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Andreas Klümper

Publications and source records attributed to Andreas Klümper.

52 records · Page 3Linked to original sources
arXiv2010

The complete conformal spectrum of a $sl(2|1)$ invariant network model and logarithmic corrections

We investigate the low temperature asymptotics and the finite size spectrum of a class of Temperley-Lieb models. As reference system we use the spin-1/2 Heisenberg chain with anisotropy parameter $Δ$ and twisted boundary conditions. Special emphasis is placed on the study of logarithmic corrections appearing in the case of $Δ=1/2$ in the bulk susceptibility data and in the low-energy spectrum yielding the conformal dimensions. For the $sl(2|1)$ invariant 3-state representation of the Temperley-Lieb algebra with $Δ=1/2$ we give the complete set of scaling dimensions which show huge degeneracies.

cond-mat.stat-mech↗
arXiv2010

Thermodynamics and short-range correlations of the XXZ chain close to its triple point

The XXZ quantum spin chain has a triple point in its ground state $h$-$1/Δ$ phase diagram. This first order critical point is located at the joint end point of the two second order phase transition lines marking the transition from the gapless phase to the fully polarized phase and to the Néel ordered phase, respectively. We explore the magnetization and the short-range correlation functions in its vicinity using the exact solution of the model. In the critical regime above the triple point we observe a strong variation of all physical quantities on a low energy scale of order $1/Δ$ induced by the transversal quantum fluctuations. We interpret this phenomenon starting from a strong-coupling perturbation theory about the highly degenerate ground state of the Ising chain at the triple point. From the perturbation theory we identify the relevant scaling of the magnetic field and of the temperature. Applying the scaling to the exact solutions we obtain explicit formulae for the magnetization and short-range correlation functions at low temperatures.

cond-mat.stat-mech↗
arXiv2009

Exact calculation of the magnetocaloric effect in the spin-1/2 XXZ chain

We calculate the entropy and cooling rate of the antiferromagnetic spin-1/2 XXZ chain under an adiabatic demagnetization process using the quantum transfer-matrix technique and non-linear integral equations. The limiting case of the Ising chain (corresponding to infinitely large anisotropy) is presented for comparison. Our exact results for the Heisenberg chain are used as a crosscheck for the numerical exact diagonalization as well as Quantum Monte Carlo simulations and allow us to benchmark the numerical methods. Close to field-induced quantum phase transitions we observe a large magnetocaloric effect. Furthermore, we verify universal low-temperature power laws in the cooling rate and entropy, in particular linear scaling of entropy with temperature T in the gapless Luttinger-liquid state and scaling as \sqrt{T} at field-induced transitions to gapped phases.

cond-mat.str-el↗
arXiv2009

Short-distance thermal correlations in the massive XXZ chain

We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field in the massive regime $Δ>1$, extending our previous results to the full parameter plane of the antiferromagnetic chain ($Δ> -1$ and arbitrary field $h$). The factorized formulae are numerically efficient and allow for taking the isotropic limit ($Δ= 1$) and the Ising limit ($Δ= \infty$). At the critical field separating the fully polarized phase from the Néel phase, the Ising chain possesses exponentially many ground states. The residual entropy is lifted by quantum fluctuations for large but finite $Δ$ inducing unexpected crossover phenomena in the correlations.

cond-mat.str-el↗
arXiv2007

From multiple integrals to Fredholm determinants

We consider a multiple integral representation for the finite temperature density-density correlation functions of the one-dimensional Bose gas with delta function interaction in the limits of infinite and vanishing repulsion. In the former case a known Fredholm determinant is recovered. In the latter case a similar expression appears with permanents replacing determinants.

math-ph↗
arXiv2007

A note on the spin-1/2 XXZ chain concerning its relation to the Bose gas

By considering the one-particle and two-particle scattering data of the spin-1/2 Heisenberg chain at T=0 we derive a continuum limit relating the spin chain to the 1D Bose gas. Applying this limit to the quantum transfer matrix approach of the Heisenberg chain we obtain expressions for the correlation functions of the Bose gas at arbitrary temperatures.

cond-mat.stat-mech↗
arXiv2007

Quantum phase transitions and thermodynamics of quantum antiferromagnets with competing interactions

We study the isotropic Heisenberg chain with nearest and next-nearest neighbour interactions. The ground state phase diagram is constructed in dependence on the additonal interactions and an external magnetic field. The thermodynamics is studied by use of finite sets of non-linear integral equations resulting from integrabiliy. The equations are solved numerically and analytically in suitable limiting cases. We find second and first order transition lines. The exponents of the low temperature asymptotics at the phase transitions are determined.

