arXiv subjects

Nathan Salwen

Publications and source records attributed to Nathan Salwen.

15 recordsLinked to original sources

arXiv2009

N=(1,1) super Yang--Mills theory in 1+1 dimensions at finite temperature

We present a formulation of N=(1,1) super Yang-Mills theory in 1+1 dimensions at finite temperature. The partition function is constructed by finding a numerical approximation to the entire spectrum. We solve numerically for the spectrum using Supersymmetric Discrete Light-Cone Quantization (SDLCQ) in the large-N_c approximation and calculate the density of states. We find that the density of states grows exponentially and the theory has a Hagedorn temperature, which we extract. We find that the Hagedorn temperature at infinite resolution is slightly less than one in units of (g^(2) N_c/pi)^(1/2). We use the density of states to also calculate a standard set of thermodynamic functions below the Hagedorn temperature. In this temperature range, we find that the thermodynamics is dominated by the massless states of the theory.

hep-th↗

arXiv2007

Spectrum and thermodynamic properties of two-dimensional N=(1,1) super Yang-Mills theory with fundamental matter and a Chern-Simons term

We consider N=(1,1) super Yang-Mills theory in 1+1 dimensions with fundamentals at large-N_c. A Chern-Simons term is included to give mass to the adjoint partons. Using the spectrum of the theory, we calculate thermodynamic properties of the system as a function of the temperature and the Yang-Mills coupling. In the large-N_c limit there are two non-communicating sectors, the glueball sector, which we presented previously, and the meson-like sector that we present here. We find that the meson-like sector dominates the thermodynamics. Like the glueball sector, the meson sector has a Hagedorn temperature T_H, and we show that the Hagedorn temperature grows with the coupling. We calculate the temperature and coupling dependence of the free energy for temperatures below T_H. As expected, the free energy for weak coupling and low temperature grows quadratically with the temperature. Also the ratio of the free energies at strong coupling compared to weak coupling, r_{s-w}, for low temperatures grows quadratically with T. In addition, our data suggest that r_{s-w} tends to zero in the continuum limit at low temperatures.

hep-th↗

arXiv2004

Improved results for N=(2,2) super Yang-Mills theory using supersymmetric discrete light-cone quantization

We consider the (1+1)-dimensional ${\cal N}=(2,2)$ super Yang--Mills theory which is obtained by dimensionally reducing ${\cal N}=1$ super Yang--Mills theory in four dimension to two dimensions. We do our calculations in the large-$N_c$ approximation using Supersymmetric Discrete Light Cone Quantization. The objective is to calculate quantities that might be investigated by researchers using other numerical methods. We present a precision study of the low-mass spectrum and the stress-energy correlator $ $. We find that the mass gap of this theory closes as the numerical resolution goes to infinity and that the correlator in the intermediate $r$ region behaves like $r^{-4.75}$.

hep-th↗

arXiv2003

BCS and Attractive Hubbard Model Comparative Study

We extend previous studies of the BCS canonical approach for the attractive Hubbard model. A derivation of the BCS formulation is presented for both the Hubbard and a simpler reduced Hamiltonian. Using direct diagonalization, exact one and two dimensional solutions for both Hamiltonians are compared to BCS variational calculations. Approximate and exact ground state energies and energy gaps are computed for different electron number systems as well as correlation observables not previously predicted. Reproducing published one dimensional findings, the BCS is an excellent approximation for the Hubbard ground state energy but not energy gap, a finding that remains true in two dimensions. Propagators and correlators are found more sensitive to wavefunctions and appreciable differences are computed with the Hubbard model exhibiting a weaker degree of superconductivity than the BCS. However for the reduced Hamiltonian model the BCS is an excellent approximation for all observables in both one and two dimensions.

cond-mat.supr-con↗

arXiv2002

Non-perturbative Methods in Modal Field Theory

Several issues in the modal approach to quantum field theory are discussed. Within the formalism of spherical field theory, differential renormalization is presented and shown to result in a finite number of renormalization parameters. Computations of the massless Thirring model in 1+1 dimensions are presented using this approach. Diagonalization techniques in periodic field theory are demonstrated. Issues of very large Hilbert spaces are considered and several approaches are presented. The quasi sparse eigenvector (QSE) approach takes advantage of the relatively small number of basis states that typically contribute significantly to any particular eigenvector. Stochastic correction methods use Monte Carlo calculations to calculate higher order corrections to the quasi sparse result. The quasi sparse eigenvector method and stochastic error correction are applied to the Hubbard model. With U/t=4, the shift in the ground energy below the U=0 value is found to within 1% for the 8x8 Hubbard model with 25/64 filling.

