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Fabian H. L. Essler

Publications and source records attributed to Fabian H. L. Essler.

At least 109 records · Page 6Linked to original sources
arXiv1999

A note on density correlations in the half-filled Hubbard model

We consider density-density correlations in the one-dimensional Hubbard model at half filling. On intuitive grounds one might expect them to exhibit an exponential decay. However, as has been noted recently, this is not obvious from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by supplementing the BA/CFT analysis with simple symmetry arguments one can easily prove that correlations of the lattice density operators decay exponentially.

cond-mat.str-el↗
arXiv1998

Formfactors in the half-filled Hubbard model

We consider dynamical spin-spin correlation functions in the one dimensional repulsive half-filled Hubbard model. We propose an exact expression for the two spinon formfactor of spin operators. We use this to derive the two spinon contribution to the dynamical structure factor.

cond-mat.str-el↗
arXiv1998

Incommensurate spin correlations in Heisenberg spin-1/2 zig-zag ladders

We develop a low-energy effective theory for spin-1/2 frustrated two-leg Heisenberg spin ladders. We obtain a new type of interchain coupling that breaks parity symmetry. In the presence of an XXZ-type anisotropy, this interaction gives rise to a novel ground state, characterized by incommensurate correlations. In the case of a single ladder, this state corresponds to a spin nematic phase. For a frustrated quasi-one-dimensional system of infinitely many weakly coupled chains, this state develops true three dimensional spiral order. We apply our theory to recent neutron scattering experiments on $Cs_2CuCl_4$.

cond-mat.str-el↗
arXiv1998

Temperature Corrections to Conformal Field Theory

We consider finite temperature dynamical correlation functions in the interacting delta-function Bose gas. In the low-temperature limit the asymptotic behaviour of correlation functions can be determined from conformal field theory. In the present work we determine the deviations from conformal behaviour at low temperatures.

cond-mat.stat-mech↗
arXiv1997

Dynamical Magnetic Susceptibilities in Cu Benzoate

Recent experiments on the quasi 1-D antiferromagnet Cu Benzoate revealed a magentic field induced gap coexisting with (ferro)magnetic order. A theory explaining these findings has been proposed by Oshikawa and Affleck. In the present work we discuss consequences of this theory for inelastic neutron scattering experiments by calculating the dynamical magnetic susceptibilities close to the antiferromagnetic wave vector by the formfactor method.

cond-mat.str-el↗
arXiv1997

X-ray edge singularity in integrable lattice models of correlated electrons

We study the singularities in X-ray absorption spectra of one-dimensional Hubbard and $t$--$J$ models. We use Boundary Conformal Field Theory and the Bethe Ansatz solutions of these models with both periodic and open boundary conditions to calculate the exponents describing the power-law decay near the edges of X-ray absorption spectra in the case where the core-hole potential has bound states.

cond-mat.str-el↗
arXiv1997

Quasi-1D spin-1/2 Heisenberg magnets in their ordered phase: correlation functions

We study weakly coupled antiferromagnetic spin chains in their ordered phase by combinining an exact solution of the single-chain problem with an RPA analysis of the interchain interaction. A single chain is described by a quantum Sine-Gordon model and dynamical staggered susceptibilities are determined by employing the formfactor approach to quantum correlation functions. We consider both antiferromagnetic order encountered in quasi-1D materials like $KCuF_3$ and spin-Peierls order as found in $CuGeO_3$.

cond-mat.str-el↗
arXiv1997

The Supersymmetric t-J Model with a Boundary

An open supersymmetric t-J chain with boundary fields is studied by means of the Bethe Ansatz. Ground state properties for the case of an almost half-filled band and a bulk magnetic field are determined. Boundary susceptibilities are calculated as functions of the boundary fields. The effects of the boundary on excitations are investigated by constructing the exact boundary S-matrix. From the analytic structure of the boundary S-matrices one deduces that holons can form boundary bound states for sufficiently strong boundary fields.

cond-mat↗
arXiv1996

Determinant representation for a quantum correlation function of the lattice sine-Gordon model

We consider a completely integrable lattice regularization of the sine-Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the correlation function of local fields. The determinant is then embedded into a system of integrable integro-differential equations. The leading asymptotic behaviour of the correlation function is described in terms of the solution of a Riemann Hilbert Problem (RHP) related to the system of integro-differential equations. The leading term in the asymptotical decomposition of the solution of the RHP is obtained.

