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Multiparameter Integrable QFTs with N bosons

Hubert Saleur, Simonetti, P

Published Apr 13, 1998• 6 citations
OpenAlex

Abstract

We introduce a new family of integrable theories with $N$ bosons and $N$ freely adjustable mass parameters. These theories restrict in particular limits to the ``generalized supersymmetric'' sine-Gordon models, as well as to the flavor anisotropic chiral Gross Neveu models (studied recently by N. Andrei and collaborators). The scattering theory involves scalar particles that are no bound states, and bears an intriguing resemblance wih the results of a sharp cut-off analysis of the Thirring model carried out by Korepin in (1980). Various physical applications are discussed. In particular, we demonstrate that our theories are the appropriate continuum limit of integrable quantum spin chains with mixtures of spins.

Related papers

Non relativistic limit of integrable QFT with fermionic excitations

Alvise Bastianello, Andrea De Luca, Giuseppe Mussardo

Abstract The aim of this paper is to investigate the non-relativistic limit of integrable quantum field theories with fermionic fields, such as the O ( N ) Gross–Neveu model, the supersymmetric Sinh–Gordon and non-linear sigma models. The non-relativistic limit of these theories is implemented by a double scaling limit which consists of sending the speed of light c to infinity and rescaling at the same time the relevant coupling constant of the model in such a way to have finite energy excitations. For the general purpose of mapping the space of continuous non-relativistic integrable models, this paper completes and integrates the analysis done in Bastianello A et al (2016 J. Stat. Mech . 123104) on the non-relativistic limit of purely bosonic theories.

arXiv:1701.06542•Journal of Physics A Mathematical and Theoretical•May 12, 2017•11 citations

Continuum limit of spin-1 chain

Takeo Inami, Satoru Odake

We study the continuum limit of the spin-1 chain in the non-Abelian bosonization approach of Affleck and show that the Hamiltonian of the integrable spin-1 chain yields the Lagrangian of the supersymmetric sine-Gordon model in the zero lattice spacing limit. We also show that the quantum group generators of the spin-1 chain give nonlocal charges of the supersymmetric sine-Gordon theory.

Physical Review Letters•Mar 29, 1993•7 citations

Continuum Limit of Spin-1 Chain (the only change is added references)

Takeo Inami, Satoru Odake

We study the continuum limit of the spin-1 chain in the non-Abelian bosonization approach of Affleck and show that the Hamiltonian of integrable spin-1 chain yields the Lagrangian of supersymmetric sine-Gordon model in the zero lattice spacing limit. We also show that the quantum group generators of the spin-1 chain give non-local charges of the supersymmetric sine-Gordon theory.

arXiv:hep-th/9209019•Sep 7, 1992•0 citations

The Bethe ansatz

Fedor Levkovich-Maslyuk

Abstract We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S -matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU (2) chiral Gross–Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU (3) chiral Gross–Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU (3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.

arXiv:1606.02950•Journal of Physics A Mathematical and Theoretical•Jul 20, 2016•70 citations

Continuum Limit of gl(M/N) Spin Chains

Constantin Candu

We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All antiferromagnetic gl(n + N|N)spin chains with n, N > 0 are shown to possess in the continuum limit 2n −2 multiplets of massive particles which scatter with gl(n)Gross-Neveu like S-matrices, meaning that their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model, that is the massive deformation of the $ {{s\hat{l}}}{\left( {M\left| N \right.} \right)_1} $ Wess-Zumino-Witten model. As we can see in the example of gl(2 m|1) spin chains, the full particle spectrum is much richer. Our analysis suggests that for a complete characterization of the latter it is not enough to restrict to large volume calculations, as we do in this work.

•Jan 1, 2011•6 citations

The continuum limit of gl(M|N) spin chains

Constantin Candu

We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All antiferromagnetic gl(n + N|N)spin chains with n, N > 0 are shown to possess in the continuum limit 2n −2 multiplets of massive particles which scatter with gl(n)Gross-Neveu like S-matrices, meaning that their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model, that is the massive deformation of the $ {{s\hat{l}}}{\left( {M\left| N \right.} \right)_1} $ Wess-Zumino-Witten model. As we can see in the example of gl(2 m|1) spin chains, the full particle spectrum is much richer. Our analysis suggests that for a complete characterization of the latter it is not enough to restrict to large volume calculations, as we do in this work.

arXiv:1012.0050•Journal of High Energy Physics•Jul 1, 2011•9 citations
We introduce a new family of integrable theories with NNN bosons and NNN freely adjustable mass parameters. These theories restrict in particular limits to the ``generalized supersymmetric'' sine-Gordon models, as well as to the flavor anisotropic chiral Gross Neveu models (studied recently by N. Andrei and collaborators). The scattering theory involves scalar particles that are no bound states, and bears an intriguing resemblance wih the results of a sharp cut-off analysis of the Thirring model carried out by Korepin in (1980). Various physical applications are discussed. In particular, we demonstrate that our theories are the appropriate continuum limit of integrable quantum spin chains with mixtures of spins.
Abstract The aim of this paper is to investigate the non-relativistic limit of integrable quantum field theories with fermionic fields, such as the O ( N ) Gross–Neveu model, the supersymmetric Sinh–Gordon and non-linear sigma models. The non-relativistic limit of these theories is implemented by a double scaling limit which consists of sending the speed of light c to infinity and rescaling at the same time the relevant coupling constant of the model in such a way to have finite energy excitations. For the general purpose of mapping the space of continuous non-relativistic integrable models, this paper completes and integrates the analysis done in Bastianello A et al (2016 J. Stat. Mech . 123104) on the non-relativistic limit of purely bosonic theories.
Abstract We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S -matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU (2) chiral Gross–Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU (3) chiral Gross–Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU (3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.
We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All antiferromagnetic gl(n + N|N)spin chains with n, N > 0 are shown to possess in the continuum limit 2n −2 multiplets of massive particles which scatter with gl(n)Gross-Neveu like S-matrices, meaning that their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model, that is the massive deformation of the $ {{s\hat{l}}}{\left( {M\left| N \right.} \right)_1} $ Wess-Zumino-Witten model. As we can see in the example of gl(2 m|1) spin chains, the full particle spectrum is much richer. Our analysis suggests that for a complete characterization of the latter it is not enough to restrict to large volume calculations, as we do in this work.
We study the spectrum of an integrable antiferromagnetic Hamiltonian of the gl(M|N) spin chain of alternating fundamental and dual representations. After extensive numerical analysis, we identify the vacuum and low lying excitations and with this knowledge perform the continuum limit, while keeping a finite gap. All antiferromagnetic gl(n + N|N)spin chains with n, N > 0 are shown to possess in the continuum limit 2n −2 multiplets of massive particles which scatter with gl(n)Gross-Neveu like S-matrices, meaning that their eigenvalues do not depend on N. We argue that the continuum theory is the gl(M|N) Gross-Neveu model, that is the massive deformation of the $ {{s\hat{l}}}{\left( {M\left| N \right.} \right)_1} $ Wess-Zumino-Witten model. As we can see in the example of gl(2 m|1) spin chains, the full particle spectrum is much richer. Our analysis suggests that for a complete characterization of the latter it is not enough to restrict to large volume calculations, as we do in this work.