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A. Klümper

Publications and source records attributed to A. Klümper.

At least 37 records · Page 2Linked to original sources
arXiv2011

On the universal R-matrix for the Izergin-Korepin model

We continue our exercises with the universal $R$-matrix based on the Khoroshkin and Tolstoy formula. Here we present our results for the case of the twisted affine Kac--Moody Lie algebra of type $A^{(2)}_2$. Our interest in this case is inspired by the fact that the Tzitzéica equation is associated with $A^{(2)}_2$ in a similar way as the sine-Gordon equation is related to $A^{(1)}_1$. The fundamental spin-chain Hamiltonian is constructed systematically as the logarithmic derivative of the transfer matrix. $L$-operators of two types are obtained by using q-deformed oscillators.

math-ph↗
arXiv2011

Double occupancy as a universal probe for antiferromagnetic correlations and entropy in cold fermions on optical lattices

We verify signatures of antiferromagnetic (AF) correlations in the double occupancy D [Gorelik et al., PRL 105, 065301 (2010)] and study their dimensional dependence using direct quantum Monte Carlo in dimensions d=2,3 and Bethe Ansatz in d=1. We find quantitative agreement with dynamical mean-field theory (DMFT) in the cubic case and qualitative agreement down to d=1. As a function of entropy s=S/(N k_B), D is nearly universal with respect to d; the minimum in D(s) approaches s=log(2) at strong coupling, as predicted by DMFT. Long-range order appears hardly relevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve s<log(2)/2 and should consider lower dimensions, for which the AF effects are larger.

cond-mat.quant-gas↗
arXiv2010

The thermal conductivity of alternating spin chains

We study a class of integrable alternating (S1,S2) quantum spin chains with critical ground state properties. Our main result is the description of the thermal Drude weight of the one-dimensional alternating spin chain as a function of temperature. We have identified the thermal current of the model with alternating spins as one of the conserved currents underlying the integrability. This allows for the derivation of a finite set of non-linear integral equations for the thermal conductivity. Numerical solutions to the integral equations are presented for specific cases of the spins S1 and S2. In the low-temperature limit a universal picture evolves where the thermal Drude weight is proportional to temperature T and central charge c.

cond-mat.stat-mech↗
arXiv2009

Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model

The low energy behaviour of the 2d antiferromagnetic Heisenberg model is studied in the sector with total spins $S=0,1,2$ by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix $Δ_S^{(n+1)}$ of 4 neighbouring "$n$ clusters" of size $2^n\times 2^n$, $n=1,2,3,...$ from the corresponding quantities $Δ_S^{(n)}$. Conservation of total spin $S$ is implemented explicitly and plays an important role. It is shown, how the ground state energies $E_S^{(n+1)}$, $S=0,1,2$ approach each other for increasing $n$, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions $ $ between the ground states $|S,m;n+1>$ ($m=-S,...,S$) on an $(n+1)$-cluster of size $2^{n+1}\times 2^{n+1}$, mediated by the staggered spin operator $S_q^*$

cond-mat.str-el↗
arXiv2009

Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes

A two-dimensional model of interacting plaquettes is studied by means of the real space renormalization group approach. Interactions between the plaquettes are mediated solely by spin excitations on the plaquettes. Depending on the plaquette-plaquette coupling $J$, we find two regimes: "confinement" $J_c< J\leq 1$, where the singlet ground state forms an infinite ("confined") cluster in the thermodynamical limit. Here the singlet-triplet gap vanishes, which is the signature for long range spin-spin correlators. "deconfinement" $0\leq J< J_c$, where the singlet ground state "deconfines" - i.e. factorizes - into finite $n$-clusters of size $2^n\times 2^n$, with $n\leq n_c(J)$. Here the singlet-triplet gap is finite. The critical value turns out to be $J_c=0.473528..$.

cond-mat.str-el↗
arXiv2008

Doping a Mott insulator with orbital degrees of freedom

We study the effects of hole doping on one-dimensional Mott insulators with orbital degrees of freedom. We describe the system in terms of a generalized t-J model. At a specific point in parameter space the model becomes integrable in analogy to the one-band supersymmetric t-J model. We use the Bethe ansatz to derive a set of nonlinear integral equations which allow us to study the thermodynamics exactly. Moving away from this special point in parameter space we use the density-matrix renormalization group applied to transfer matrices to study the evolution of various phases of the undoped system with doping and temperature. Finally, we study a one-dimensional version of a realistic model for cubic titanates which includes the anisotropy of the orbital sector due to Hund's coupling. We find a transition from a phase with antiferromagnetically correlated spins to a phase where the spins are fully ferromagnetically polarized, a strong tendency towards phase separation at large Hund's coupling, as well as the possibility of an instability towards triplet superconductivity.

