arXiv subjects
Publications and source records attributed to F. H. L. Essler.
We develop a low-temperature expansion for the finite temperature dynamical structure factor of the spin half Heisenberg chain with alternating nearest neighbour exchange in the limit of strong alternation of the exchange constants. We determine both the broadening of the low lying triplet lines and the contribution of the thermally activated intraband scattering.
We consider the spin-1/2 Heisenberg XXZ chain in the regime of large Ising-like anisotropy $Δ$. By a combination of duality and Jordan-Wigner transformations we derive a mapping to weakly interacting spinless fermions, which represent domain walls between the two degenerate ground states. We develop a perturbative expansion in $1Δ$ for the transverse dynamical spin structure factor at finite temperatures and in an applied transverse magnetic field. We present a unified description for both the low-energy temperature-activated response and the temperature evolution of the T=0 two-spinon continuum. We find that the two-spinon continuum narrows in energy with increasing temperature. At the same time spectral weight is transferred from the two-spinon continuum to the low energy intraband scattering continuum, which is strongly peaked around the position of the (single) spinon dispersion (`Villain mode').
We consider a model of one dimensional spin-1 bosons with repulsive density-density interactions and antiferromagnetic exchange. We show that the low energy effective field theory is given by a spin-charge separated theory of a Tomonaga-Luttinger Hamiltonian and the O(3) nonlinear sigma model describing collective charge and spin excitations respectively. At a particular ratio of the density-density to spin-spin interaction the model is integrable, and we use the exact solutions to provide an independent derivation of the low energy effective theory. The system is in a superfluid phase made of singlet pairs of bosons, and we calculate the long-distance asymptotics of certain correlation functions.
The nature of the interplay between superconductivity and magnetism in the cuprates remains one of the fundamental unsolved problems in high temperature superconductivity. Whether and how these two phenomena are interdependent is perhaps most sharply seen in the stripe phases of various copper-oxide materials. These phases, involving a mixture of spin and charge density waves, do not yet admit a complete, overarching theoretical treatment. However aspects of this problem can be analyzed. In this work, we focus on the magnetic side of stripe physics. To this end, we study a simple model of a stripe-ordered phase consisting of an array of alternating coupled doped and undoped two-leg Hubbard-like ladders. To obtain the magnetic response, we employ already available dynamical susceptibilities of the individual two-leg ladders and treat the interladder coupling in a random phase approximation. Strikingly, we find two possible scenarios for the ordered state induced by the coupling between ladders: the spin modulation can occur either along or perpendicular to the direction of the stripes. These two scenarios are differentiated according to different microscopic realizations of the component doped ladders. However inelastic neutron scattering experiments on the two stripe ordered cuprates, La_{1.875}Ba_{0.125}CuO_4 and La_{2-x}Sr_xCuO_4, do not readily distinguish between these two scenarios due to manner in which stripes form in these materials.
We study a lattice realization of a Luttinger liquid interacting with a bath of quantum spins in terms of an antiferromagnetic S=1/2 Heisenberg chain, where each spin is also coupled to a σ=1/2 Kondo spin degree of freedom. This model describes the low-energy spin dynamics in quasi one dimensional materials, where the electronic spins of the magnetic ions interact with those of impurities, nuclei and possibly other spin species present in their environment. For large ferromagnetic and antiferromagnetic Kondo interaction J' there are two phases corresponding to an effective spin-1 Heisenberg chain and a dimerised spin-1/2 ladder, respectively. For weak Kondo interaction we establish that the Kondo interaction drives the system to a strong coupling regime. This suggests that J'=0 is the only critical point in the system.
We present exact derivations of the effective capillary wave fluctuation induced forces resulting from pinning of an interface between two coexisting phases at two points separated by a distance r. In two dimensions the Ising ferromagnet calculations based on the transfer matrix approach give an attractive force decaying as 1/r for large distances. In three dimensions mapping of the body-centered solid-on-solid model onto the 6-vertex model allows for exact solution using the bosonization analysis of the equivalent XXZ Heisenberg quantum chain. The exact result gives the attractive force which decays asymptotically as 1/(r\log r).
We study the dynamical spin response of doped two-leg Hubbard-like ladders in the framework of a low-energy effective field theory description given by the SO(6) Gross Neveu model. Using the integrability of the SO(6) Gross-Neveu model, we derive the low energy dynamical magnetic susceptibility. The susceptibility is characterized by an incommensurate coherent mode near $(π,π)$ and by broad two excitation scattering continua at other $k$-points. In our computation we are able to estimate the relative weights of these contributions. All calculations are performed using form-factor expansions which yield exact low energy results in the context of the SO(6) Gross-Neveu model. To employ this expansion, a number of hitherto undetermined form factors were computed. To do so, we developed a general approach for the computation of matrix elements of semi-local SO(6) Gross-Neveu operators. While our computation takes place in the context of SO(6) Gross-Neveu, we also consider the effects of perturbations away from an SO(6) symmetric model, showing that small perturbations at best quantitatively change the physics.
