942 research outputs found

### Differential equations and duality in massless integrable field theories at zero temperature

Functional relations play a key role in the study of integrable models. We
argue in this paper that for massless field theories at zero temperature, these
relations can in fact be interpreted as monodromy relations. Combined with a
recently discovered duality, this gives a way to bypass the Bethe ansatz, and
compute directly physical quantities as solutions of a linear differential
equation, or as integrals over a hyperelliptic curve. We illustrate these ideas
in details in the case of the $c=1$ theory, and the associated boundary
sine-Gordon model.Comment: 18 pages, harvma

### Free parafermions

The spectrum of the quantum Ising chain can be found by expressing the spins
in terms of free fermions. An analogous transformation exists for clock chains
with $Z_n$ symmetry, but is of less use because the resulting parafermionic
operators remain interacting. Nonetheless, Baxter showed that a certain
non-hermitian (but PT-symmetric) clock Hamiltonian is "free", in the sense that
the entire spectrum is found in terms of independent energy levels, with the
striking feature that there are $n$ possibilities for occupying each level.
Here I show this directly explicitly finding shift operators obeying a $Z_n$
generalization of the Clifford algebra. I also find higher Hamiltonians that
commute with Baxter's and prove their spectrum comes from the same set of
energy levels. This thus provides an explicit notion of a "free parafermion". A
byproduct is an elegant method for the solution of the Ising/Kitaev chain with
spatially varying couplings.Comment: 44 pages. v2: minor rewriting, added several reference

### Reflection Matrices for Integrable $N=1$ Supersymmetric Theories

We study two-dimensional integrable $N=1$ supersymmetric theories (without
topological charges) in the presence of a boundary. We find a universal ratio
between the reflection amplitudes for particles that are related by
supersymmetry and we propose exact reflection matrices for the supersymmetric
extensions of the multi-component Yang-Lee models and for the breather
multiplets of the supersymmetric sine-Gordon theory. We point out the
connection between our reflection matrices and the classical boundary actions
for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and
Zhang \cite{IOZ}.Comment: 29 pages, Revtex, 4 figure

### Integrable sigma models and perturbed coset models

Sigma models arise frequently in particle physics and condensed-matter
physics as low-energy effective theories. In this paper I compute the exact
free energy at any temperature in two hierarchies of integrable sigma models in
two dimensions. These theories, the SU(N)/SO(N) and O(2P)/O(P) x O(P) models,
are asymptotically free and exhibit charge fractionalization. When the
instanton coupling theta=pi, they flow to the SU(N)_1 and O(2P)_1 conformal
field theories, respectively. I also generalize the free energy computation to
massive and massless perturbations of the coset conformal field theories
SU(N)_k/SO(N)_{2k} and O(2P)_k/O(P)_k x O(P)_k.Comment: 39 pages, 6 figure

### Correlations in one dimensional quantum impurity problems with an external field

We study response functions of integrable quantum impurity problems with an
external field at $T=0$ using non perturbative techniques derived from the
Bethe ansatz. We develop the first steps of the theory of excitations over the
new, field dependent ground state, leading to renormalized (or ``dressed'')
form-factors. We obtain exactly the low frequency behaviour of the dynamical
susceptibility $\chi''(\omega)$ in the double well problem of dissipative
quantum mechanics (or equivalently the anisotropic Kondo problem),and the low
frequency behaviour of the AC noise $S_t(\omega)$ for tunneling between edges
in fractional quantum Hall devices. We also obtain exactly the structure of
singularities in $\chi''(\omega)$ and $S_t(\omega)$. Our results differ
significantly from previous perturbative approaches.Comment: harvmac, epsf, 37pgs, 2figs. modified some reference

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