hep-th↗
arXiv1996

Painlevé Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point

We consider quantum correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg XXZ spin chain in a magnetic field. We show that for a magnetic field close to the critical field $h_c$ (for the critical magnetic field the ground state is ferromagnetic) certain correlation functions can be expressed in terms of the solution of the Painlevé V transcendent. This establishes a relation between solutions of Painlevé differential equations and quantum correlation functions in models of {\sl interacting} fermions. Painlevé transcendents were known to describe correlation functions in models with free fermionic spectra.

solv-int↗
arXiv1996

Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries

We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are injected and extracted. By means of the method of Derrida, Evans, Hakim and Pasquier the stationary probability measure can be expressed as a matrix-product state involving two matrices subject to a quadratic algebra. We obtain the representations of this algebra and use the two-dimensional one to derive exact expressions for the density profile and correlation functions. Using the correspondence between the stochastic model and a quantum spin chain, we obtain exact correlation functions for a spin-$\frac{1}{2}$ Heisenberg XXZ chain with non-diagonal boundary terms. Generalizations to other reaction-diffusion models are discussed.

cond-mat↗
arXiv1995

Dual Field Approach to Correlation Functions in the Heisenberg Xxz Spin Chain

We study zero temperature correlation functions of the spin-$1\over 2$ Heisenberg XXZ model in the critical regime $-1< Δ\leq 1$ in a magnetic field by means of the {\tenit Dual Field Approach}. We show for one particular example how to derive determinant representations for correlation functions and how to use these to embed the correlation functions in integrable systems of integro-difference equations (IDE). These IDE are associated with a Riemann-Hilbert problem.

solv-int↗
arXiv1994

A Note on Dressed S-Matrices in Models with Long-Range Interactions

The {\sl dressed} Scattering matrix describing scattering of quasiparticles in various models with long-range interactions is evaluated by means of Korepin's method\upref vek1/. For models with ${1\over\sin^2(r)}$-interactions the S-matrix is found to be a momentum-independent phase, which clearly demonstrates the ideal gas character of the quasiparticles in such models. We then determine S-matrices for some models with ${1\over\sinh^2(r)}$-interaction and find them to be in general nontrivial. For the ${1\over r^2}$-limit of the ${1\over\sinh^2(r)}$-interaction we recover trivial S-matrices, thus exhibiting a crossover from interacting to noninteracting quasiparticles. The relation of the S-matrix to fractional statistics is discussed.

cond-mat↗
arXiv1994

Correlation Function of the Spin-1/2 XXX Antiferromagnet

We consider a special correlation function in the isotropic spin-$\half$ Heisenberg antiferromagnet. It is the probability of finding a ferromagnetic string of (adjacent) spins in the antiferromagnetic ground state. We give two different representations for this correlation function. Both of them are exact at any distance, but one becomes more effective for the description of long distance behaviour, the other for the description of short distance behaviour.

cond-mat↗
arXiv1993

SU(2)xSU(2) Invariant Scattering Matrix of the Hubbard Model

We consider the one-dimensional half-filled Hubbard model. We show that the excitation spectrum is given by the scattering states of four elementary excitations, which form the fundamental representation of $SU(2)\times SU(2)$. We determine the exact two-particle Scattering matrix, which a solution of the Yang-Baxter equation and reflects the $SO(4)$ symmetry of the model. The results for repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.

cond-mat↗
arXiv1993

Scattering Matrix and Excitation Spectrum of the Hubbard Model

We consider the one-dimensional Hubbard model at half filling. We show that both excitation spectrum and S-matrix are determined by the SO(4) symmetry of the model. The complete set of excitations is given by the scattering states four elementary excitations, which form the fundamental representation of SO(4). We evaluate the exact S-matrix, which satisfies the Yang-Baxter relation. The results for the repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.

cond-mat↗
arXiv1993

Spectrum of Low-Lying Excitations in a Supersymmetric Extended Hubbard Model

We continue the study of the $u(2|2)$-supersymmetric extension of the Hubbard model in one dimension. We determine the excitation spectrum at zero temperature even in the sectors where the ground states are $u(2|2)$-descendants of Bethe states. The excitations include spinons, holons, electrons, localons (local electrons pairs, moving coherently through the lattice) and their bound states. The spectra are found to be very different for repulsive and attractive on-site interaction. We also study the thermodynamics of the model.

cond-mat↗