hep-lat↗

arXiv2002

Lower energy bounds for quantum lattice Hamiltonians

We derive general lower energy bounds for the ground state energy of any translationally invariant quantum lattice Hamiltonian. The bounds are given by the ground state energy of renormalized Hamiltonians on finite clusters.

cond-mat↗

arXiv2000

The diagonalization of quantum field Hamiltonians

We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach which combines both diagonalization and Monte Carlo techniques.

hep-th↗

arXiv2000

Introduction to stochastic error correction methods

We propose a method for eliminating the truncation error associated with any subspace diagonalization calculation. The new method, called stochastic error correction, uses Monte Carlo sampling to compute the contribution of the remaining basis vectors not included in the initial diagonalization. The method is part of a new approach to computational quantum physics which combines both diagonalization and Monte Carlo techniques.

hep-lat↗

arXiv2000

EQSE Diagonalization of the Hubbard Model

The application of enhanced quasi-sparse eigenvector methods (EQSE) to the Hubbard model is attempted. The ground state energy for the 4x4 Hubbard model is calculated with a relatively small set of basis vectors. The results agree to high precision with the exact answer. For the 8x8 case, exact answers are not available but a simple first order correction to the quasi-sparse eigenvector (QSE) result is presented.

cond-mat↗

arXiv2000

Modal expansions and non-perturbative quantum field theory in Minkowski space

We introduce a spectral approach to non-perturbative field theory within the periodic field formalism. As an example we calculate the real and imaginary parts of the propagator in 1+1 dimensional phi^4 theory, identifying both one-particle and multi-particle contributions. We discuss the computational limits of existing diagonalization algorithms and suggest new quasi-sparse eigenvector methods to handle very large Fock spaces and higher dimensional field theories.

hep-th↗

arXiv1999

The massless Thirring model in spherical field theory

We use the massless Thirring model to demonstrate a new approach to non-perturbative fermion calculations based on the spherical field formalism. The methods we present are free from the problems of fermion doubling and difficulties associated with integrating out massless fermions. Using a non-perturbative regularization, we compute the two-point correlator and find agreement with the known analytic solution.

hep-th↗

arXiv1999

Renormalization in spherical field theory

We derive several results concerning non-perturbative renormalization in the spherical field formalism. Using a small set of local counterterms, we are able to remove all ultraviolet divergences in a manner such that the renormalized theory is finite and translationally invariant. As an explicit example we consider massless phi^4 theory in four dimensions.

hep-th↗

arXiv1998

Still Baking

We present here a simple proof of the non-existence of a non-periodic invariant point for the quantum baker's map propagator presented in Rubin and Salwen (Annals of Physics, 1998), for Planck's constant h=1/N and N a positive integer.

quant-ph↗

arXiv1998

A Canonical Quantization of the Baker's Map

We present here a canonical quantization for the baker's map. The method we use is quite different from that used in Balazs and Voros (ref. \QCITE{cite}{}{BV}) and Saraceno (ref. \QCITE{cite}{}{S}). We first construct a natural ``baker covering map'' on the plane $\QTO{mathbb}{\mathbb{R}}^{2}$. We then use as the quantum algebra of observables the subalgebra of operators on $L^{2}(\QTO{mathbb}{\mathbb{R}}) $ generated by $\left\{\exp (2πi\hat{x}) ,\exp (2πi\hat{p}) \right\} $ . We construct a unitary propagator such that as $\hbar \to 0$ the classical dynamics is returned. For Planck's constant $h=1/N$, we show that the dynamics can be reduced to the dynamics on an $N$-dimensional Hilbert space, and the unitary $N\times N$ matrix propagator is the same as given in ref. \QCITE{cite}{}{BV} except for a small correction of order $h$. This correction is shown to preserve the classical symmetry $x\to 1-x$ and $p\to 1-p$ in the quantum dynamics for periodic boundary conditions.

quant-ph↗

arXiv1998

A Parity-Conserving Canonical Quantization for the Baker's Map

We present here a complete description of the quantization of the baker's map. The method we use is quite different from that used in Balazs and Voros [BV] and Saraceno [S]. We use as the quantum algebra of observables the operators generated by {exp(2 Pi ix),exp (2 Pi ip)} and construct a unitary propagator such that as Planck's constant tends to zero,the classical dynamics is returned. For Planck's constant satisfying the integrality condition 1/N with N even, and for periodic boundary conditions for the wave functions on the torus, we show that the dynamics can be reduced to the dynamics on an N-dimensional Hilbert space, and the unitary N by N matrix propagator is the same as given in [BV] except for a small correction of order Planck's constant. This correction is is shown to preserve the symmetry x->1-x and p->1-p of the classical map for periodic boundary conditions.

quant-ph↗