We analyze the Thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the "spin-disordered regime", which is characterized by the temperature being much larger than the magnetic energy scale but small compared to the Mott-Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal-insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott-Hubbard transition in the limit of infinite dimensions.
We consider the one-dimensional extended Hubbard model in the presence of an explicit dimerization $δ$. For a sufficiently strong nearest neighbour repulsion we establish the existence of a quantum phase transition between a mixed bond-order wave and charge-density wave phase from a pure bond-order wave phase. This phase transition is in the universality class of the two-dimensional Ising model.
We develop a theory of a hybrid state, where quasi-particles coexist with strong collective modes, taking as a starting point a model of infinitely many 1D Mott insulators coupled by a weak interchain tunneling. This state exists at an intermediate temperature range and undergoes an antiferromagnetic phase transition at temperatures much smaller than the Mott-Hubbard gap. The most peculiar feature of the hybrid state is that the volume of the Fermi surface is unrelated to the electron density. We present a self-consistent derivation of the low energy effective action for our model.
We calculate the low temperature spectral function of one-dimensional incommensurate charge density wave (CDW) states and half-filled Mott insulators (MI). At $T=0$ there are two dispersing features associated with the spin and charge degrees of freedom respectively. We show that already at very low temperatures (compared to the gap) one of these features gets severely damped. We comment on implications of this result for photoemission experiments.
We report a resonant inelastic x-ray scattering study of charge excitations in the quasi-one-dimensional Mott insulator SrCuO2. We observe a continuum of low-energy excitations, in which a highly dispersive feature with a large sinusoidal dispersion (~1.1 eV) resides. We have also measured the optical conductivity, and studied the dynamic response of the extended Hubbard model with realistic parameters, using a dynamical density-matrix renormalization group method. In contrast to earlier work, we do not find a long-lived exciton, but rather these results suggest that the excitation spectrum comprises a holon-antiholon continuum together with a broad resonance.
We consider spin correlations in the one dimensional half filled repulsive Hubbard model. For very large values of the on-site repulsion U the spin correlations are dominated by virtual hopping processes of electrons and are described in terms of a spin-1/2 Heisenberg chain. As U is decreased real hopping processes of electrons become important and eventually dominate the spin response. We discuss the evolution of the dynamical structure factor as a function of U. We comment on the relevance of our results for inelastic neutron scattering experiments on quasi-1D materials.
Recent experiments of the quasi-one-dimensional spin-1/2 antiferromagnet Copper Benzoate established the existence of a magnetic field induced gap. The observed neutron scattering intensity exhibits resolution limited peaks at both the antiferromagnetic wave number and at incommensurate wave numbers related to the applied magnetic field. We determine the ratio of spectral weights of these peaks within the framework of a low-energy effective field theory description of the problem.
We consider the anisotropic Heisenberg spin-1/2 chain in a transverse magnetic field at zero temperature. We first determine all components of the dynamical structure factor by combining exact results with a mean-field approximation recently proposed by Dmitriev {\it et al}., JETP 95, 538 (2002). We then turn to the small anisotropy limit, in which we use field theory methods to obtain exact results. We discuss the relevance of our results to Neutron scattering experiments on the 1D Heisenberg chain compound ${\rm Cs_2CoCl_4}$.
The polarization dependence of magnetic excitations in the quasi one-dimensional antiferromagnet BaCu2Si2O7 is studied as a function of momentum and energy transfer. The results of inelastic neutron scattering measurements are directly compared to semi-analytical calculations based on the chain-Mean Field and Random Phase approximations. A quantitative agreement between theoretically calculated and experimentally measured dynamic structure factors of transverse spin fluctuations is obtained. In contrast, substantial discrepancies are found for longitudinal polarization. This behavior is attributed to intrinsic limitations of the RPA that ignores correlation effects.
We study a two-leg antiferromagnetic spin-1/2 ladder in the presence of a staggered magnetic field. We consider two parameter regimes: strong (weak) coupling along the legs and weak (strong) coupling along the rungs. In both cases, the staggered field drives the Haldane spin-liquid phase of the ladder towards a Gaussian quantum criticality. In a generalized spin ladder with a non-Haldane, spontaneously dimerized phase, the staggered magnetic field induces an Ising quantum critical regime. In the vicinity of the critical lines, we derive low-energy effective field theories and use these descriptions to determine the dynamical response functions, the staggered spin susceptibility and the string order parameter.
We employ dynamical density-matrix renormalization group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of `small' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations (`holon-antiholon' pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.