Stolze, Joachim Prof. Dr.

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http://hdl.handle.net/2003/25414

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Quantum integrability and non-integrability in the spin-boson model
(The American Physical Society, 2008-06-04) Stolze, Joachim; Stepanov, Vyacheslav V.; Müller, Gerhard
Dynamic properties of the spin-1/2 XX chain with three-spin interactions
(The American Physical Society, 2008-05-02) Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras
We consider a spin-(1/2) XY chain in a transverse (z) field with multisite interactions. The additional terms introduced into the Hamiltonian involve products of spin components related to three adjacent sites. A Jordan–Wigner transformation leads to a simple bilinear Fermi form for the resulting Hamiltonian and, hence, the spin model admits a rigorous analysis. We point out the close relationships between several variants of the model, which were discussed separately in previous studies. The ground-state phases (ferromagnet and two kinds of spin liquid) of the model are reflected in the dynamic structure factors of the spin chains, which are the main focus in this study. First, we consider the zz dynamic structure factor, reporting for this quantity a closed-form expression and analyzing the properties of the two-fermion (particle-hole) excitation continuum, which governs the dynamics of transverse spin component fluctuations and of some other local operator fluctuations. Then we examine the xx dynamic structure factor, which is governed by many-fermion excitations, reporting both analytical and numerical results. We discuss some easily recognized features of the dynamic structure factors, which are signatures of the presence of the three-site interactions.
Spin-1/2 XX Chains with Three-Spin Interactions
(ICM, 2008) Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras
We consider a spin-1/2 XX chain with three-spin interactions which is equivalent to a system of noninteracting spinless fermions.We examine some dynamic quantities of the spin model.In particular, we calculate analytically the dynamic transverse (zz) structure factor which is governed by a two-fermion excitation continuum. Moreover, we compute numerically the dynamic xx structure factor which is a many-fermion dynamic quantity.We illustrate how the three-spin interactions manifest themselves in the dynamic probes.
Dynamic correlations in a random spin-1/2 XY chain
(ICM, 2008) Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras
We examine dynamic quantities of a random spin-1/2 isotropic XY chain in a transverse field. The randomness is related to the sign of the nearest-neighbor exchange interaction and can be eliminated by a suitable transformation. As a result, the dynamic quantities for the random spin chain are related to the same dynamic quantities for the homogeneous spin chain. We use the available results for the latter model to discuss the effect of randomness on the dynamic structure factors of the quantum spin chain.
Spin- and entanglement-dynamics in the central-spin model with homogeneous couplings
(IOP Publishing, 2007) Stolze, Joachim; Bortz, Michael
We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviours are found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the central spin decays to zero in the thermodynamic limit, while its entanglement entropy becomes maximal. On the other hand, if the unpolarized environment is initially in an eigenstate of the total bath spin, the central spin and the entanglement entropy exhibit persistent monochromatic large-amplitude oscillations. This raises the question of to what extent entanglement of the bath spins prevents decoherence of the central spin.
Exact dynamics in the inhomogeneous central-spin model
(The American Physical Society, 2007-07-26) Stolze, Joachim; Bortz, Michael
We study the dynamics of a single spin 1/2 coupled to a bath of spins 1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. For initially completely polarized bath spins and small magnetic field, we find persistent oscillations of the central spin about a nonzero mean value. For a large number of bath spins Nb, the oscillation frequency is proportional to Nb, whereas the amplitude behaves as 1/Nb, to leading order. No asymptotic decay of the oscillations due to the nonuniform couplings is observed, in contrast to some recent studies.
Dynamic properties of quantum spin chains
(The American Physical Society, 2007-10-15) Stolze, Joachim; Verkholyak, Taras; Derzhko, Oleg; Krokhmalskii, Taras
Dynamics of quantum spin chains and multi-fermion excitation continua
(Elsevier, 2006-02-17) Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras; Müller, Gerhard
Dimer and Trimer fluctuations in the s=1/2 transverse XX chain
(The American Physical Society, 2005) Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras; Müller, Gerhard
Spin Chains as Perfect Quantum State Mirrors
(The American Physical Society, 2005) Stolze, Joachim; Karbach, Peter
Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions that display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics, any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at an arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.