cond-mat.str-el↗
arXiv2008

Effects of Two Energy Scales in Weakly Dimerized Antiferromagnetic Quantum Spin Chains

By means of thermal expansion and specific heat measurements on the high-pressure phase of (VO)$_2$P$_2$O$_7$, the effects of two energy scales of the weakly dimerized antiferromagnetic $S$ = 1/2 Heisenberg chain are explored. The low energy scale, given by the spin gap $Δ$, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing T-DMRG calculations, shows that this feature originates from changes in the magnetic entropy with respect to $Δ$, $\partial S^{m}/ \partial Δ$. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in $Δ$.

cond-mat.str-el↗
arXiv2007

Thermodynamics of antiferromagnetic alternating spin chains

We consider integrable quantum spin chains with alternating spins (S_1,S_2). We derive a finite set of non-linear integral equations for the thermodynamics of these models by use of the quantum transfer matrix approach. Numerical solutions of the integral equations are provided for quantities like specific heat, magnetic susceptibility and in the case S_1=S_2 for the thermal Drude weight. At low temperatures one class of models shows finite magnetization and the other class presents antiferromagnetic behaviour. The thermal Drude weight behaves linearly on T at low temperatures and is proportional to the central charge c of the system. Quite generally, we observe residual entropy for S_1\neq S_2.

nlin.SI↗
arXiv2007

The Half-Filled One-Dimensional Extended Hubbard Model: Phase diagram and Thermodynamics

We study the thermodynamics of the one-dimensional extended Hubbard model at half-filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be detected by measuring usual thermodynamic quantities like the isothermal compressibility and the uniform magnetic susceptibility. For the isothermal compressibility we show that universal crossing points exist which allow to accurately determine the line where the charge gap vanishes. By studying in addition several correlation functions, we confirm the existence of a phase with long-range dimer order (bond order) which has been a matter of debate for several years. According to our calculations this phase is located in a narrow region between the spin-density and charge-density wave phases up to a tricritical point which we estimate to be at $U_t=6.7\pm 0.2$, $V_t =3.5\pm 0.1$. Our results for the phase diagram are in good agreement with the most recent zero-temperature density-matrix renormalization group study, however, they disagree in some important aspects from the most recent Quantum-Monte-Carlo study.

cond-mat.str-el↗
arXiv2006

The density-matrix renormalization group applied to transfer matrices: Static and dynamical properties of one-dimensional quantum systems at finite temperature

The density-matrix renormalization group (DMRG) applied to transfer matrices allows it to calculate static as well as dynamical properties of one-dimensional quantum systems at finite temperature in the thermodynamic limit. To this end the quantum system is mapped onto a two-dimensional classical system by a Trotter-Suzuki decomposition. Here we discuss two different mappings: The standard mapping onto a two-dimensional lattice with checkerboard structure as well as an alternative mapping introduced by two of us. For the classical system an appropriate quantum transfer matrix is defined which is then treated using a DMRG scheme. As applications, the calculation of thermodynamic properties for a spin-1/2 Heisenberg chain in a staggered magnetic field and the calculation of boundary contributions for open spin chains are discussed. Finally, we show how to obtain real time dynamics from a classical system with complex Boltzmann weights and present results for the autocorrelation function of the XXZ-chain.

cond-mat.str-el↗
arXiv2006

S=1/2 antiferromagnetic Heisenberg chain with staggered fields: Copper pyrimidine and copper benzoate using the density matrix renormalization group for transfer matrices

We consider the spin-1/2 antiferromagnetic Heisenberg chain in a staggered magnetic field describing materials such as copper benzoate and copper pyrimidine dinitrate. Using the density-matrix renormalization group for transfer matrices (TMRG) we calculate the magnetization of these materials at finite temperature and arbitrary magnetic field. These results are in excellent agreement with experimental data, allowing for a determination of the inhomogeneity parameter c of copper benzoate (c = 0.043) and copper pyrimidine dinitrate (c= 0.11). The TMRG approach can be applied to rather low temperatures yielding singular field and temperature dependences of susceptibilities.