cond-mat.str-el↗
arXiv2007

Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field

We present a conjecture for the density matrix of a finite segment of the XXZ chain coupled to a heat bath and to a constant longitudinal magnetic field. It states that the inhomogeneous density matrix, conceived as a map which associates with every local operator its thermal expectation value, can be written as the trace of the exponential of an operator constructed from weighted traces of the elements of certain monodromy matrices related to $U_q (\hat{\mathfrak{sl}}_2)$ and only two transcendental functions pertaining to the one-point function and the neighbour correlators, respectively. Our conjecture implies that all static correlation functions of the XXZ chain are polynomials in these two functions and their derivatives with coefficients of purely algebraic origin.

hep-th↗
arXiv2006

Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model

We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical potentials. We recover the NLIE for sl(3) as a limiting case. In comparison to other recently derived NLIE, the evaluation at low temperature poses no problem in our formulation. The model shows a rich ground-state phase diagram. We obtain the critical fields from the T to zero limit of our NLIE. As an example for the application of the NLIE, we give numerical results for the SU(4) spin-orbital model. The magnetic susceptibility shows divergences at critical fields in the low-temperature limit and logarithmic singularities for zero magnetic field.

cond-mat.stat-mech↗
arXiv2006

Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain

We consider the inhomogeneous generalization of the density matrix of a finite segment of length $m$ of the antiferromagnetic Heisenberg chain. It is a function of the temperature $T$ and the external magnetic field $h$, and further depends on $m$ `spectral parameters' $ξ_j$. For short segments of length 2 and 3 we decompose the known multiple integrals for the elements of the density matrix into finite sums over products of single integrals. This provides new numerically efficient expressions for the two-point functions of the infinite Heisenberg chain at short distances. It further leads us to conjecture an exponential formula for the density matrix involving only a double Cauchy-type integral in the exponent. We expect this formula to hold for arbitrary $m$ and $T$ but zero magnetic field.

hep-th↗
arXiv2006

Structural and magnetic instabilities of layered magnetic systems

We present a study of the magnetic order and the structural stability of two-dimensional quantum spin systems in the presence of spin-lattice coupling. For a square lattice it is shown that the plaquette formation is the most favourable form of static two-dimensional dimerization. We also demonstrate that such distortions may coexist with long range magnetic order, in contrast to the one-dimensional case. Similarly, the coupling to Einstein phonons is found to reduce, but not to eliminate the staggered magnetic moment. In addition, we consider the renormalization of the square lattice phonon spectrum due to spin-phonon coupling in the adiabatic approximation. Towards low temperatures significant softening mainly of zone boundary phonons is found, especially around the $(π,0)$ point of the Brillouin zone. This result is compatible with the tendency to plaquette formation in the static limit. We also point out the importance of a "magnetic pressure" on the lattice due to spin-phonon coupling. At low temperatures, this results in a tendency towards shear instabilities of the lattice.

cond-mat.stat-mech↗
arXiv2005

Crossover from Anderson- to Kondo-like behavior: Universality induced by spin-charge separation

The thermodynamics of a lattice regularized asymmetric Anderson impurity in a correlated host is obtained by an exact solution. The crossover from the Anderson- to the Kondo-regime is studied, thus making contact with predictions by scaling theory. On the basis of the exact solution, the transition to universal Kondo behavior is shown to be realized by a graduate separation of the energy scales of spin and charge excitations.

cond-mat.str-el↗
arXiv2005

Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain

In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively we present the treatment of integrable quantum systems at finite temperature on the basis of a lattice path integral formulation and a suitable transfer matrix approach (quantum transfer matrix). The general method is carried out for the seminal model of the spin-1/2 $XXZ$ chain for which thermodynamic properties like specific heat, magnetic susceptibility and the finite temperature Drude weight of the thermal conductivity are derived.

cond-mat.str-el↗
arXiv1998

Temperature dependent spatial oscillations in the correlations of the XXZ spin chain

We study the correlation $<σ^z_0σ^z_n>$ for the XXZ chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.

cond-mat.stat-mech↗
arXiv1993

Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains

The free energy and correlation lengths of the spin-1/2 $XYZ$ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the critical $XXZ$ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-critical $XXZ$ chain and the related spin-1 biquadratic chain at arbitrary temperature.

cond-mat↗