Multiparticle entanglement and ranks of density matrices
(arXiv, 2005) Stolze, Joachim; Chong, Bo; Keiter, Hellmut
Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we obtain necessary conditions for the separability of a given mixed state with respect to partitions of all particles of the system into subsets. The special case of pure states is discussed separately.
Dynamics of alternating spin chains
(Springer, 2002-02) Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras
Dynamic properties of the dimerized spin-1/2 isotropic XY chain in a transverse field
(IOP Publishing, 2002-04-26) Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras
The zz and xx(yy) dynamic structure factors of the dimerized spin-½ isotropic XY chain in a transverse (z) field are calculated for arbitrary temperatures. The zz structure factor can be given in analytical terms, involving a single integration, whereas the xx dynamic structure factor can be evaluated completely numerically for very long chains. We compare the two structure factors and discuss in some detail how a dimerization manifests itself in the dynamic structure factors at different external fields and temperatures. We compare our results to corresponding results for the dimerized Heisenberg chain obtained by approximate techniques.
Disorder Induced Quantum Phase transitions in Random-Exchange Spin-1/2 Chains
(The American Physical Society, 2002-08-28) Stolze, Joachim; Hamacher, Kay; Wenzel, Wolfgang
We investigate the effect of quenched bond disorder on the anisotropic antiferromagnetic spin-1/2 (XXZ) chain as a model for disorder-induced quantum phase transitions. We find nonuniversal behavior of the average correlation functions for weak disorder, followed by a quantum phase transition into a strongly disordered phase with only short-range xy correlations. We find no evidence for the universal strong-disorder fixed point predicted by the real-space renormalization group, suggesting a qualitatively different view of the relationship between quantum fluctuations and disorder.
Impurity spin relaxation in S=1/2 XX chains
(The American Physical Society, 2000) Stolze, Joachim; Vogel, Michael
Dynamics of the spin-1/2 isotropic XY chain in a transverse field
(IOP Publishing, 2000-04-28) Stolze, Joachim; Derzhko, Oleg; Krokhmalskii, Taras
Numerical evaluation of coherent-state path integrals in quantum dynamics
(IOP Publishing, 1999-03-19) Stolze, Joachim; Burghardt, Bernd
The numerical evaluation of coherent-state path integrals for quantum dynamical problems is discussed for one-dimensional examples. To propagate an initial state, we use the normal and antinormal ordered coherent-state path integrals combined with a split-operator technique dividing the Hamiltonian into harmonic and anharmonic parts. For numerical purposes integrations must be approximated by quadrature formulae. This leads to a matrix multiplication scheme which is systematically tested for the double-well and Morse potentials. The method is accurate for propagation times much longer than the natural time scale of the system, and it allows for short as well as long time steps without loss of stability.
Numerical evaluation of coherent-state path integrals with application to time-dependent problems
(World Scientific, 1999) Stolze, Joachim; Burghardt, Bernd
We study the application of the coherent-state path integral as a numerical tool for wave-packet propagation. The numerical evaluation of path integrals is reduced to a matrix-vector multiplication scheme. Together with a split-operator technique we apply our method to a time-dependent double-well potential.
Evaluation of coherent-state path integrals in statistical mechanics by matrix multiplication
(American Institute of Physics, 1998-01-22) Stolze, Joachim; Burghardt, Bernd; Eicke, Joachim
The numerical evaluation of coherent-state path-integral representations for partition functions and other quantities in equilibrium quantum statistical mechanics is discussed. Several coherent-state path-integral schemes are introduced, which differ from each other by the order of approximation and by the operator ordering employed in the high-temperature approximation of the density operator. Simple one-dimensional systems are used to test these schemes. For the harmonic oscillator, finite-dimensional approximations to the coherent-state path integral are calculated analytically and compared to each other and to the real-space path integral. For anharmonic systems, integrations must be approximated by quadrature formulas. This leads to a matrix multiplication scheme which is tested for the double-well potential. The results obtained are accurate from zero temperature way up into the high-temperature regime where quantum effects become negligible. This is a significant advantage over traditional real-space path integral schemes which break down at low temperatures.
Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization
(The American Physical Society, 1997) Stolze, Joachim; Fabricius, Klaus; Löw, Ute

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