cond-mat.str-el↗
arXiv2005

Real-time dynamics at finite temperature by DMRG: A path-integral approach

We propose a path-integral variant of the DMRG method to calculate real-time correlation functions at arbitrary finite temperatures. To illustrate the method we study the longitudinal autocorrelation function of the $XXZ$-chain. By comparison with exact results at the free fermion point we show that our method yields accurate results up to a limiting time which is determined by the spectrum of the reduced density matrix.

cond-mat.str-el↗
arXiv2005

On the finite temperature Drude weight of the anisotropic Heisenberg chain

We present a study of the Drude weight $D(T)$ of the spin-1/2 $XXZ$ chain in the gapless regime. The thermodynamic Bethe ansatz (TBA) is applied in two different ways. In the first application we employ the particle basis of magnons and their bound states. In this case we rederive and considerably extend earlier work in the literature. However, in the course of our investigation we find arguments that cast doubt on the applicability of the TBA in this case. In a second application by use of the spinon and anti-spinon particle basis we obtain completely different results. Only for anisotropy parameter $Δ$ close to 0 we find that $D(T)$ is a monotonously decaying function of temperature. For $Δ$ close to 1 the behaviour is entirely different showing a finite temperature maximum. Also for the isotropic antiferromagnetic chain ($Δ=1$) the results for $D(T)$ are finite for T=0 as well as for $T>0$ with an infinite positive slope at T=0.

cond-mat.str-el↗
arXiv2004

The anisotropic multichannel spin-$S$ Kondo model: Calculation of scales from a novel exact solution

A novel exact solution of the multichannel spin-$S$ Kondo model is presented, based on a lattice path integral approach of the single channel spin-1/2 case. The spin exchange between the localized moment and the host is of $XXZ$-type, including the isotropic $XXX$ limit. The free energy is given by a finite set of non-linear integral equations, which allow for an accurate determination of high- and low-temperature scales.

cond-mat.str-el↗
arXiv2004

Integral representations for correlation functions of the XXZ chain at finite temperature

We derive a novel multiple integral representation for a generating function of the $\s^z$-$\s^z$ correlation functions of the spin-$\2$ XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic Bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics.

hep-th↗
arXiv2004

High-field magnetization study of the S = 1/2 antiferromagnetic Heisenberg chain [PM Cu(NO$_3$)$_2$(H$_2$O)$_2$]$_n$ with a field-induced gap

We present a high-field magnetization study of the $S$ = 1/2 antiferromagnetic Heisenberg chain [PM Cu(NO$_3$)$_2$(H$_2$O)$_2$]$_n$. For this material, as result of the Dzyaloshinskii-Moriya interaction and a staggered $g$ tensor, the ground state is characterized by an anisotropic field-induced spin excitation gap and a staggered magnetization. Our data reveal the qualitatively different behavior in the directions of maximum and zero spin excitation gap. The data are analyzed via exact diagonalization of a linear spin chain with up to 20 sites and on basis of the Bethe ansatz equations, respectively. For both directions we find very good agreement between experimental data and theoretical calculations. We extract the magnetic coupling strength $J/k_B$ along the chain direction to 36.3(5) K and determine the field dependence of the staggered magnetization component $m_s$.

cond-mat.mtrl-sci↗
arXiv2002

Thermodynamics and Crossover Phenomena in the Correlation Lengths of the One-Dimensional t-J Model

We investigate the thermodynamics of the one-dimensional t-J model using transfer matrix renormalization group (TMRG) algorithms and present results for quantities like particle number, specific heat, spin susceptibility and compressibility. Based on these results we confirm a phase diagram consisting of a Tomonaga-Luttinger liquid (TLL) phase for small J/t and a phase separated state for J/t large. Close to phase separation we find a spin-gap (Luther-Emery) phase at low densities consistent with predictions by other studies. At the supersymmetric point we compare our results with exact results from the Bethe ansatz and find excellent agreement. In particular we focus on the calculation of correlation lengths and static correlation functions and study the crossover from the non-universal high T lattice into the quantum critical regime. At the supersymmetric point we compare in detail with predictions by conformal field theory (CFT) and TLL theory and show the importance of logarithmic corrections.

cond-mat.str-el↗