneous breaking of Lorentz and CPT symmetry. By studying the effective potential, we verified that the chiral current {psi}{gamma}{sup {mu}}{gamma}{sub 5}{psi} may assume a nonzero vacuum expectation value which triggers Lorentz and CPT violations. Furthermore, by making fluctuations on the minimum of the potential we dynamically induce a bumblebee-like model containing a Chern-Simons term.

DUAL BOSONIC THERMAL GREEN FUNCTION AND FERMION CORRELATORS OF THE MASSIVE THIRRING MODEL AT FINITE TEMPERATURE

The Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space is written as the real part of a complex analytic function of a variable that conformally maps the infinite strip -∞ < x < ∞ (0 < τ < β) of the z = x + iτ (τ: imaginary time) plane into the upper-half-plane. Using this fact and the Cauchy–Riemann conditions, we identify the dual thermal Green function as the imaginary part of that function. Using both the thermal Green function and its dual, we obtain an explicit series expression for the fermionic correlation functions of the massive Thirring model (MTM) at a finite temperature.

Applications of Thirring model to inhomogenous rolling tachyon and dissipative quantum mechanics

We study the rolling tachyon and the dissipative quantum mechanics using the Thirring model with a boundary mass. We construct a boundary state for the dissipative quantum system in one dimension, which describes the system at the off-critical points as well as at the critical point. Then we extend the Thirring model with a boundary mass in order to depict the time evolution of an unstable D-branes with one direction wrapped on a circle of radius R, which is termed the inhomogeneous rolling tachyon. The analysis based on the Thirring model shows that the time dependent evolution of the inhomogeneous tachyon is possible only when 2/(3)1/2 < R < 2.

Two-dimensional thermofield bosonization II: Massive fermions

We consider the perturbative computation of the N-point function of chiral densities of massive free fermions at finite temperature within the thermofield dynamics approach. The infinite series in the mass parameter for the N-point functions are computed in the fermionic formulation and compared with the corresponding perturbative series in the interaction parameter in the bosonized thermofield formulation. Thereby we establish in thermofield dynamics the formal equivalence of the massive free fermion theory with the sine-Gordon thermofield model for a particular value of the sine-Gordon parameter. We extend the thermofield bosonization to include the massive Thirring model.

Gap solitons in spatiotemporal photonic crystals

We generalize the concept of nonlinear periodic structures to systems that show arbitrary spacetime variations of the refractive index. Nonlinear pulse propagation through these spatiotemporal photonic crystals can be described, for shallow nonstationary gratings, by coupled mode equations which are a generalization of the traditional equations used for stationary photonic crystals. Novel gap soliton solutions are found by solving a modified massive Thirring model. They represent the missing link between the gap solitons in static photonic crystals and resonance solitons found in dynamic gratings.

Exact solution of SU(2)-invariant Thirring model with non-diagonal open boundaries

The SU(2)-invariant Thirring model with non-diagonal open boundaries in one spatial and one time dimensions is studied in the framework of quantum inverse scattering method. With the help of guage transformation independent of spectral parameter in the auxiliary space, suitable Fock vacuum state is constructed. The eigenvalues and its Bethe Ansatz equations of the transfer matrix are obtained by mean of Bethe Ansatz, and finally the boundary freedom degrees of the system are discussed.

One-loop beta functions for the orientable non-commutative Gross–Neveu model

We compute at the one-loop order the β-functions for a renormalisable non-commutative analog of the Gross–Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The β-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.

The S-matrix of the Faddeev-Reshetikhin model, diagonalizability andPTsymmetry

We study the question of diagonalizability of the Hamiltonian for the Faddeev-Reshetikhin (FR) model in the two particle sector. Although the two particle S-matrix element for the FR model, which may be relevant for the quantization of strings on $AdS_{5}\times S^{5}$, has been calculated recently using field theoretic methods, we find that the Hamiltonian for the system in this sector is not diagonalizable. We trace the difficulty to the fact that the interaction term in the Hamiltonian violating Lorentz invariance leads to discontinuity conditions (matching conditions) that cannot be satisfied. We determine the most general quartic interaction Hamiltonian that can be diagonalized. This includes the bosonic Thirring model as well as the bosonic chiral Gross-Neveu model which we find share the same S-matrix. We explain this by showing, through a Fierz transformation, that these two models are in fact equivalent. In addition, we find a general quartic interaction Hamiltonian, violating Lorentz invariance, that can be diagonalized with the same two particle S-matrix element as calculated by Klose and Zarembo for the FR model. This family of generalized interaction Hamiltonians is not Hermitian, but is $PT$ symmetric. We show that the wave functions for this system are also $PT$ symmetric. Thus, the theory is in a $PT$ unbroken phase which guarantees the reality of the energy spectrum as well as the unitarity of the S-matrix.